Implementation of Hopcroft–Karp algorithm.
The Hopcroft–Karp algorithm is an algorithm that takes as input a bipartite graph and produces as output a maximum cardinality matching, it runs in O(E√V) time in worst case.
-
+
Bipartite graph
A bipartite graph (or bigraph) is a graph whose vertices can be divided into two disjoint and independent sets U and V such that every edge connects a vertex in U to one in V. Vertex sets U and V are usually called the parts of the graph. Equivalently, a bipartite graph is a graph that does not contain any odd-length cycles.
-
+
Matching and Not-Matching edges
Given a matching M, edges that are part of matching are called Matching edges and edges that are not part of M (or connect free nodes) are called Not-Matching edges.
-
+
Maximum cardinality matching
Given a bipartite graphs G = ( V = ( X , Y ) , E ) whose partition has the parts X and Y, with E denoting the edges of the graph, the goal is to find a matching with as many edges as possible. Equivalently, a matching that covers as many vertices as possible.
-
+
Augmenting paths
Given a matching M, an augmenting path is an alternating path that starts from and ends on free vertices. All single edge paths that start and end with free vertices are augmenting paths.
-
+
Concept
A matching M is not maximum if there exists an augmenting path. It is also true other way, i.e, a matching is maximum if no augmenting path exists.
-
+
Algorithm
1) Initialize the Maximal Matching M as empty. 2) While there exists an Augmenting Path P Remove matching edges of P from M and add not-matching edges of P to M (This increases size of M by 1 as P starts and ends with a free vertex i.e. a node that is not part of matching.) 3) Return M.
diff --git a/d2/d26/count__inversions_8cpp.html b/d2/d26/count__inversions_8cpp.html index 2d31a3018..40208957e 100644 --- a/d2/d26/count__inversions_8cpp.html +++ b/d2/d26/count__inversions_8cpp.html @@ -152,7 +152,7 @@ Functionstwo elements a[i] and a[j] form an inversion if a[i] > a[j] and i < j
Time Complexity --> O(n.log n)
Space Complexity --> O(n) ; additional array temp[1..n]
+
Algorithm
- The idea is similar to merge sort, divide the array into two equal or almost equal halves in each step until the base case is reached.
diff --git a/d3/df9/recursive__bubble__sort_8cpp.html b/d3/df9/recursive__bubble__sort_8cpp.html
index 50dc0fbe0..d73293669 100644
--- a/d3/df9/recursive__bubble__sort_8cpp.html
+++ b/d3/df9/recursive__bubble__sort_8cpp.html
@@ -136,7 +136,7 @@ Functions
The working principle of the Bubble sort algorithm.
Bubble sort is a simple sorting algorithm used to rearrange a set of ascending or descending order elements. Bubble sort gets its name from the fact that data "bubbles" to the top of the dataset.
-
+
Algorithm
What is Swap?
Swapping two numbers means that we interchange their values. Often, an additional variable is required for this operation. This is further illustrated in the following:
diff --git a/d4/d32/inorder__successor__of__bst_8cpp.html b/d4/d32/inorder__successor__of__bst_8cpp.html
index 936913f35..5c630a667 100644
--- a/d4/d32/inorder__successor__of__bst_8cpp.html
+++ b/d4/d32/inorder__successor__of__bst_8cpp.html
@@ -164,21 +164,21 @@ Functions
Detailed Description
An implementation for finding the Inorder successor of a binary search tree Inorder successor of a node is the next node in Inorder traversal of the Binary Tree. Inorder Successor is NULL for the last node in Inorder traversal.
-
+
Case 1: The given node has the right node/subtree
* In this case, the left-most deepest node in the right subtree will
come just after the given node as we go to left deep in inorder.
- Go deep to left most node in right subtree. OR, we can also say in case if BST, find the minimum of the subtree for a given node.
-
+
Case 2: The given node does not have a right node/subtree
-
+
Method 1: Use parent pointer (store the address of parent nodes)
- If a node does not have the right subtree, and we already visited the node itself, then the next node will be its parent node according to inorder traversal, and if we are going to parent from left, then the parent would be unvisited.
- In other words, go to the nearest ancestor for which given node would be in left subtree.
-
+
Method 2: Search from the root node
- In case if there is no link from a child node to the parent node, we need to walk down the tree starting from the root node to the given node, by doing so, we are visiting every ancestor of the given node.
diff --git a/d4/d38/power__of__two_8cpp.html b/d4/d38/power__of__two_8cpp.html
index d260dc329..a9469166b 100644
--- a/d4/d38/power__of__two_8cpp.html
+++ b/d4/d38/power__of__two_8cpp.html
@@ -126,7 +126,7 @@ Functions
Detailed Description
Implementation to check whether a number is a power of 2 or not.
This algorithm uses bit manipulation to check if a number is a power of 2 or not.
-
+
Algorithm
Let the input number be n, then the bitwise and between n and n-1 will let us know whether the number is power of 2 or not
For Example, If N= 32 then N-1 is 31, if we perform bitwise and of these two numbers then the result will be zero, which indicates that it is the power of 2 If N=23 then N-1 is 22, if we perform bitwise and of these two numbers then the result will not be zero , which indicates that it is not the power of 2
- Note
- This implementation is better than naive recursive or iterative approach.
diff --git a/d4/d8d/jarvis__algorithm_8cpp.html b/d4/d8d/jarvis__algorithm_8cpp.html
index 7c2e56183..0f2d46191 100644
--- a/d4/d8d/jarvis__algorithm_8cpp.html
+++ b/d4/d8d/jarvis__algorithm_8cpp.html
@@ -137,7 +137,7 @@ Functions
Detailed Description
Implementation of Jarvis’s algorithm.
Given a set of points in the plane. the convex hull of the set is the smallest convex polygon that contains all the points of it.
-
+
Algorithm
The idea of Jarvis’s Algorithm is simple, we start from the leftmost point (or point with minimum x coordinate value) and we keep wrapping points in counterclockwise direction.
The idea is to use orientation() here. Next point is selected as the point that beats all other points at counterclockwise orientation, i.e., next point is q if for any other point r, we have “orientation(p, q, r) = counterclockwise”.
diff --git a/d5/d33/gram__schmidt_8cpp.html b/d5/d33/gram__schmidt_8cpp.html
index bb3d6e860..e6b3367c4 100644
--- a/d5/d33/gram__schmidt_8cpp.html
+++ b/d5/d33/gram__schmidt_8cpp.html
@@ -140,7 +140,7 @@ Functions
Detailed Description
Gram Schmidt Orthogonalisation Process
Takes the input of Linearly Independent Vectors, returns vectors orthogonal to each other.
-
+
Algorithm
Take the first vector of given LI vectors as first vector of Orthogonal vectors. Take projection of second input vector on the first vector of Orthogonal vector and subtract it from the 2nd LI vector. Take projection of third vector on the second vector of Othogonal vectors and subtract it from the 3rd LI vector. Keep repeating the above process until all the vectors in the given input array are exhausted.
For Example: In R2, Input LI Vectors={(3,1),(2,2)} then Orthogonal Vectors= {(3, 1),(-0.4, 1.2)}
diff --git a/d5/d45/sublist__search_8cpp.html b/d5/d45/sublist__search_8cpp.html
index 36b5c562f..f64e9beba 100644
--- a/d5/d45/sublist__search_8cpp.html
+++ b/d5/d45/sublist__search_8cpp.html
@@ -149,14 +149,14 @@ Functions
Detailed Description
Implementation of the Sublist Search Algorithm
-
+
Algorithm
- Sublist search is used to detect a presence of one list in another list.
- Suppose we have a single-node list (let's say the first list), and we want to ensure that the list is present in another list (let's say the second list), then we can perform the sublist search to find it.
- For instance, the first list contains these elements: 23 -> 30 -> 41, and the second list contains these elements: 10 -> 15 -> 23 -> 30 -> 41 -> 49. At a glance, we see that the first list presents in the second list.
-
+
Working
- The sublist search algorithm works by comparing the first element of the first list with the first element of the second list.
diff --git a/d5/d88/md__d_i_r_e_c_t_o_r_y.html b/d5/d88/md__d_i_r_e_c_t_o_r_y.html
index 6f7beabdb..de20372a4 100644
--- a/d5/d88/md__d_i_r_e_c_t_o_r_y.html
+++ b/d5/d88/md__d_i_r_e_c_t_o_r_y.html
@@ -170,6 +170,11 @@ Data Structures
- Trie Using Hashmap
+Divide And Conquer
+
+
Dynamic Programming
- 0 1 Knapsack
@@ -200,13 +205,13 @@ Dynamic Programming
- Tree Height
- Word Break
-
+
Geometry
-
+
Graph
- Bidirectional Dijkstra
@@ -229,12 +234,12 @@ Graph
- Topological Sort
- Topological Sort By Kahns Algo
-
+
Graphics
-
+
Greedy Algorithms
- Dijkstra
@@ -244,7 +249,7 @@ Greedy Algorithms
- Kruskals Minimum Spanning Tree
- Prims Minimum Spanning Tree
-
+
Hashing
- Chaining
@@ -252,12 +257,12 @@ Hashing
- Linear Probing Hash Table
- Quadratic Probing Hash Table
-
+
Linear Algebra
-
+
Machine Learning
- A Star Search
@@ -268,7 +273,7 @@ Machine Learning
- Ordinary Least Squares Regressor
- Vector Ops
-
+
Math
- Armstrong Number
@@ -320,7 +325,7 @@ Math
- Sum Of Digits
- Vector Cross Product
-
+
Numerical Methods
- Bisection Method
@@ -341,7 +346,7 @@ Numerical Methods
- Rungekutta
- Successive Approximation
-
+
Operations On Datastructures
- Array Left Rotation
@@ -356,7 +361,7 @@ Operations On Datastructures
- Trie Multiple Search
- Union Of 2 Arrays
-
+
Others
- Buzz Number
@@ -379,7 +384,7 @@ Others
- Tower Of Hanoi
- Vector Important Functions
-
+
Probability
- Addition Rule
@@ -387,7 +392,7 @@ Probability
- Binomial Dist
- Poisson Dist
-
+
Range Queries
- Fenwick Tree
@@ -397,7 +402,7 @@ Range Queries
- Segtree
- Sparse Table
-
+
Search
- Binary Search
@@ -415,7 +420,7 @@ Search
- Ternary Search
- Text Search
-
+
Sorting
- Bead Sort
@@ -456,7 +461,7 @@ Sorting
- Wave Sort
- Wiggle Sort
-
+
Strings
- Brute Force String Searching
diff --git a/d5/ddb/bogo__sort_8cpp.html b/d5/ddb/bogo__sort_8cpp.html
index 94b9002b6..9ebef65a9 100644
--- a/d5/ddb/bogo__sort_8cpp.html
+++ b/d5/ddb/bogo__sort_8cpp.html
@@ -136,7 +136,7 @@ Functions
Detailed Description
Implementation of Bogosort algorithm
In computer science, bogosort (also known as permutation sort, stupid sort, slowsort, shotgun sort, random sort, monkey sort, bobosort or shuffle sort) is a highly inefficient sorting algorithm based on the generate and test paradigm. Two versions of this algorithm exist: a deterministic version that enumerates all permutations until it hits a sorted one, and a randomized version that randomly permutes its input.Randomized version is implemented here.
-
+
Algorithm
Shuffle the array untill array is sorted.
diff --git a/d6/d10/cut__rod_8cpp.html b/d6/d10/cut__rod_8cpp.html
index 6d78b405a..19ba0d116 100644
--- a/d6/d10/cut__rod_8cpp.html
+++ b/d6/d10/cut__rod_8cpp.html
@@ -136,7 +136,7 @@ Functions
Detailed Description
Implementation of cutting a rod problem.
Given a rod of length n inches and an array of prices that contains prices of all pieces of size<=n. Determine the maximum profit obtainable by cutting up the rod and selling the pieces.
-
+
Algorithm
The idea is to break the given rod into every smaller piece as possible and then check profit for each piece, by calculating maximum profit for smaller pieces we will build the solution for larger pieces in bottom-up manner.
- Capitalize zero or more of
a's lowercase letters.
- Delete all of the remaining lowercase letters in
a.
-
+
Algorithm
The idea is in the problem statement itself: iterate through characters of string a and b (for character indexes i and j respectively):
- If
a[i] and b[j] are equal, then move to next position
diff --git a/d8/d90/iterative__tree__traversals_8cpp.html b/d8/d90/iterative__tree__traversals_8cpp.html
index 3e6d60baa..6b5f02a15 100644
--- a/d8/d90/iterative__tree__traversals_8cpp.html
+++ b/d8/d90/iterative__tree__traversals_8cpp.html
@@ -158,13 +158,13 @@ Functions
Detailed Description
Iterative version of Preorder, Postorder, and preorder Traversal of the Tree
-
+
Iterative Preorder Traversal of a tree
Create a Stack that will store the Node of Tree. Push the root node into the stack. Save the root into the variabe named as current, and pop and elemnt from the stack. Store the data of current into the result array, and start traversing from it. Push both the child node of the current node into the stack, first right child then left child. Repeat the same set of steps untill the Stack becomes empty. And return the result array as the preorder traversal of a tree.
-
+
Iterative Postorder Traversal of a tree
Create a Stack that will store the Node of Tree. Push the root node into the stack. Save the root into the variabe named as current, and pop and elemnt from the stack. Store the data of current into the result array, and start traversing from it. Push both the child node of the current node into the stack, first left child then right child. Repeat the same set of steps untill the Stack becomes empty. Now reverse the result array and then return it to the calling function as a postorder traversal of a tree.
-
+
Iterative Inorder Traversal of a tree
Create a Stack that will store the Node of Tree. Push the root node into the stack. Save the root into the variabe named as current. Now iterate and take the current to the extreme left of the tree by traversing only to its left. Pop the elemnt from the stack and assign it to the current. Store the data of current into the result array. Repeat the same set of steps until the Stack becomes empty or the current becomes NULL. And return the result array as the inorder traversal of a tree.
Function Documentation
diff --git a/d8/d99/connected__components__with__dsu_8cpp.html b/d8/d99/connected__components__with__dsu_8cpp.html
index 20a095355..947a3d0d0 100644
--- a/d8/d99/connected__components__with__dsu_8cpp.html
+++ b/d8/d99/connected__components__with__dsu_8cpp.html
@@ -156,7 +156,7 @@ uint32_t graph::disjoint_u
Detailed Description
The Disjoint union is the technique to find connected component in graph efficiently.
-
+
Algorithm
In Graph, if you have to find out the number of connected components, there are 2 options
- Depth first search
diff --git a/da/d52/minimum__edit__distance_8cpp.html b/da/d52/minimum__edit__distance_8cpp.html
index 51128f6bc..ec8c27c78 100644
--- a/da/d52/minimum__edit__distance_8cpp.html
+++ b/da/d52/minimum__edit__distance_8cpp.html
@@ -137,7 +137,7 @@ Functions
Detailed Description
Implementation of Minimum Edit Distance using Dynamic Programing.
Given two strings str1 & str2 and we have to calculate the minimum number of operations (Insert, Remove, Replace) required to convert str1 to str2.
-
+
Algorithm
We will solve this problem using Naive recursion. But as we are approaching with a DP solution. So, we will take a DP array to store the solution of all sub-problems so that we don't have to perform recursion again and again. Now to solve the problem, We can traverse all characters from either right side of the strings or left side. Suppose we will do it from the right side. So, there are two possibilities for every pair of characters being traversed.
- If the last characters of two strings are the same, Ignore the characters and get the count for the remaining string. So, we get the solution for lengths m-1 and n-1 in a DP array.
diff --git a/da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html b/da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html
new file mode 100644
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+Algorithms_in_C++: divide_and_conquer/karatsuba_algorithm_for_fast_multiplication.cpp File Reference
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+ Algorithms_in_C++
+ 1.0.0
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+ Set of algorithms implemented in C++.
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+Namespaces |
+Functions
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+karatsuba_algorithm_for_fast_multiplication.cpp File Reference
+
+
+
+Implementation of the Karatsuba algorithm for fast multiplication
+More...
+#include <cassert>
+#include <cstring>
+#include <iostream>
+#include <vector>
+
+Include dependency graph for karatsuba_algorithm_for_fast_multiplication.cpp:
+
+
+
+
+
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+Namespaces
divide_and_conquer for std::vector
karatsuba_algorithm Functions for the Karatsuba algorithm for fast multiplication
+
+Functions
std::string divide_and_conquer::karatsuba_algorithm::addStrings (std::string first, std::string second) Helper function for the main function, that implements Karatsuba's algorithm for fast multiplication. More...
int64_t divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm (std::string str1, std::string str2) The main function implements Karatsuba's algorithm for fast multiplication. More...
static void test () Self-test implementations. More...
int main () Main function. More...
+Detailed Description
+Implementation of the Karatsuba algorithm for fast multiplication
+Given two strings in binary notation we want to multiply them and return the value Simple approach is to multiply bits one by one which will give the time complexity of around O(n^2). To make it more efficient we will be using Karatsuba' algorithm to find the product which will solve the problem O(nlogn) of time.
+Function Documentation
+
+◆ addStrings()
+
+
+
+
+
+ std::string divide_and_conquer::karatsuba_algorithm::addStrings
+ (
+ std::string
+ first,
+
+
+ std::string
+ second
+
+
+ )
+
+
+
+
+Helper function for the main function, that implements Karatsuba's algorithm for fast multiplication.
+- Parameters
-
+
+ first the input string 1 second the input string 2
+
+
+- Returns
- the concatenated string
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+T at(T... args)
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+T max(T... args)
+
+T size(T... args)
+T to_string(T... args)
+
+Here is the call graph for this function:
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+
+◆ karatsuba_algorithm()
+
+
+
+
+
+ int64_t divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm
+ (
+ std::string
+ str1,
+
+
+ std::string
+ str2
+
+
+ )
+
+
+
+
+The main function implements Karatsuba's algorithm for fast multiplication.
+- Parameters
-
+
+ str1 the input string 1 str2 the input string 2
+
+
+- Returns
- the multiplicative number value
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+Functions for the Karatsuba algorithm for fast multiplication
+T substr(T... args)
+
+Here is the call graph for this function:
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+
+◆ main()
+
+
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+ int main
+ (
+ void
+ )
+
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+◆ test()
+
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+ static void test
+ (
+ )
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+static
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+Self-test implementations.
+- Returns
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+T endl(T... args)
+
+Here is the call graph for this function:
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+
+ - Generated by
1.9.1
+
+
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+
diff --git a/da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.js b/da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.js
new file mode 100644
index 000000000..dd00fedc3
--- /dev/null
+++ b/da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.js
@@ -0,0 +1,7 @@
+var karatsuba__algorithm__for__fast__multiplication_8cpp =
+[
+ [ "addStrings", "da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#a7d1dbae365c7746295d3322e6f7f80b6", null ],
+ [ "karatsuba_algorithm", "da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#a7a890d2f26855ada3b9f1d43aec70a86", null ],
+ [ "main", "da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4", null ],
+ [ "test", "da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aa8dca7b867074164d5f45b0f3851269d", null ]
+];
\ No newline at end of file
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@@ -136,7 +136,7 @@ Functions
Detailed Description
Implementation of 0-1 Knapsack Problem
Given weights and values of n items, put these items in a knapsack of capacity W to get the maximum total value in the knapsack. In other words, given two integer arrays val[0..n-1] and wt[0..n-1] which represent values and weights associated with n items respectively. Also given an integer W which represents knapsack capacity, find out the maximum value subset of val[] such that sum of the weights of this subset is smaller than or equal to W. You cannot break an item, either pick the complete item or don’t pick it (0-1 property)
-
+
Algorithm
The idea is to consider all subsets of items and calculate the total weight and value of all subsets. Consider the only subsets whose total weight is smaller than W. From all such subsets, pick the maximum value subset.
- Author
- Anmol
diff --git a/db/dca/kadane2_8cpp.html b/db/dca/kadane2_8cpp.html
index 8eb7970bc..a8d85a1c6 100644
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@@ -132,7 +132,7 @@ Functions
Detailed Description
Implementation of Kadane Algorithm
Kadane algorithm is used to find the maximum sum subarray in an array and maximum sum subarray problem is the task of finding a contiguous subarray with the largest sum
-
+
Algorithm
The simple idea of the algorithm is to search for all positive contiguous segments of the array and keep track of maximum sum contiguous segment among all positive segments(curr_sum is used for this) Each time we get a positive sum we compare it with max_sum and update max_sum if it is greater than curr_sum
diff --git a/dd/d47/namespacemath.html b/dd/d47/namespacemath.html
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@@ -146,7 +146,7 @@ Functions
Mathematical algorithms
Given a recurrence relation; evaluate the value of nth term. For e.g., For fibonacci series, recurrence series is f(n) = f(n-1) + f(n-2) where f(0) = 0 and f(1) = 1. Note that the method used only demonstrates recurrence relation with one variable (n), unlike nCr problem, since it has two (n, r)
-
+
Algorithm
This problem can be solved using matrix exponentiation method.
- See also
- here for simple number exponentiation algorithm or explaination here.
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+
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+
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+
+
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+
+divide_and_conquer Namespace Reference
+
+
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+ - Generated by 1.9.1
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+++ b/de/d41/namespacekaratsuba__algorithm.html
@@ -0,0 +1,112 @@
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+Algorithms_in_C++: karatsuba_algorithm Namespace Reference
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+karatsuba_algorithm Namespace Reference
+
+
+
+Functions for the Karatsuba algorithm for fast multiplication
+More...
+Detailed Description
+Functions for the Karatsuba algorithm for fast multiplication
+
+
+
+
+
+
+ - Generated by 1.9.1
+
+
+
+
diff --git a/df/d66/vector__cross__product_8cpp.html b/df/d66/vector__cross__product_8cpp.html
index 52b7c4fe9..346554810 100644
--- a/df/d66/vector__cross__product_8cpp.html
+++ b/df/d66/vector__cross__product_8cpp.html
@@ -145,7 +145,7 @@ Functions
The direction ratios (DR) are calculated as follows: 1st DR, J: (b * z) - (c * y) 2nd DR, A: -((a * z) - (c * x)) 3rd DR, N: (a * y) - (b * x)
Therefore, the direction ratios of the cross product are: J, A, N The following C++ Program calculates the direction ratios of the cross products of two vector. The program uses a function, cross() for doing so. The direction ratios for the first and the second vector has to be passed one by one seperated by a space character.
Magnitude of a vector is the square root of the sum of the squares of the direction ratios.
-
+
Example:
An example of a running instance of the executable program:
Pass the first Vector: 1 2 3
Pass the second Vector: 4 5 6 The cross product is: -3 6 -3 Magnitude: 7.34847
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+
+
+
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+
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+
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+Files
file karatsuba_algorithm_for_fast_multiplication.cpp Implementation of the Karatsuba algorithm for fast multiplication
+
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+
+
+
+
+ - Generated by
1.9.1
+
+
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index bb23d379f..4f03426e4 100644
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- is_square()
: ordinary_least_squares_regressor.cpp
-- IsPrime()
-: primality_test.cpp
-
- isPrime()
: modular_inverse_fermat_little_theorem.cpp
+- IsPrime()
+: primality_test.cpp
+
- it_ternary_search()
: ternary_search.cpp
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index ec78c7e50..73acfcea5 100644
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, trie_modern.cpp
, trie_tree.cpp
, trie_using_hashmap.cpp
+, karatsuba_algorithm_for_fast_multiplication.cpp
, 0_1_knapsack.cpp
, abbreviation.cpp
, coin_change_topdown.cpp
diff --git a/globals_func_t.html b/globals_func_t.html
index bcfe1e6bc..075a37744 100644
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, sparse_table.cpp
, trie_tree.cpp
, trie_using_hashmap.cpp
+, karatsuba_algorithm_for_fast_multiplication.cpp
, 0_1_knapsack.cpp
, abbreviation.cpp
, coin_change_topdown.cpp
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index e0a80ea03..0e3b0d811 100644
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@@ -127,14 +127,14 @@ $(document).ready(function(){initNavTree('globals_i.html',''); initResizable();
- is_square()
: ordinary_least_squares_regressor.cpp
-- IsPrime()
-: primality_test.cpp
+
- isPrime()
+: modular_inverse_fermat_little_theorem.cpp
- isprime
: prime_factorization.cpp
-- isPrime()
-: modular_inverse_fermat_little_theorem.cpp
+
- IsPrime()
+: primality_test.cpp
- it_ternary_search()
: ternary_search.cpp
diff --git a/globals_m.html b/globals_m.html
index cff3f1311..dc05172a4 100644
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, trie_modern.cpp
, trie_tree.cpp
, trie_using_hashmap.cpp
+, karatsuba_algorithm_for_fast_multiplication.cpp
, 0_1_knapsack.cpp
, abbreviation.cpp
, coin_change_topdown.cpp
diff --git a/globals_t.html b/globals_t.html
index a96384888..9a9a89dcd 100644
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, sparse_table.cpp
, trie_tree.cpp
, trie_using_hashmap.cpp
+, karatsuba_algorithm_for_fast_multiplication.cpp
, 0_1_knapsack.cpp
, abbreviation.cpp
, coin_change_topdown.cpp
diff --git a/index.html b/index.html
index 1f62bb9e6..eddd83466 100644
--- a/index.html
+++ b/index.html
@@ -96,10 +96,10 @@ $(document).ready(function(){initNavTree('index.html',''); initResizable(); });
-
+
Overview
The repository is a collection of open-source implementation of a variety of algorithms implemented in C++ and licensed under MIT License. The algorithms span a variety of topics from computer science, mathematics and statistics, data science, machine learning, engineering, etc.. The implementations and the associated documentation are meant to provide a learning resource for educators and students. Hence, one may find more than one implementation for the same objective but using a different algorithm strategies and optimizations.
-
+
Features
- The repository provides implementations of various algorithms in one of the most fundamental general purpose languages - C++.
@@ -110,12 +110,12 @@ Features
- Self-checks within programs ensure correct implementations with confidence.
- Modular implementations and OpenSource licensing enable the functions to be utilized conveniently in other applications.
-
+
Documentation
Online Documentation is generated from the repository source codes directly. The documentation contains all resources including source code snippets, details on execution of the programs, diagrammatic representation of program flow, and links to external resources where necessary. The documentation also introduces interactive source code with links to documentation for C++ STL library functions used. Click on Files menu to see the list of all the files documented with the code.
Documentation of Algorithms in C++ by The Algorithms Contributors is licensed under CC BY-SA 4.0
-
+
Contributions
As a community developed and maintained repository, we welcome new un-plagiarized quality contributions. Please read our Contribution Guidelines.
diff --git a/namespacemembers.html b/namespacemembers.html
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- isPossible()
: backtracking
-- isSafe()
-: backtracking
-
- issafe()
: backtracking
+- isSafe()
+: backtracking
+
@@ -366,12 +366,12 @@ $(document).ready(function(){initNavTree('namespacemembers.html',''); initResiza
- quadraticProbe()
: quadratic_probing
-- quickSort()
-: sorting
-
- quicksort()
: sorting
+- quickSort()
+: sorting
+
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index c2c007a17..0c64c200b 100644
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- isPossible()
: backtracking
-- isSafe()
-: backtracking
-
- issafe()
: backtracking
+- isSafe()
+: backtracking
+
@@ -354,12 +354,12 @@ $(document).ready(function(){initNavTree('namespacemembers_func.html',''); initR
- quadraticProbe()
: quadratic_probing
-- quickSort()
-: sorting
-
- quicksort()
: sorting
+- quickSort()
+: sorting
+
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index 30f1fb490..d06908f98 100644
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];
diff --git a/search/variables_f.js b/search/variables_f.js
index 3c943184b..f3d8f5cab 100644
--- a/search/variables_f.js
+++ b/search/variables_f.js
@@ -1,5 +1,5 @@
var searchData=
[
- ['queuefront_5393',['queueFront',['../db/da9/classqueue.html#ac16ccadebb765e1ddbe415cdce1a17a5',1,'queue']]],
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The working principle of the Bubble sort algorithm.
Bubble sort is a simple sorting algorithm used to rearrange a set of ascending or descending order elements. Bubble sort gets its name from the fact that data "bubbles" to the top of the dataset.
-
+
Algorithm
What is Swap?
Swapping two numbers means that we interchange their values. Often, an additional variable is required for this operation. This is further illustrated in the following:
diff --git a/d4/d32/inorder__successor__of__bst_8cpp.html b/d4/d32/inorder__successor__of__bst_8cpp.html index 936913f35..5c630a667 100644 --- a/d4/d32/inorder__successor__of__bst_8cpp.html +++ b/d4/d32/inorder__successor__of__bst_8cpp.html @@ -164,21 +164,21 @@ FunctionsDetailed Description
An implementation for finding the Inorder successor of a binary search tree Inorder successor of a node is the next node in Inorder traversal of the Binary Tree. Inorder Successor is NULL for the last node in Inorder traversal.
-
+
Case 1: The given node has the right node/subtree
* In this case, the left-most deepest node in the right subtree will
come just after the given node as we go to left deep in inorder.
- Go deep to left most node in right subtree. OR, we can also say in case if BST, find the minimum of the subtree for a given node.
+
Case 2: The given node does not have a right node/subtree
-
+
Method 1: Use parent pointer (store the address of parent nodes)
- If a node does not have the right subtree, and we already visited the node itself, then the next node will be its parent node according to inorder traversal, and if we are going to parent from left, then the parent would be unvisited.
- In other words, go to the nearest ancestor for which given node would be in left subtree.
-
+
Method 2: Search from the root node
- In case if there is no link from a child node to the parent node, we need to walk down the tree starting from the root node to the given node, by doing so, we are visiting every ancestor of the given node.
diff --git a/d4/d38/power__of__two_8cpp.html b/d4/d38/power__of__two_8cpp.html
index d260dc329..a9469166b 100644
--- a/d4/d38/power__of__two_8cpp.html
+++ b/d4/d38/power__of__two_8cpp.html
@@ -126,7 +126,7 @@ Functions
Detailed Description
Implementation to check whether a number is a power of 2 or not.
This algorithm uses bit manipulation to check if a number is a power of 2 or not.
-
+
Algorithm
Let the input number be n, then the bitwise and between n and n-1 will let us know whether the number is power of 2 or not
For Example, If N= 32 then N-1 is 31, if we perform bitwise and of these two numbers then the result will be zero, which indicates that it is the power of 2 If N=23 then N-1 is 22, if we perform bitwise and of these two numbers then the result will not be zero , which indicates that it is not the power of 2
- Note
- This implementation is better than naive recursive or iterative approach.
diff --git a/d4/d8d/jarvis__algorithm_8cpp.html b/d4/d8d/jarvis__algorithm_8cpp.html
index 7c2e56183..0f2d46191 100644
--- a/d4/d8d/jarvis__algorithm_8cpp.html
+++ b/d4/d8d/jarvis__algorithm_8cpp.html
@@ -137,7 +137,7 @@ Functions
Detailed Description
Implementation of Jarvis’s algorithm.
Given a set of points in the plane. the convex hull of the set is the smallest convex polygon that contains all the points of it.
-
+
Algorithm
The idea of Jarvis’s Algorithm is simple, we start from the leftmost point (or point with minimum x coordinate value) and we keep wrapping points in counterclockwise direction.
The idea is to use orientation() here. Next point is selected as the point that beats all other points at counterclockwise orientation, i.e., next point is q if for any other point r, we have “orientation(p, q, r) = counterclockwise”.
diff --git a/d5/d33/gram__schmidt_8cpp.html b/d5/d33/gram__schmidt_8cpp.html
index bb3d6e860..e6b3367c4 100644
--- a/d5/d33/gram__schmidt_8cpp.html
+++ b/d5/d33/gram__schmidt_8cpp.html
@@ -140,7 +140,7 @@ Functions
Detailed Description
Gram Schmidt Orthogonalisation Process
Takes the input of Linearly Independent Vectors, returns vectors orthogonal to each other.
-
+
Algorithm
Take the first vector of given LI vectors as first vector of Orthogonal vectors. Take projection of second input vector on the first vector of Orthogonal vector and subtract it from the 2nd LI vector. Take projection of third vector on the second vector of Othogonal vectors and subtract it from the 3rd LI vector. Keep repeating the above process until all the vectors in the given input array are exhausted.
For Example: In R2, Input LI Vectors={(3,1),(2,2)} then Orthogonal Vectors= {(3, 1),(-0.4, 1.2)}
diff --git a/d5/d45/sublist__search_8cpp.html b/d5/d45/sublist__search_8cpp.html
index 36b5c562f..f64e9beba 100644
--- a/d5/d45/sublist__search_8cpp.html
+++ b/d5/d45/sublist__search_8cpp.html
@@ -149,14 +149,14 @@ Functions
Detailed Description
Implementation of the Sublist Search Algorithm
-
+
Algorithm
- Sublist search is used to detect a presence of one list in another list.
- Suppose we have a single-node list (let's say the first list), and we want to ensure that the list is present in another list (let's say the second list), then we can perform the sublist search to find it.
- For instance, the first list contains these elements: 23 -> 30 -> 41, and the second list contains these elements: 10 -> 15 -> 23 -> 30 -> 41 -> 49. At a glance, we see that the first list presents in the second list.
-
+
Working
- The sublist search algorithm works by comparing the first element of the first list with the first element of the second list.
diff --git a/d5/d88/md__d_i_r_e_c_t_o_r_y.html b/d5/d88/md__d_i_r_e_c_t_o_r_y.html
index 6f7beabdb..de20372a4 100644
--- a/d5/d88/md__d_i_r_e_c_t_o_r_y.html
+++ b/d5/d88/md__d_i_r_e_c_t_o_r_y.html
@@ -170,6 +170,11 @@ Data Structures
- Trie Using Hashmap
+Divide And Conquer
+
+
Dynamic Programming
- 0 1 Knapsack
@@ -200,13 +205,13 @@ Dynamic Programming
- Tree Height
- Word Break
-
+
Geometry
-
+
Graph
- Bidirectional Dijkstra
@@ -229,12 +234,12 @@ Graph
- Topological Sort
- Topological Sort By Kahns Algo
-
+
Graphics
-
+
Greedy Algorithms
- Dijkstra
@@ -244,7 +249,7 @@ Greedy Algorithms
- Kruskals Minimum Spanning Tree
- Prims Minimum Spanning Tree
-
+
Hashing
- Chaining
@@ -252,12 +257,12 @@ Hashing
- Linear Probing Hash Table
- Quadratic Probing Hash Table
-
+
Linear Algebra
-
+
Machine Learning
- A Star Search
@@ -268,7 +273,7 @@ Machine Learning
- Ordinary Least Squares Regressor
- Vector Ops
-
+
Math
- Armstrong Number
@@ -320,7 +325,7 @@ Math
- Sum Of Digits
- Vector Cross Product
-
+
Numerical Methods
- Bisection Method
@@ -341,7 +346,7 @@ Numerical Methods
- Rungekutta
- Successive Approximation
-
+
Operations On Datastructures
- Array Left Rotation
@@ -356,7 +361,7 @@ Operations On Datastructures
- Trie Multiple Search
- Union Of 2 Arrays
-
+
Others
- Buzz Number
@@ -379,7 +384,7 @@ Others
- Tower Of Hanoi
- Vector Important Functions
-
+
Probability
- Addition Rule
@@ -387,7 +392,7 @@ Probability
- Binomial Dist
- Poisson Dist
-
+
Range Queries
- Fenwick Tree
@@ -397,7 +402,7 @@ Range Queries
- Segtree
- Sparse Table
-
+
Search
- Binary Search
@@ -415,7 +420,7 @@ Search
- Ternary Search
- Text Search
-
+
Sorting
- Bead Sort
@@ -456,7 +461,7 @@ Sorting
- Wave Sort
- Wiggle Sort
-
+
Strings
- Brute Force String Searching
diff --git a/d5/ddb/bogo__sort_8cpp.html b/d5/ddb/bogo__sort_8cpp.html
index 94b9002b6..9ebef65a9 100644
--- a/d5/ddb/bogo__sort_8cpp.html
+++ b/d5/ddb/bogo__sort_8cpp.html
@@ -136,7 +136,7 @@ Functions
Detailed Description
Implementation of Bogosort algorithm
In computer science, bogosort (also known as permutation sort, stupid sort, slowsort, shotgun sort, random sort, monkey sort, bobosort or shuffle sort) is a highly inefficient sorting algorithm based on the generate and test paradigm. Two versions of this algorithm exist: a deterministic version that enumerates all permutations until it hits a sorted one, and a randomized version that randomly permutes its input.Randomized version is implemented here.
-
+
Algorithm
Shuffle the array untill array is sorted.
diff --git a/d6/d10/cut__rod_8cpp.html b/d6/d10/cut__rod_8cpp.html
index 6d78b405a..19ba0d116 100644
--- a/d6/d10/cut__rod_8cpp.html
+++ b/d6/d10/cut__rod_8cpp.html
@@ -136,7 +136,7 @@ Functions
Detailed Description
Implementation of cutting a rod problem.
Given a rod of length n inches and an array of prices that contains prices of all pieces of size<=n. Determine the maximum profit obtainable by cutting up the rod and selling the pieces.
-
+
Algorithm
The idea is to break the given rod into every smaller piece as possible and then check profit for each piece, by calculating maximum profit for smaller pieces we will build the solution for larger pieces in bottom-up manner.
- Capitalize zero or more of
a's lowercase letters.
- Delete all of the remaining lowercase letters in
a.
-
+
Algorithm
The idea is in the problem statement itself: iterate through characters of string a and b (for character indexes i and j respectively):
- If
a[i] and b[j] are equal, then move to next position
diff --git a/d8/d90/iterative__tree__traversals_8cpp.html b/d8/d90/iterative__tree__traversals_8cpp.html
index 3e6d60baa..6b5f02a15 100644
--- a/d8/d90/iterative__tree__traversals_8cpp.html
+++ b/d8/d90/iterative__tree__traversals_8cpp.html
@@ -158,13 +158,13 @@ Functions
Detailed Description
Iterative version of Preorder, Postorder, and preorder Traversal of the Tree
-
+
Iterative Preorder Traversal of a tree
Create a Stack that will store the Node of Tree. Push the root node into the stack. Save the root into the variabe named as current, and pop and elemnt from the stack. Store the data of current into the result array, and start traversing from it. Push both the child node of the current node into the stack, first right child then left child. Repeat the same set of steps untill the Stack becomes empty. And return the result array as the preorder traversal of a tree.
-
+
Iterative Postorder Traversal of a tree
Create a Stack that will store the Node of Tree. Push the root node into the stack. Save the root into the variabe named as current, and pop and elemnt from the stack. Store the data of current into the result array, and start traversing from it. Push both the child node of the current node into the stack, first left child then right child. Repeat the same set of steps untill the Stack becomes empty. Now reverse the result array and then return it to the calling function as a postorder traversal of a tree.
-
+
Iterative Inorder Traversal of a tree
Create a Stack that will store the Node of Tree. Push the root node into the stack. Save the root into the variabe named as current. Now iterate and take the current to the extreme left of the tree by traversing only to its left. Pop the elemnt from the stack and assign it to the current. Store the data of current into the result array. Repeat the same set of steps until the Stack becomes empty or the current becomes NULL. And return the result array as the inorder traversal of a tree.
Function Documentation
diff --git a/d8/d99/connected__components__with__dsu_8cpp.html b/d8/d99/connected__components__with__dsu_8cpp.html
index 20a095355..947a3d0d0 100644
--- a/d8/d99/connected__components__with__dsu_8cpp.html
+++ b/d8/d99/connected__components__with__dsu_8cpp.html
@@ -156,7 +156,7 @@ uint32_t graph::disjoint_u
Detailed Description
The Disjoint union is the technique to find connected component in graph efficiently.
-
+
Algorithm
In Graph, if you have to find out the number of connected components, there are 2 options
- Depth first search
diff --git a/da/d52/minimum__edit__distance_8cpp.html b/da/d52/minimum__edit__distance_8cpp.html
index 51128f6bc..ec8c27c78 100644
--- a/da/d52/minimum__edit__distance_8cpp.html
+++ b/da/d52/minimum__edit__distance_8cpp.html
@@ -137,7 +137,7 @@ Functions
Detailed Description
Implementation of Minimum Edit Distance using Dynamic Programing.
Given two strings str1 & str2 and we have to calculate the minimum number of operations (Insert, Remove, Replace) required to convert str1 to str2.
-
+
Algorithm
We will solve this problem using Naive recursion. But as we are approaching with a DP solution. So, we will take a DP array to store the solution of all sub-problems so that we don't have to perform recursion again and again. Now to solve the problem, We can traverse all characters from either right side of the strings or left side. Suppose we will do it from the right side. So, there are two possibilities for every pair of characters being traversed.
- If the last characters of two strings are the same, Ignore the characters and get the count for the remaining string. So, we get the solution for lengths m-1 and n-1 in a DP array.
diff --git a/da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html b/da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html
new file mode 100644
index 000000000..de3b3ec97
--- /dev/null
+++ b/da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html
@@ -0,0 +1,425 @@
+
+
+
+
+
+
+
+Algorithms_in_C++: divide_and_conquer/karatsuba_algorithm_for_fast_multiplication.cpp File Reference
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ Algorithms_in_C++
+ 1.0.0
+
+ Set of algorithms implemented in C++.
+
+
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+
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+Namespaces |
+Functions
+
+karatsuba_algorithm_for_fast_multiplication.cpp File Reference
+
+
+
+Implementation of the Karatsuba algorithm for fast multiplication
+More...
+#include <cassert>
+#include <cstring>
+#include <iostream>
+#include <vector>
+
+Include dependency graph for karatsuba_algorithm_for_fast_multiplication.cpp:
+
+
+
+
+
+
+Namespaces
divide_and_conquer for std::vector
karatsuba_algorithm Functions for the Karatsuba algorithm for fast multiplication
+
+Functions
std::string divide_and_conquer::karatsuba_algorithm::addStrings (std::string first, std::string second) Helper function for the main function, that implements Karatsuba's algorithm for fast multiplication. More...
int64_t divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm (std::string str1, std::string str2) The main function implements Karatsuba's algorithm for fast multiplication. More...
static void test () Self-test implementations. More...
int main () Main function. More...
+Detailed Description
+Implementation of the Karatsuba algorithm for fast multiplication
+Given two strings in binary notation we want to multiply them and return the value Simple approach is to multiply bits one by one which will give the time complexity of around O(n^2). To make it more efficient we will be using Karatsuba' algorithm to find the product which will solve the problem O(nlogn) of time.
+Function Documentation
+
+◆ addStrings()
+
+
+
+
+
+ std::string divide_and_conquer::karatsuba_algorithm::addStrings
+ (
+ std::string
+ first,
+
+
+ std::string
+ second
+
+
+ )
+
+
+
+
+Helper function for the main function, that implements Karatsuba's algorithm for fast multiplication.
+- Parameters
-
+
+ first the input string 1 second the input string 2
+
+
+- Returns
- the concatenated string
+
+
+
+
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+T at(T... args)
+
+
+T max(T... args)
+
+T size(T... args)
+T to_string(T... args)
+
+Here is the call graph for this function:
+
+
+
+
+
+
+
+
+◆ karatsuba_algorithm()
+
+
+
+
+
+ int64_t divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm
+ (
+ std::string
+ str1,
+
+
+ std::string
+ str2
+
+
+ )
+
+
+
+
+The main function implements Karatsuba's algorithm for fast multiplication.
+- Parameters
-
+
+ str1 the input string 1 str2 the input string 2
+
+
+- Returns
- the multiplicative number value
+
+
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+
+Functions for the Karatsuba algorithm for fast multiplication
+T substr(T... args)
+
+Here is the call graph for this function:
+
+
+
+
+
+
+
+
+◆ main()
+
+
+
+
+
+ int main
+ (
+ void
+ )
+
+
+
+
+
+◆ test()
+
+
+
+
+
+
+
+
+ static void test
+ (
+ )
+
+
+
+
+static
+
+
+
+
+Self-test implementations.
+- Returns
- void
+
+
+
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+
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+
+
+T endl(T... args)
+
+Here is the call graph for this function:
+
+
+
+
+
+
+
+
+
+
+
+
+
+ - Generated by 1.9.1
+
+
+
+
diff --git a/da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.js b/da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.js
new file mode 100644
index 000000000..dd00fedc3
--- /dev/null
+++ b/da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.js
@@ -0,0 +1,7 @@
+var karatsuba__algorithm__for__fast__multiplication_8cpp =
+[
+ [ "addStrings", "da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#a7d1dbae365c7746295d3322e6f7f80b6", null ],
+ [ "karatsuba_algorithm", "da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#a7a890d2f26855ada3b9f1d43aec70a86", null ],
+ [ "main", "da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4", null ],
+ [ "test", "da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aa8dca7b867074164d5f45b0f3851269d", null ]
+];
\ No newline at end of file
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+
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+++ b/db/d16/0__1__knapsack_8cpp.html
@@ -136,7 +136,7 @@ Functions
Detailed Description
Implementation of 0-1 Knapsack Problem
Given weights and values of n items, put these items in a knapsack of capacity W to get the maximum total value in the knapsack. In other words, given two integer arrays val[0..n-1] and wt[0..n-1] which represent values and weights associated with n items respectively. Also given an integer W which represents knapsack capacity, find out the maximum value subset of val[] such that sum of the weights of this subset is smaller than or equal to W. You cannot break an item, either pick the complete item or don’t pick it (0-1 property)
-
+
Algorithm
The idea is to consider all subsets of items and calculate the total weight and value of all subsets. Consider the only subsets whose total weight is smaller than W. From all such subsets, pick the maximum value subset.
- Author
- Anmol
diff --git a/db/dca/kadane2_8cpp.html b/db/dca/kadane2_8cpp.html
index 8eb7970bc..a8d85a1c6 100644
--- a/db/dca/kadane2_8cpp.html
+++ b/db/dca/kadane2_8cpp.html
@@ -132,7 +132,7 @@ Functions
Detailed Description
Implementation of Kadane Algorithm
Kadane algorithm is used to find the maximum sum subarray in an array and maximum sum subarray problem is the task of finding a contiguous subarray with the largest sum
-
+
Algorithm
The simple idea of the algorithm is to search for all positive contiguous segments of the array and keep track of maximum sum contiguous segment among all positive segments(curr_sum is used for this) Each time we get a positive sum we compare it with max_sum and update max_sum if it is greater than curr_sum
diff --git a/dd/d47/namespacemath.html b/dd/d47/namespacemath.html
index 2050416db..17df5d494 100644
--- a/dd/d47/namespacemath.html
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@@ -146,7 +146,7 @@ Functions
Mathematical algorithms
Given a recurrence relation; evaluate the value of nth term. For e.g., For fibonacci series, recurrence series is f(n) = f(n-1) + f(n-2) where f(0) = 0 and f(1) = 1. Note that the method used only demonstrates recurrence relation with one variable (n), unlike nCr problem, since it has two (n, r)
-
+
Algorithm
This problem can be solved using matrix exponentiation method.
- See also
- here for simple number exponentiation algorithm or explaination here.
diff --git a/dd/dba/namespacedivide__and__conquer.html b/dd/dba/namespacedivide__and__conquer.html
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+ Algorithms_in_C++
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+
+ Set of algorithms implemented in C++.
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+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+divide_and_conquer Namespace Reference
+
+
+
+
+
+
+
+ - Generated by 1.9.1
+
+
+
+
diff --git a/de/d41/namespacekaratsuba__algorithm.html b/de/d41/namespacekaratsuba__algorithm.html
new file mode 100644
index 000000000..e7be124e5
--- /dev/null
+++ b/de/d41/namespacekaratsuba__algorithm.html
@@ -0,0 +1,112 @@
+
+
+
+
+
+
+
+Algorithms_in_C++: karatsuba_algorithm Namespace Reference
+
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+
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+ Algorithms_in_C++
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+ Set of algorithms implemented in C++.
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+
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+
+
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+
+
+
+
+
+
+karatsuba_algorithm Namespace Reference
+
+
+
+Functions for the Karatsuba algorithm for fast multiplication
+More...
+Detailed Description
+Functions for the Karatsuba algorithm for fast multiplication
+
+
+
+
+
+
+ - Generated by 1.9.1
+
+
+
+
diff --git a/df/d66/vector__cross__product_8cpp.html b/df/d66/vector__cross__product_8cpp.html
index 52b7c4fe9..346554810 100644
--- a/df/d66/vector__cross__product_8cpp.html
+++ b/df/d66/vector__cross__product_8cpp.html
@@ -145,7 +145,7 @@ Functions
The direction ratios (DR) are calculated as follows: 1st DR, J: (b * z) - (c * y) 2nd DR, A: -((a * z) - (c * x)) 3rd DR, N: (a * y) - (b * x)
Therefore, the direction ratios of the cross product are: J, A, N The following C++ Program calculates the direction ratios of the cross products of two vector. The program uses a function, cross() for doing so. The direction ratios for the first and the second vector has to be passed one by one seperated by a space character.
Magnitude of a vector is the square root of the sum of the squares of the direction ratios.
-
+
Example:
An example of a running instance of the executable program:
Pass the first Vector: 1 2 3
Pass the second Vector: 4 5 6 The cross product is: -3 6 -3 Magnitude: 7.34847
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+Algorithms_in_C++: divide_and_conquer Directory Reference
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+ Algorithms_in_C++
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+
+ Set of algorithms implemented in C++.
+
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+
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+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+divide_and_conquer Directory Reference
+
+
+
+
+Files
file karatsuba_algorithm_for_fast_multiplication.cpp Implementation of the Karatsuba algorithm for fast multiplication
+
+
+
+
+
+
+ - Generated by 1.9.1
+
+
+
+
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+var dir_93bc990c5cceb745f78af6949e9ef947 =
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+];
\ No newline at end of file
diff --git a/files.html b/files.html
index bb23d379f..4f03426e4 100644
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@@ -143,194 +143,196 @@ solve-a-rat-in-a-maze-c-java-pytho/"
- ► dynamic_programming ► geometry ► graph ► graphics ► greedy_algorithms ► hashing ► linear_algebra ► machine_learning ► math ► numerical_methods ► operations_on_datastructures ► others ► probability ► range_queries ► search ► sorting ► strings ► divide_and_conquer ► dynamic_programming ► geometry ► graph ► graphics ► greedy_algorithms ► hashing ► linear_algebra ► machine_learning ► math ► numerical_methods ► operations_on_datastructures ► others ► probability ► range_queries ► search ► sorting ► strings
diff --git a/files_dup.js b/files_dup.js
index 1c7b2311f..927c6694b 100644
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[ "data_structures", "dir_2e746e9d06bf2d8ff842208bcc6ebcfc.html", "dir_2e746e9d06bf2d8ff842208bcc6ebcfc" ],
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- is_square()
: ordinary_least_squares_regressor.cpp
-- IsPrime()
-: primality_test.cpp
-
- isPrime()
: modular_inverse_fermat_little_theorem.cpp
+- IsPrime()
+: primality_test.cpp
+
- it_ternary_search()
: ternary_search.cpp
diff --git a/globals_func_m.html b/globals_func_m.html
index ec78c7e50..73acfcea5 100644
--- a/globals_func_m.html
+++ b/globals_func_m.html
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, trie_modern.cpp
, trie_tree.cpp
, trie_using_hashmap.cpp
+, karatsuba_algorithm_for_fast_multiplication.cpp
, 0_1_knapsack.cpp
, abbreviation.cpp
, coin_change_topdown.cpp
diff --git a/globals_func_t.html b/globals_func_t.html
index bcfe1e6bc..075a37744 100644
--- a/globals_func_t.html
+++ b/globals_func_t.html
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, sparse_table.cpp
, trie_tree.cpp
, trie_using_hashmap.cpp
+, karatsuba_algorithm_for_fast_multiplication.cpp
, 0_1_knapsack.cpp
, abbreviation.cpp
, coin_change_topdown.cpp
diff --git a/globals_i.html b/globals_i.html
index e0a80ea03..0e3b0d811 100644
--- a/globals_i.html
+++ b/globals_i.html
@@ -127,14 +127,14 @@ $(document).ready(function(){initNavTree('globals_i.html',''); initResizable();
- is_square()
: ordinary_least_squares_regressor.cpp
-- IsPrime()
-: primality_test.cpp
+
- isPrime()
+: modular_inverse_fermat_little_theorem.cpp
- isprime
: prime_factorization.cpp
-- isPrime()
-: modular_inverse_fermat_little_theorem.cpp
+
- IsPrime()
+: primality_test.cpp
- it_ternary_search()
: ternary_search.cpp
diff --git a/globals_m.html b/globals_m.html
index cff3f1311..dc05172a4 100644
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+++ b/globals_m.html
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, trie_modern.cpp
, trie_tree.cpp
, trie_using_hashmap.cpp
+, karatsuba_algorithm_for_fast_multiplication.cpp
, 0_1_knapsack.cpp
, abbreviation.cpp
, coin_change_topdown.cpp
diff --git a/globals_t.html b/globals_t.html
index a96384888..9a9a89dcd 100644
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, sparse_table.cpp
, trie_tree.cpp
, trie_using_hashmap.cpp
+, karatsuba_algorithm_for_fast_multiplication.cpp
, 0_1_knapsack.cpp
, abbreviation.cpp
, coin_change_topdown.cpp
diff --git a/index.html b/index.html
index 1f62bb9e6..eddd83466 100644
--- a/index.html
+++ b/index.html
@@ -96,10 +96,10 @@ $(document).ready(function(){initNavTree('index.html',''); initResizable(); });
-
+
Overview
The repository is a collection of open-source implementation of a variety of algorithms implemented in C++ and licensed under MIT License. The algorithms span a variety of topics from computer science, mathematics and statistics, data science, machine learning, engineering, etc.. The implementations and the associated documentation are meant to provide a learning resource for educators and students. Hence, one may find more than one implementation for the same objective but using a different algorithm strategies and optimizations.
-
+
Features
- The repository provides implementations of various algorithms in one of the most fundamental general purpose languages - C++.
@@ -110,12 +110,12 @@ Features
- Self-checks within programs ensure correct implementations with confidence.
- Modular implementations and OpenSource licensing enable the functions to be utilized conveniently in other applications.
-
+
Documentation
Online Documentation is generated from the repository source codes directly. The documentation contains all resources including source code snippets, details on execution of the programs, diagrammatic representation of program flow, and links to external resources where necessary. The documentation also introduces interactive source code with links to documentation for C++ STL library functions used. Click on Files menu to see the list of all the files documented with the code.
Documentation of Algorithms in C++ by The Algorithms Contributors is licensed under CC BY-SA 4.0
-
+
Contributions
As a community developed and maintained repository, we welcome new un-plagiarized quality contributions. Please read our Contribution Guidelines.
diff --git a/namespacemembers.html b/namespacemembers.html
index 76cc12229..0138c4e4e 100644
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+++ b/namespacemembers.html
@@ -223,12 +223,12 @@ $(document).ready(function(){initNavTree('namespacemembers.html',''); initResiza
- isPossible()
: backtracking
-- isSafe()
-: backtracking
-
- issafe()
: backtracking
+- isSafe()
+: backtracking
+
@@ -366,12 +366,12 @@ $(document).ready(function(){initNavTree('namespacemembers.html',''); initResiza
- quadraticProbe()
: quadratic_probing
-- quickSort()
-: sorting
-
- quicksort()
: sorting
+- quickSort()
+: sorting
+
diff --git a/namespacemembers_func.html b/namespacemembers_func.html
index c2c007a17..0c64c200b 100644
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- isPossible()
: backtracking
-- isSafe()
-: backtracking
-
- issafe()
: backtracking
+- isSafe()
+: backtracking
+
@@ -354,12 +354,12 @@ $(document).ready(function(){initNavTree('namespacemembers_func.html',''); initR
- quadraticProbe()
: quadratic_probing
-- quickSort()
-: sorting
-
- quicksort()
: sorting
+- quickSort()
+: sorting
+
diff --git a/namespaces.html b/namespaces.html
index 30f1fb490..d06908f98 100644
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+ ['pvalue_5398',['pvalue',['../de/d9d/classdata__structures_1_1linked__list_1_1link.html#ac121ce37b6ea864b160ebcada0bce936',1,'data_structures::linked_list::link']]]
];
diff --git a/search/variables_f.js b/search/variables_f.js
index 3c943184b..f3d8f5cab 100644
--- a/search/variables_f.js
+++ b/search/variables_f.js
@@ -1,5 +1,5 @@
var searchData=
[
- ['queuefront_5393',['queueFront',['../db/da9/classqueue.html#ac16ccadebb765e1ddbe415cdce1a17a5',1,'queue']]],
- ['queuerear_5394',['queueRear',['../db/da9/classqueue.html#ae2a7a36270f5d15218a180fa59e5b3a5',1,'queue']]]
+ ['queuefront_5399',['queueFront',['../db/da9/classqueue.html#ac16ccadebb765e1ddbe415cdce1a17a5',1,'queue']]],
+ ['queuerear_5400',['queueRear',['../db/da9/classqueue.html#ae2a7a36270f5d15218a180fa59e5b3a5',1,'queue']]]
];
Method 1: Use parent pointer (store the address of parent nodes)
- If a node does not have the right subtree, and we already visited the node itself, then the next node will be its parent node according to inorder traversal, and if we are going to parent from left, then the parent would be unvisited.
- In other words, go to the nearest ancestor for which given node would be in left subtree.
+
Method 2: Search from the root node
- In case if there is no link from a child node to the parent node, we need to walk down the tree starting from the root node to the given node, by doing so, we are visiting every ancestor of the given node.
diff --git a/d4/d38/power__of__two_8cpp.html b/d4/d38/power__of__two_8cpp.html
index d260dc329..a9469166b 100644
--- a/d4/d38/power__of__two_8cpp.html
+++ b/d4/d38/power__of__two_8cpp.html
@@ -126,7 +126,7 @@ Functions
Detailed Description
Implementation to check whether a number is a power of 2 or not.
This algorithm uses bit manipulation to check if a number is a power of 2 or not.
-
+
Algorithm
Let the input number be n, then the bitwise and between n and n-1 will let us know whether the number is power of 2 or not
For Example, If N= 32 then N-1 is 31, if we perform bitwise and of these two numbers then the result will be zero, which indicates that it is the power of 2 If N=23 then N-1 is 22, if we perform bitwise and of these two numbers then the result will not be zero , which indicates that it is not the power of 2
- Note
- This implementation is better than naive recursive or iterative approach.
diff --git a/d4/d8d/jarvis__algorithm_8cpp.html b/d4/d8d/jarvis__algorithm_8cpp.html
index 7c2e56183..0f2d46191 100644
--- a/d4/d8d/jarvis__algorithm_8cpp.html
+++ b/d4/d8d/jarvis__algorithm_8cpp.html
@@ -137,7 +137,7 @@ Functions
Detailed Description
Implementation of Jarvis’s algorithm.
Given a set of points in the plane. the convex hull of the set is the smallest convex polygon that contains all the points of it.
-
+
Algorithm
The idea of Jarvis’s Algorithm is simple, we start from the leftmost point (or point with minimum x coordinate value) and we keep wrapping points in counterclockwise direction.
The idea is to use orientation() here. Next point is selected as the point that beats all other points at counterclockwise orientation, i.e., next point is q if for any other point r, we have “orientation(p, q, r) = counterclockwise”.
diff --git a/d5/d33/gram__schmidt_8cpp.html b/d5/d33/gram__schmidt_8cpp.html
index bb3d6e860..e6b3367c4 100644
--- a/d5/d33/gram__schmidt_8cpp.html
+++ b/d5/d33/gram__schmidt_8cpp.html
@@ -140,7 +140,7 @@ Functions
Detailed Description
Gram Schmidt Orthogonalisation Process
Takes the input of Linearly Independent Vectors, returns vectors orthogonal to each other.
-
+
Algorithm
Take the first vector of given LI vectors as first vector of Orthogonal vectors. Take projection of second input vector on the first vector of Orthogonal vector and subtract it from the 2nd LI vector. Take projection of third vector on the second vector of Othogonal vectors and subtract it from the 3rd LI vector. Keep repeating the above process until all the vectors in the given input array are exhausted.
For Example: In R2, Input LI Vectors={(3,1),(2,2)} then Orthogonal Vectors= {(3, 1),(-0.4, 1.2)}
diff --git a/d5/d45/sublist__search_8cpp.html b/d5/d45/sublist__search_8cpp.html
index 36b5c562f..f64e9beba 100644
--- a/d5/d45/sublist__search_8cpp.html
+++ b/d5/d45/sublist__search_8cpp.html
@@ -149,14 +149,14 @@ Functions
Detailed Description
Implementation of the Sublist Search Algorithm
-
+
Algorithm
- Sublist search is used to detect a presence of one list in another list.
- Suppose we have a single-node list (let's say the first list), and we want to ensure that the list is present in another list (let's say the second list), then we can perform the sublist search to find it.
- For instance, the first list contains these elements: 23 -> 30 -> 41, and the second list contains these elements: 10 -> 15 -> 23 -> 30 -> 41 -> 49. At a glance, we see that the first list presents in the second list.
-
+
Working
- The sublist search algorithm works by comparing the first element of the first list with the first element of the second list.
diff --git a/d5/d88/md__d_i_r_e_c_t_o_r_y.html b/d5/d88/md__d_i_r_e_c_t_o_r_y.html
index 6f7beabdb..de20372a4 100644
--- a/d5/d88/md__d_i_r_e_c_t_o_r_y.html
+++ b/d5/d88/md__d_i_r_e_c_t_o_r_y.html
@@ -170,6 +170,11 @@ Data Structures
- Trie Using Hashmap
+Divide And Conquer
+
+
Dynamic Programming
- 0 1 Knapsack
@@ -200,13 +205,13 @@ Dynamic Programming
- Tree Height
- Word Break
-
+
Geometry
-
+
Graph
- Bidirectional Dijkstra
@@ -229,12 +234,12 @@ Graph
- Topological Sort
- Topological Sort By Kahns Algo
-
+
Graphics
-
+
Greedy Algorithms
- Dijkstra
@@ -244,7 +249,7 @@ Greedy Algorithms
- Kruskals Minimum Spanning Tree
- Prims Minimum Spanning Tree
-
+
Hashing
- Chaining
@@ -252,12 +257,12 @@ Hashing
- Linear Probing Hash Table
- Quadratic Probing Hash Table
-
+
Linear Algebra
-
+
Machine Learning
- A Star Search
@@ -268,7 +273,7 @@ Machine Learning
- Ordinary Least Squares Regressor
- Vector Ops
-
+
Math
- Armstrong Number
@@ -320,7 +325,7 @@ Math
- Sum Of Digits
- Vector Cross Product
-
+
Numerical Methods
- Bisection Method
@@ -341,7 +346,7 @@ Numerical Methods
- Rungekutta
- Successive Approximation
-
+
Operations On Datastructures
- Array Left Rotation
@@ -356,7 +361,7 @@ Operations On Datastructures
- Trie Multiple Search
- Union Of 2 Arrays
-
+
Others
- Buzz Number
@@ -379,7 +384,7 @@ Others
- Tower Of Hanoi
- Vector Important Functions
-
+
Probability
- Addition Rule
@@ -387,7 +392,7 @@ Probability
- Binomial Dist
- Poisson Dist
-
+
Range Queries
- Fenwick Tree
@@ -397,7 +402,7 @@ Range Queries
- Segtree
- Sparse Table
-
+
Search
- Binary Search
@@ -415,7 +420,7 @@ Search
- Ternary Search
- Text Search
-
+
Sorting
- Bead Sort
@@ -456,7 +461,7 @@ Sorting
- Wave Sort
- Wiggle Sort
-
+
Strings
- Brute Force String Searching
diff --git a/d5/ddb/bogo__sort_8cpp.html b/d5/ddb/bogo__sort_8cpp.html
index 94b9002b6..9ebef65a9 100644
--- a/d5/ddb/bogo__sort_8cpp.html
+++ b/d5/ddb/bogo__sort_8cpp.html
@@ -136,7 +136,7 @@ Functions
Detailed Description
Implementation of Bogosort algorithm
In computer science, bogosort (also known as permutation sort, stupid sort, slowsort, shotgun sort, random sort, monkey sort, bobosort or shuffle sort) is a highly inefficient sorting algorithm based on the generate and test paradigm. Two versions of this algorithm exist: a deterministic version that enumerates all permutations until it hits a sorted one, and a randomized version that randomly permutes its input.Randomized version is implemented here.
-
+
Algorithm
Shuffle the array untill array is sorted.
diff --git a/d6/d10/cut__rod_8cpp.html b/d6/d10/cut__rod_8cpp.html
index 6d78b405a..19ba0d116 100644
--- a/d6/d10/cut__rod_8cpp.html
+++ b/d6/d10/cut__rod_8cpp.html
@@ -136,7 +136,7 @@ Functions
Detailed Description
Implementation of cutting a rod problem.
Given a rod of length n inches and an array of prices that contains prices of all pieces of size<=n. Determine the maximum profit obtainable by cutting up the rod and selling the pieces.
-
+
Algorithm
The idea is to break the given rod into every smaller piece as possible and then check profit for each piece, by calculating maximum profit for smaller pieces we will build the solution for larger pieces in bottom-up manner.
- Capitalize zero or more of
a's lowercase letters.
- Delete all of the remaining lowercase letters in
a.
-
+
Algorithm
The idea is in the problem statement itself: iterate through characters of string a and b (for character indexes i and j respectively):
- If
a[i] and b[j] are equal, then move to next position
diff --git a/d8/d90/iterative__tree__traversals_8cpp.html b/d8/d90/iterative__tree__traversals_8cpp.html
index 3e6d60baa..6b5f02a15 100644
--- a/d8/d90/iterative__tree__traversals_8cpp.html
+++ b/d8/d90/iterative__tree__traversals_8cpp.html
@@ -158,13 +158,13 @@ Functions
Detailed Description
Iterative version of Preorder, Postorder, and preorder Traversal of the Tree
-
+
Iterative Preorder Traversal of a tree
Create a Stack that will store the Node of Tree. Push the root node into the stack. Save the root into the variabe named as current, and pop and elemnt from the stack. Store the data of current into the result array, and start traversing from it. Push both the child node of the current node into the stack, first right child then left child. Repeat the same set of steps untill the Stack becomes empty. And return the result array as the preorder traversal of a tree.
-
+
Iterative Postorder Traversal of a tree
Create a Stack that will store the Node of Tree. Push the root node into the stack. Save the root into the variabe named as current, and pop and elemnt from the stack. Store the data of current into the result array, and start traversing from it. Push both the child node of the current node into the stack, first left child then right child. Repeat the same set of steps untill the Stack becomes empty. Now reverse the result array and then return it to the calling function as a postorder traversal of a tree.
-
+
Iterative Inorder Traversal of a tree
Create a Stack that will store the Node of Tree. Push the root node into the stack. Save the root into the variabe named as current. Now iterate and take the current to the extreme left of the tree by traversing only to its left. Pop the elemnt from the stack and assign it to the current. Store the data of current into the result array. Repeat the same set of steps until the Stack becomes empty or the current becomes NULL. And return the result array as the inorder traversal of a tree.
Function Documentation
diff --git a/d8/d99/connected__components__with__dsu_8cpp.html b/d8/d99/connected__components__with__dsu_8cpp.html
index 20a095355..947a3d0d0 100644
--- a/d8/d99/connected__components__with__dsu_8cpp.html
+++ b/d8/d99/connected__components__with__dsu_8cpp.html
@@ -156,7 +156,7 @@ uint32_t graph::disjoint_u
Detailed Description
The Disjoint union is the technique to find connected component in graph efficiently.
-
+
Algorithm
In Graph, if you have to find out the number of connected components, there are 2 options
- Depth first search
diff --git a/da/d52/minimum__edit__distance_8cpp.html b/da/d52/minimum__edit__distance_8cpp.html
index 51128f6bc..ec8c27c78 100644
--- a/da/d52/minimum__edit__distance_8cpp.html
+++ b/da/d52/minimum__edit__distance_8cpp.html
@@ -137,7 +137,7 @@ Functions
Detailed Description
Implementation of Minimum Edit Distance using Dynamic Programing.
Given two strings str1 & str2 and we have to calculate the minimum number of operations (Insert, Remove, Replace) required to convert str1 to str2.
-
+
Algorithm
We will solve this problem using Naive recursion. But as we are approaching with a DP solution. So, we will take a DP array to store the solution of all sub-problems so that we don't have to perform recursion again and again. Now to solve the problem, We can traverse all characters from either right side of the strings or left side. Suppose we will do it from the right side. So, there are two possibilities for every pair of characters being traversed.
- If the last characters of two strings are the same, Ignore the characters and get the count for the remaining string. So, we get the solution for lengths m-1 and n-1 in a DP array.
diff --git a/da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html b/da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html
new file mode 100644
index 000000000..de3b3ec97
--- /dev/null
+++ b/da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html
@@ -0,0 +1,425 @@
+
+
+
+
+
+
+
+Algorithms_in_C++: divide_and_conquer/karatsuba_algorithm_for_fast_multiplication.cpp File Reference
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ Algorithms_in_C++
+ 1.0.0
+
+ Set of algorithms implemented in C++.
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
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+
+
+
+
+
+
+Namespaces |
+Functions
+
+karatsuba_algorithm_for_fast_multiplication.cpp File Reference
+
+
+
+Implementation of the Karatsuba algorithm for fast multiplication
+More...
+#include <cassert>
+#include <cstring>
+#include <iostream>
+#include <vector>
+
+Include dependency graph for karatsuba_algorithm_for_fast_multiplication.cpp:
+
+
+
+
+
+
+Namespaces
divide_and_conquer for std::vector
karatsuba_algorithm Functions for the Karatsuba algorithm for fast multiplication
+
+Functions
std::string divide_and_conquer::karatsuba_algorithm::addStrings (std::string first, std::string second) Helper function for the main function, that implements Karatsuba's algorithm for fast multiplication. More...
int64_t divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm (std::string str1, std::string str2) The main function implements Karatsuba's algorithm for fast multiplication. More...
static void test () Self-test implementations. More...
int main () Main function. More...
+Detailed Description
+Implementation of the Karatsuba algorithm for fast multiplication
+Given two strings in binary notation we want to multiply them and return the value Simple approach is to multiply bits one by one which will give the time complexity of around O(n^2). To make it more efficient we will be using Karatsuba' algorithm to find the product which will solve the problem O(nlogn) of time.
+Function Documentation
+
+◆ addStrings()
+
+
+
+
+
+ std::string divide_and_conquer::karatsuba_algorithm::addStrings
+ (
+ std::string
+ first,
+
+
+ std::string
+ second
+
+
+ )
+
+
+
+
+Helper function for the main function, that implements Karatsuba's algorithm for fast multiplication.
+- Parameters
-
+
+ first the input string 1 second the input string 2
+
+
+- Returns
- the concatenated string
+
+
+
+
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+
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+T at(T... args)
+
+
+T max(T... args)
+
+T size(T... args)
+T to_string(T... args)
+
+Here is the call graph for this function:
+
+
+
+
+
+
+
+
+◆ karatsuba_algorithm()
+
+
+
+
+
+ int64_t divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm
+ (
+ std::string
+ str1,
+
+
+ std::string
+ str2
+
+
+ )
+
+
+
+
+The main function implements Karatsuba's algorithm for fast multiplication.
+- Parameters
-
+
+ str1 the input string 1 str2 the input string 2
+
+
+- Returns
- the multiplicative number value
+
+
+
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+
+
+Functions for the Karatsuba algorithm for fast multiplication
+T substr(T... args)
+
+Here is the call graph for this function:
+
+
+
+
+
+
+
+
+◆ main()
+
+
+
+
+
+ int main
+ (
+ void
+ )
+
+
+
+
+
+◆ test()
+
+
+
+
+
+
+
+
+ static void test
+ (
+ )
+
+
+
+
+static
+
+
+
+
+Self-test implementations.
+- Returns
- void
+
+
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+
+
+T endl(T... args)
+
+Here is the call graph for this function:
+
+
+
+
+
+
+
+
+
+
+
+
+
+ - Generated by 1.9.1
+
+
+
+
diff --git a/da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.js b/da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.js
new file mode 100644
index 000000000..dd00fedc3
--- /dev/null
+++ b/da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.js
@@ -0,0 +1,7 @@
+var karatsuba__algorithm__for__fast__multiplication_8cpp =
+[
+ [ "addStrings", "da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#a7d1dbae365c7746295d3322e6f7f80b6", null ],
+ [ "karatsuba_algorithm", "da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#a7a890d2f26855ada3b9f1d43aec70a86", null ],
+ [ "main", "da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4", null ],
+ [ "test", "da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aa8dca7b867074164d5f45b0f3851269d", null ]
+];
\ No newline at end of file
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diff --git a/db/d16/0__1__knapsack_8cpp.html b/db/d16/0__1__knapsack_8cpp.html
index c0cfe26cd..81c519815 100644
--- a/db/d16/0__1__knapsack_8cpp.html
+++ b/db/d16/0__1__knapsack_8cpp.html
@@ -136,7 +136,7 @@ Functions
Detailed Description
Implementation of 0-1 Knapsack Problem
Given weights and values of n items, put these items in a knapsack of capacity W to get the maximum total value in the knapsack. In other words, given two integer arrays val[0..n-1] and wt[0..n-1] which represent values and weights associated with n items respectively. Also given an integer W which represents knapsack capacity, find out the maximum value subset of val[] such that sum of the weights of this subset is smaller than or equal to W. You cannot break an item, either pick the complete item or don’t pick it (0-1 property)
-
+
Algorithm
The idea is to consider all subsets of items and calculate the total weight and value of all subsets. Consider the only subsets whose total weight is smaller than W. From all such subsets, pick the maximum value subset.
- Author
- Anmol
diff --git a/db/dca/kadane2_8cpp.html b/db/dca/kadane2_8cpp.html
index 8eb7970bc..a8d85a1c6 100644
--- a/db/dca/kadane2_8cpp.html
+++ b/db/dca/kadane2_8cpp.html
@@ -132,7 +132,7 @@ Functions
Detailed Description
Implementation of Kadane Algorithm
Kadane algorithm is used to find the maximum sum subarray in an array and maximum sum subarray problem is the task of finding a contiguous subarray with the largest sum
-
+
Algorithm
The simple idea of the algorithm is to search for all positive contiguous segments of the array and keep track of maximum sum contiguous segment among all positive segments(curr_sum is used for this) Each time we get a positive sum we compare it with max_sum and update max_sum if it is greater than curr_sum
diff --git a/dd/d47/namespacemath.html b/dd/d47/namespacemath.html
index 2050416db..17df5d494 100644
--- a/dd/d47/namespacemath.html
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@@ -146,7 +146,7 @@ Functions
Mathematical algorithms
Given a recurrence relation; evaluate the value of nth term. For e.g., For fibonacci series, recurrence series is f(n) = f(n-1) + f(n-2) where f(0) = 0 and f(1) = 1. Note that the method used only demonstrates recurrence relation with one variable (n), unlike nCr problem, since it has two (n, r)
-
+
Algorithm
This problem can be solved using matrix exponentiation method.
- See also
- here for simple number exponentiation algorithm or explaination here.
diff --git a/dd/dba/namespacedivide__and__conquer.html b/dd/dba/namespacedivide__and__conquer.html
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+ Algorithms_in_C++
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+ Set of algorithms implemented in C++.
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+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+divide_and_conquer Namespace Reference
+
+
+
+
+
+
+
+ - Generated by 1.9.1
+
+
+
+
diff --git a/de/d41/namespacekaratsuba__algorithm.html b/de/d41/namespacekaratsuba__algorithm.html
new file mode 100644
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--- /dev/null
+++ b/de/d41/namespacekaratsuba__algorithm.html
@@ -0,0 +1,112 @@
+
+
+
+
+
+
+
+Algorithms_in_C++: karatsuba_algorithm Namespace Reference
+
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+
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+
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+
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+
+ Algorithms_in_C++
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+ Set of algorithms implemented in C++.
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+
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+
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+
+
+
+
+
+
+
+
+
+karatsuba_algorithm Namespace Reference
+
+
+
+Functions for the Karatsuba algorithm for fast multiplication
+More...
+Detailed Description
+Functions for the Karatsuba algorithm for fast multiplication
+
+
+
+
+
+
+ - Generated by 1.9.1
+
+
+
+
diff --git a/df/d66/vector__cross__product_8cpp.html b/df/d66/vector__cross__product_8cpp.html
index 52b7c4fe9..346554810 100644
--- a/df/d66/vector__cross__product_8cpp.html
+++ b/df/d66/vector__cross__product_8cpp.html
@@ -145,7 +145,7 @@ Functions
The direction ratios (DR) are calculated as follows: 1st DR, J: (b * z) - (c * y) 2nd DR, A: -((a * z) - (c * x)) 3rd DR, N: (a * y) - (b * x)
Therefore, the direction ratios of the cross product are: J, A, N The following C++ Program calculates the direction ratios of the cross products of two vector. The program uses a function, cross() for doing so. The direction ratios for the first and the second vector has to be passed one by one seperated by a space character.
Magnitude of a vector is the square root of the sum of the squares of the direction ratios.
-
+
Example:
An example of a running instance of the executable program:
Pass the first Vector: 1 2 3
Pass the second Vector: 4 5 6 The cross product is: -3 6 -3 Magnitude: 7.34847
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+
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+
+
+ Algorithms_in_C++
+ 1.0.0
+
+ Set of algorithms implemented in C++.
+
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+
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+
+
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+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+divide_and_conquer Directory Reference
+
+
+
+
+Files
file karatsuba_algorithm_for_fast_multiplication.cpp Implementation of the Karatsuba algorithm for fast multiplication
+
+
+
+
+
+
+ - Generated by 1.9.1
+
+
+
+
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+var dir_93bc990c5cceb745f78af6949e9ef947 =
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+];
\ No newline at end of file
diff --git a/files.html b/files.html
index bb23d379f..4f03426e4 100644
--- a/files.html
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@@ -143,194 +143,196 @@ solve-a-rat-in-a-maze-c-java-pytho/"
- ► dynamic_programming ► geometry ► graph ► graphics ► greedy_algorithms ► hashing ► linear_algebra ► machine_learning ► math ► numerical_methods ► operations_on_datastructures ► others ► probability ► range_queries ► search ► sorting ► strings ► divide_and_conquer ► dynamic_programming ► geometry ► graph ► graphics ► greedy_algorithms ► hashing ► linear_algebra ► machine_learning ► math ► numerical_methods ► operations_on_datastructures ► others ► probability ► range_queries ► search ► sorting ► strings
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index 1c7b2311f..927c6694b 100644
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[ "data_structures", "dir_2e746e9d06bf2d8ff842208bcc6ebcfc.html", "dir_2e746e9d06bf2d8ff842208bcc6ebcfc" ],
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- is_square()
: ordinary_least_squares_regressor.cpp
-- IsPrime()
-: primality_test.cpp
-
- isPrime()
: modular_inverse_fermat_little_theorem.cpp
+- IsPrime()
+: primality_test.cpp
+
- it_ternary_search()
: ternary_search.cpp
diff --git a/globals_func_m.html b/globals_func_m.html
index ec78c7e50..73acfcea5 100644
--- a/globals_func_m.html
+++ b/globals_func_m.html
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, trie_modern.cpp
, trie_tree.cpp
, trie_using_hashmap.cpp
+, karatsuba_algorithm_for_fast_multiplication.cpp
, 0_1_knapsack.cpp
, abbreviation.cpp
, coin_change_topdown.cpp
diff --git a/globals_func_t.html b/globals_func_t.html
index bcfe1e6bc..075a37744 100644
--- a/globals_func_t.html
+++ b/globals_func_t.html
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, sparse_table.cpp
, trie_tree.cpp
, trie_using_hashmap.cpp
+, karatsuba_algorithm_for_fast_multiplication.cpp
, 0_1_knapsack.cpp
, abbreviation.cpp
, coin_change_topdown.cpp
diff --git a/globals_i.html b/globals_i.html
index e0a80ea03..0e3b0d811 100644
--- a/globals_i.html
+++ b/globals_i.html
@@ -127,14 +127,14 @@ $(document).ready(function(){initNavTree('globals_i.html',''); initResizable();
- is_square()
: ordinary_least_squares_regressor.cpp
-- IsPrime()
-: primality_test.cpp
+
- isPrime()
+: modular_inverse_fermat_little_theorem.cpp
- isprime
: prime_factorization.cpp
-- isPrime()
-: modular_inverse_fermat_little_theorem.cpp
+
- IsPrime()
+: primality_test.cpp
- it_ternary_search()
: ternary_search.cpp
diff --git a/globals_m.html b/globals_m.html
index cff3f1311..dc05172a4 100644
--- a/globals_m.html
+++ b/globals_m.html
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, trie_modern.cpp
, trie_tree.cpp
, trie_using_hashmap.cpp
+, karatsuba_algorithm_for_fast_multiplication.cpp
, 0_1_knapsack.cpp
, abbreviation.cpp
, coin_change_topdown.cpp
diff --git a/globals_t.html b/globals_t.html
index a96384888..9a9a89dcd 100644
--- a/globals_t.html
+++ b/globals_t.html
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, sparse_table.cpp
, trie_tree.cpp
, trie_using_hashmap.cpp
+, karatsuba_algorithm_for_fast_multiplication.cpp
, 0_1_knapsack.cpp
, abbreviation.cpp
, coin_change_topdown.cpp
diff --git a/index.html b/index.html
index 1f62bb9e6..eddd83466 100644
--- a/index.html
+++ b/index.html
@@ -96,10 +96,10 @@ $(document).ready(function(){initNavTree('index.html',''); initResizable(); });
-
+
Overview
The repository is a collection of open-source implementation of a variety of algorithms implemented in C++ and licensed under MIT License. The algorithms span a variety of topics from computer science, mathematics and statistics, data science, machine learning, engineering, etc.. The implementations and the associated documentation are meant to provide a learning resource for educators and students. Hence, one may find more than one implementation for the same objective but using a different algorithm strategies and optimizations.
-
+
Features
- The repository provides implementations of various algorithms in one of the most fundamental general purpose languages - C++.
@@ -110,12 +110,12 @@ Features
- Self-checks within programs ensure correct implementations with confidence.
- Modular implementations and OpenSource licensing enable the functions to be utilized conveniently in other applications.
-
+
Documentation
Online Documentation is generated from the repository source codes directly. The documentation contains all resources including source code snippets, details on execution of the programs, diagrammatic representation of program flow, and links to external resources where necessary. The documentation also introduces interactive source code with links to documentation for C++ STL library functions used. Click on Files menu to see the list of all the files documented with the code.
Documentation of Algorithms in C++ by The Algorithms Contributors is licensed under CC BY-SA 4.0
-
+
Contributions
As a community developed and maintained repository, we welcome new un-plagiarized quality contributions. Please read our Contribution Guidelines.
diff --git a/namespacemembers.html b/namespacemembers.html
index 76cc12229..0138c4e4e 100644
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+++ b/namespacemembers.html
@@ -223,12 +223,12 @@ $(document).ready(function(){initNavTree('namespacemembers.html',''); initResiza
- isPossible()
: backtracking
-- isSafe()
-: backtracking
-
- issafe()
: backtracking
+- isSafe()
+: backtracking
+
@@ -366,12 +366,12 @@ $(document).ready(function(){initNavTree('namespacemembers.html',''); initResiza
- quadraticProbe()
: quadratic_probing
-- quickSort()
-: sorting
-
- quicksort()
: sorting
+- quickSort()
+: sorting
+
diff --git a/namespacemembers_func.html b/namespacemembers_func.html
index c2c007a17..0c64c200b 100644
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- isPossible()
: backtracking
-- isSafe()
-: backtracking
-
- issafe()
: backtracking
+- isSafe()
+: backtracking
+
@@ -354,12 +354,12 @@ $(document).ready(function(){initNavTree('namespacemembers_func.html',''); initR
- quadraticProbe()
: quadratic_probing
-- quickSort()
-: sorting
-
- quicksort()
: sorting
+- quickSort()
+: sorting
+
diff --git a/namespaces.html b/namespaces.html
index 30f1fb490..d06908f98 100644
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Ndepth_first_search Functions for Depth First Search algorithm Ndisjoint_union Functions for Disjoint union implementation ►Ndouble_hashing An implementation of hash table using double hashing algorithm Ndynamic_programming Dynamic Programming algorithms Nfalse_position Functions for False Position method Nfibonacci_sum Functions for the sum of the Fibonacci Sequence: \(\mathrm{F}(n) + \mathrm{F}(n+1) + .. + \mathrm{F}(m)\) ►Ngeometry Geometry algorithms Ngram_schmidt Functions for Gram Schmidt Orthogonalisation Process ►Ngraph Graph Algorithms Nhamming_distance Functions for Hamming distance implementation Nheavy_light_decomposition Heavy light decomposition algorithm Nhorspool Functions for Horspool's algorithm Nhouse_robber Functions for the House Robber algorithm Ninorder_successor_of_bst Functions for the Inorder successor of a binary search tree implementation Ninversion Functions for counting inversions using Merge Sort algorithm Nis_graph_bipartite Functions for checking whether a graph is bipartite or not Niterative_tree_traversals Functions for the Traversal of the Tree algorithm Njarvis Functions for Jarvis’s algorithm Nkadane Functions for Kadane algorithm NKnapsack Implementation of 0-1 Knapsack problem Nlayers This namespace contains layers used in MLP Nlinear_algebra For io operations ►Nlinear_probing An implementation of hash table using linear probing algorithm Nlinear_recurrence_matrix Functions for Linear Recurrence Matrix implementation Nlinked_list Functions for singly linked list algorithm Nlist_array Functions for Dynamic Array algorithm ►Nmachine_learning A* search algorithm Nmagic_sequence Functions for the Magic sequence implementation ►Nmath For IO operations Nmedian_search Functions for Median search algorithm Nmerge_insertion Combined Intersion-Merge sorting algorithm Nmincoins_topdown Functions for minimum coin exchange problem NMinimum Implementation of Minimum Edit Distance algorithm Nmodular_division Functions for Modular Division implementation Nmorse Functions for Morse Code Nn_bonacci Functions for the N-bonacci implementation Nn_queens Functions for Eight Queens puzzle Nn_queens_all_solutions Functions for Eight Queens puzzle with all solutions Nn_queens_optimized Functions for Eight Queens puzzle optimized Nncr_modulo_p Functions for nCr modulo p implementation Nneural_network Neural Network or Multilayer Perceptron Nnumerical_methods For io operations ►Noperations_on_datastructures For std::vector ►Nothers For vector Npalindrome_partitioning Functions for Palindrome Partitioning algorithm Npancake_sort Functions for Pancake sort algorithm Npostfix_expression Functions for Postfix Expression algorithm Nqr_algorithm Functions to compute QR decomposition of any rectangular matrix ►Nquadratic_probing An implementation of hash table using quadratic probing algorithm Nqueue_using_array Functions for Queue using Array implementation Nradix_sort Functions for Radix sort algorithm Nrandom_pivot_quick_sort Functions for the Random Pivot Quick Sort implementation ►Nrange_queries Algorithms and Data Structures that support range queries and updates Nrat_maze Functions for <a href="https://www.codesdope.com/blog/article/backtracking-to-
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+ ['pvalue_5398',['pvalue',['../de/d9d/classdata__structures_1_1linked__list_1_1link.html#ac121ce37b6ea864b160ebcada0bce936',1,'data_structures::linked_list::link']]]
];
diff --git a/search/variables_f.js b/search/variables_f.js
index 3c943184b..f3d8f5cab 100644
--- a/search/variables_f.js
+++ b/search/variables_f.js
@@ -1,5 +1,5 @@
var searchData=
[
- ['queuefront_5393',['queueFront',['../db/da9/classqueue.html#ac16ccadebb765e1ddbe415cdce1a17a5',1,'queue']]],
- ['queuerear_5394',['queueRear',['../db/da9/classqueue.html#ae2a7a36270f5d15218a180fa59e5b3a5',1,'queue']]]
+ ['queuefront_5399',['queueFront',['../db/da9/classqueue.html#ac16ccadebb765e1ddbe415cdce1a17a5',1,'queue']]],
+ ['queuerear_5400',['queueRear',['../db/da9/classqueue.html#ae2a7a36270f5d15218a180fa59e5b3a5',1,'queue']]]
];
Detailed Description
Implementation to check whether a number is a power of 2 or not.
This algorithm uses bit manipulation to check if a number is a power of 2 or not.
-
+
Algorithm
Let the input number be n, then the bitwise and between n and n-1 will let us know whether the number is power of 2 or not
For Example, If N= 32 then N-1 is 31, if we perform bitwise and of these two numbers then the result will be zero, which indicates that it is the power of 2 If N=23 then N-1 is 22, if we perform bitwise and of these two numbers then the result will not be zero , which indicates that it is not the power of 2
- Note
- This implementation is better than naive recursive or iterative approach.
Detailed Description
Implementation of Jarvis’s algorithm.
Given a set of points in the plane. the convex hull of the set is the smallest convex polygon that contains all the points of it.
-
+
Algorithm
The idea of Jarvis’s Algorithm is simple, we start from the leftmost point (or point with minimum x coordinate value) and we keep wrapping points in counterclockwise direction.
The idea is to use orientation() here. Next point is selected as the point that beats all other points at counterclockwise orientation, i.e., next point is q if for any other point r, we have “orientation(p, q, r) = counterclockwise”.
diff --git a/d5/d33/gram__schmidt_8cpp.html b/d5/d33/gram__schmidt_8cpp.html index bb3d6e860..e6b3367c4 100644 --- a/d5/d33/gram__schmidt_8cpp.html +++ b/d5/d33/gram__schmidt_8cpp.html @@ -140,7 +140,7 @@ FunctionsDetailed Description
Gram Schmidt Orthogonalisation Process
Takes the input of Linearly Independent Vectors, returns vectors orthogonal to each other.
-
+
Algorithm
Take the first vector of given LI vectors as first vector of Orthogonal vectors. Take projection of second input vector on the first vector of Orthogonal vector and subtract it from the 2nd LI vector. Take projection of third vector on the second vector of Othogonal vectors and subtract it from the 3rd LI vector. Keep repeating the above process until all the vectors in the given input array are exhausted.
For Example: In R2, Input LI Vectors={(3,1),(2,2)} then Orthogonal Vectors= {(3, 1),(-0.4, 1.2)}
diff --git a/d5/d45/sublist__search_8cpp.html b/d5/d45/sublist__search_8cpp.html index 36b5c562f..f64e9beba 100644 --- a/d5/d45/sublist__search_8cpp.html +++ b/d5/d45/sublist__search_8cpp.html @@ -149,14 +149,14 @@ FunctionsDetailed Description
Implementation of the Sublist Search Algorithm
-
+
Algorithm
- Sublist search is used to detect a presence of one list in another list.
- Suppose we have a single-node list (let's say the first list), and we want to ensure that the list is present in another list (let's say the second list), then we can perform the sublist search to find it.
- For instance, the first list contains these elements: 23 -> 30 -> 41, and the second list contains these elements: 10 -> 15 -> 23 -> 30 -> 41 -> 49. At a glance, we see that the first list presents in the second list.
-
+
Working
- The sublist search algorithm works by comparing the first element of the first list with the first element of the second list.
diff --git a/d5/d88/md__d_i_r_e_c_t_o_r_y.html b/d5/d88/md__d_i_r_e_c_t_o_r_y.html
index 6f7beabdb..de20372a4 100644
--- a/d5/d88/md__d_i_r_e_c_t_o_r_y.html
+++ b/d5/d88/md__d_i_r_e_c_t_o_r_y.html
@@ -170,6 +170,11 @@ Data Structures
- Trie Using Hashmap
+Divide And Conquer
+
+
Dynamic Programming
- 0 1 Knapsack
@@ -200,13 +205,13 @@ Dynamic Programming
- Tree Height
- Word Break
-
+
Geometry
-
+
Graph
- Bidirectional Dijkstra
@@ -229,12 +234,12 @@ Graph
Working
- The sublist search algorithm works by comparing the first element of the first list with the first element of the second list. diff --git a/d5/d88/md__d_i_r_e_c_t_o_r_y.html b/d5/d88/md__d_i_r_e_c_t_o_r_y.html index 6f7beabdb..de20372a4 100644 --- a/d5/d88/md__d_i_r_e_c_t_o_r_y.html +++ b/d5/d88/md__d_i_r_e_c_t_o_r_y.html @@ -170,6 +170,11 @@ Data Structures
- Trie Using Hashmap
+Divide And Conquer
+ +Dynamic Programming
- 0 1 Knapsack @@ -200,13 +205,13 @@ Dynamic Programming
- Tree Height
- Word Break
+
Geometry
-
+
Graph
- Bidirectional Dijkstra
@@ -229,12 +234,12 @@ Graph
Graph
- Bidirectional Dijkstra @@ -229,12 +234,12 @@ Graph
+
Graphics
-
+
Greedy Algorithms
- Dijkstra
@@ -244,7 +249,7 @@ Greedy Algorithms
Greedy Algorithms
- Dijkstra @@ -244,7 +249,7 @@ Greedy Algorithms
+
Hashing
- Chaining
@@ -252,12 +257,12 @@ Hashing
+
Linear Algebra
-
+
Machine Learning
- A Star Search
@@ -268,7 +273,7 @@ Machine Learning
Machine Learning
- A Star Search @@ -268,7 +273,7 @@ Machine Learning
+
Math
- Armstrong Number
@@ -320,7 +325,7 @@ Math
+
Numerical Methods
- Bisection Method
@@ -341,7 +346,7 @@ Numerical Methods
+
Operations On Datastructures
- Array Left Rotation
@@ -356,7 +361,7 @@ Operations On Datastructures
+
Others
- Buzz Number
@@ -379,7 +384,7 @@ Others
+
Probability
- Addition Rule
@@ -387,7 +392,7 @@ Probability
+
Range Queries
- Fenwick Tree
@@ -397,7 +402,7 @@ Range Queries
+
Search
- Binary Search
@@ -415,7 +420,7 @@ Search
+
Sorting
- Bead Sort
@@ -456,7 +461,7 @@ Sorting
+
Strings
- Brute Force String Searching
diff --git a/d5/ddb/bogo__sort_8cpp.html b/d5/ddb/bogo__sort_8cpp.html
index 94b9002b6..9ebef65a9 100644
--- a/d5/ddb/bogo__sort_8cpp.html
+++ b/d5/ddb/bogo__sort_8cpp.html
@@ -136,7 +136,7 @@ Functions
Detailed Description
Implementation of Bogosort algorithm
In computer science, bogosort (also known as permutation sort, stupid sort, slowsort, shotgun sort, random sort, monkey sort, bobosort or shuffle sort) is a highly inefficient sorting algorithm based on the generate and test paradigm. Two versions of this algorithm exist: a deterministic version that enumerates all permutations until it hits a sorted one, and a randomized version that randomly permutes its input.Randomized version is implemented here.
-
+
Algorithm
Shuffle the array untill array is sorted.
diff --git a/d6/d10/cut__rod_8cpp.html b/d6/d10/cut__rod_8cpp.html
index 6d78b405a..19ba0d116 100644
--- a/d6/d10/cut__rod_8cpp.html
+++ b/d6/d10/cut__rod_8cpp.html
@@ -136,7 +136,7 @@ Functions
Detailed Description
Implementation of cutting a rod problem.
Given a rod of length n inches and an array of prices that contains prices of all pieces of size<=n. Determine the maximum profit obtainable by cutting up the rod and selling the pieces.
-
+
Algorithm
The idea is to break the given rod into every smaller piece as possible and then check profit for each piece, by calculating maximum profit for smaller pieces we will build the solution for larger pieces in bottom-up manner.
- Capitalize zero or more of
a's lowercase letters.
- Delete all of the remaining lowercase letters in
a.
-
+
Algorithm
The idea is in the problem statement itself: iterate through characters of string a and b (for character indexes i and j respectively):
- If
a[i] and b[j] are equal, then move to next position
diff --git a/d8/d90/iterative__tree__traversals_8cpp.html b/d8/d90/iterative__tree__traversals_8cpp.html
index 3e6d60baa..6b5f02a15 100644
--- a/d8/d90/iterative__tree__traversals_8cpp.html
+++ b/d8/d90/iterative__tree__traversals_8cpp.html
@@ -158,13 +158,13 @@ Functions
Detailed Description
Iterative version of Preorder, Postorder, and preorder Traversal of the Tree
-
+
Iterative Preorder Traversal of a tree
Create a Stack that will store the Node of Tree. Push the root node into the stack. Save the root into the variabe named as current, and pop and elemnt from the stack. Store the data of current into the result array, and start traversing from it. Push both the child node of the current node into the stack, first right child then left child. Repeat the same set of steps untill the Stack becomes empty. And return the result array as the preorder traversal of a tree.
-
+
Iterative Postorder Traversal of a tree
Create a Stack that will store the Node of Tree. Push the root node into the stack. Save the root into the variabe named as current, and pop and elemnt from the stack. Store the data of current into the result array, and start traversing from it. Push both the child node of the current node into the stack, first left child then right child. Repeat the same set of steps untill the Stack becomes empty. Now reverse the result array and then return it to the calling function as a postorder traversal of a tree.
-
+
Iterative Inorder Traversal of a tree
Create a Stack that will store the Node of Tree. Push the root node into the stack. Save the root into the variabe named as current. Now iterate and take the current to the extreme left of the tree by traversing only to its left. Pop the elemnt from the stack and assign it to the current. Store the data of current into the result array. Repeat the same set of steps until the Stack becomes empty or the current becomes NULL. And return the result array as the inorder traversal of a tree.
Function Documentation
diff --git a/d8/d99/connected__components__with__dsu_8cpp.html b/d8/d99/connected__components__with__dsu_8cpp.html
index 20a095355..947a3d0d0 100644
--- a/d8/d99/connected__components__with__dsu_8cpp.html
+++ b/d8/d99/connected__components__with__dsu_8cpp.html
@@ -156,7 +156,7 @@ uint32_t graph::disjoint_u
Detailed Description
The Disjoint union is the technique to find connected component in graph efficiently.
-
+
Algorithm
In Graph, if you have to find out the number of connected components, there are 2 options
- Depth first search
diff --git a/da/d52/minimum__edit__distance_8cpp.html b/da/d52/minimum__edit__distance_8cpp.html
index 51128f6bc..ec8c27c78 100644
--- a/da/d52/minimum__edit__distance_8cpp.html
+++ b/da/d52/minimum__edit__distance_8cpp.html
@@ -137,7 +137,7 @@ Functions
Detailed Description
Implementation of Minimum Edit Distance using Dynamic Programing.
Given two strings str1 & str2 and we have to calculate the minimum number of operations (Insert, Remove, Replace) required to convert str1 to str2.
-
+
Algorithm
We will solve this problem using Naive recursion. But as we are approaching with a DP solution. So, we will take a DP array to store the solution of all sub-problems so that we don't have to perform recursion again and again. Now to solve the problem, We can traverse all characters from either right side of the strings or left side. Suppose we will do it from the right side. So, there are two possibilities for every pair of characters being traversed.
- If the last characters of two strings are the same, Ignore the characters and get the count for the remaining string. So, we get the solution for lengths m-1 and n-1 in a DP array.
diff --git a/da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html b/da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html
new file mode 100644
index 000000000..de3b3ec97
--- /dev/null
+++ b/da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html
@@ -0,0 +1,425 @@
+
+
+
+
+
+
+
+Algorithms_in_C++: divide_and_conquer/karatsuba_algorithm_for_fast_multiplication.cpp File Reference
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+ Algorithms_in_C++
+ 1.0.0
+
+ Set of algorithms implemented in C++.
+
+
+
+
+
+
+
+
+
+
+
+
+
+
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+
+Namespaces |
+Functions
+
+karatsuba_algorithm_for_fast_multiplication.cpp File Reference
+
+
+
+Implementation of the Karatsuba algorithm for fast multiplication
+More...
+#include <cassert>
+#include <cstring>
+#include <iostream>
+#include <vector>
+
+Include dependency graph for karatsuba_algorithm_for_fast_multiplication.cpp:
+
+
+
+
+
+
+Namespaces
divide_and_conquer for std::vector
karatsuba_algorithm Functions for the Karatsuba algorithm for fast multiplication
+
+Functions
std::string divide_and_conquer::karatsuba_algorithm::addStrings (std::string first, std::string second) Helper function for the main function, that implements Karatsuba's algorithm for fast multiplication. More...
int64_t divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm (std::string str1, std::string str2) The main function implements Karatsuba's algorithm for fast multiplication. More...
static void test () Self-test implementations. More...
int main () Main function. More...
+Detailed Description
+Implementation of the Karatsuba algorithm for fast multiplication
+Given two strings in binary notation we want to multiply them and return the value Simple approach is to multiply bits one by one which will give the time complexity of around O(n^2). To make it more efficient we will be using Karatsuba' algorithm to find the product which will solve the problem O(nlogn) of time.
+Function Documentation
+
+◆ addStrings()
+
+
+
+
+
+ std::string divide_and_conquer::karatsuba_algorithm::addStrings
+ (
+ std::string
+ first,
+
+
+ std::string
+ second
+
+
+ )
+
+
+
+
+Helper function for the main function, that implements Karatsuba's algorithm for fast multiplication.
+- Parameters
-
+
+ first the input string 1 second the input string 2
+
+
+- Returns
- the concatenated string
+
+
+
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+T at(T... args)
+
+
+T max(T... args)
+
+T size(T... args)
+T to_string(T... args)
+
+Here is the call graph for this function:
+
+
+
+
+
+
+
+
+◆ karatsuba_algorithm()
+
+
+
+
+
+ int64_t divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm
+ (
+ std::string
+ str1,
+
+
+ std::string
+ str2
+
+
+ )
+
+
+
+
+The main function implements Karatsuba's algorithm for fast multiplication.
+- Parameters
-
+
+ str1 the input string 1 str2 the input string 2
+
+
+- Returns
- the multiplicative number value
+
+
+
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+
+Functions for the Karatsuba algorithm for fast multiplication
+T substr(T... args)
+
+Here is the call graph for this function:
+
+
+
+
+
+
+
+
+◆ main()
+
+
+
+
+
+ int main
+ (
+ void
+ )
+
+
+
+
+
+◆ test()
+
+
+
+
+
+
+
+
+ static void test
+ (
+ )
+
+
+
+
+static
+
+
+
+
+Self-test implementations.
+- Returns
- void
+
+
+
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+
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+
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+
+
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+
+
+T endl(T... args)
+
+Here is the call graph for this function:
+
+
+
+
+
+
+
+
+
+
+
+
+
+ - Generated by 1.9.1
+
+
+
+
diff --git a/da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.js b/da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.js
new file mode 100644
index 000000000..dd00fedc3
--- /dev/null
+++ b/da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.js
@@ -0,0 +1,7 @@
+var karatsuba__algorithm__for__fast__multiplication_8cpp =
+[
+ [ "addStrings", "da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#a7d1dbae365c7746295d3322e6f7f80b6", null ],
+ [ "karatsuba_algorithm", "da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#a7a890d2f26855ada3b9f1d43aec70a86", null ],
+ [ "main", "da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4", null ],
+ [ "test", "da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aa8dca7b867074164d5f45b0f3851269d", null ]
+];
\ No newline at end of file
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diff --git a/db/d16/0__1__knapsack_8cpp.html b/db/d16/0__1__knapsack_8cpp.html
index c0cfe26cd..81c519815 100644
--- a/db/d16/0__1__knapsack_8cpp.html
+++ b/db/d16/0__1__knapsack_8cpp.html
@@ -136,7 +136,7 @@ Functions
Detailed Description
Implementation of 0-1 Knapsack Problem
Given weights and values of n items, put these items in a knapsack of capacity W to get the maximum total value in the knapsack. In other words, given two integer arrays val[0..n-1] and wt[0..n-1] which represent values and weights associated with n items respectively. Also given an integer W which represents knapsack capacity, find out the maximum value subset of val[] such that sum of the weights of this subset is smaller than or equal to W. You cannot break an item, either pick the complete item or don’t pick it (0-1 property)
-
+
Algorithm
The idea is to consider all subsets of items and calculate the total weight and value of all subsets. Consider the only subsets whose total weight is smaller than W. From all such subsets, pick the maximum value subset.
- Author
- Anmol
diff --git a/db/dca/kadane2_8cpp.html b/db/dca/kadane2_8cpp.html
index 8eb7970bc..a8d85a1c6 100644
--- a/db/dca/kadane2_8cpp.html
+++ b/db/dca/kadane2_8cpp.html
@@ -132,7 +132,7 @@ Functions
Detailed Description
Implementation of Kadane Algorithm
Kadane algorithm is used to find the maximum sum subarray in an array and maximum sum subarray problem is the task of finding a contiguous subarray with the largest sum
-
+
Algorithm
The simple idea of the algorithm is to search for all positive contiguous segments of the array and keep track of maximum sum contiguous segment among all positive segments(curr_sum is used for this) Each time we get a positive sum we compare it with max_sum and update max_sum if it is greater than curr_sum
diff --git a/dd/d47/namespacemath.html b/dd/d47/namespacemath.html
index 2050416db..17df5d494 100644
--- a/dd/d47/namespacemath.html
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@@ -146,7 +146,7 @@ Functions
Mathematical algorithms
Given a recurrence relation; evaluate the value of nth term. For e.g., For fibonacci series, recurrence series is f(n) = f(n-1) + f(n-2) where f(0) = 0 and f(1) = 1. Note that the method used only demonstrates recurrence relation with one variable (n), unlike nCr problem, since it has two (n, r)
-
+
Algorithm
This problem can be solved using matrix exponentiation method.
- See also
- here for simple number exponentiation algorithm or explaination here.
diff --git a/dd/dba/namespacedivide__and__conquer.html b/dd/dba/namespacedivide__and__conquer.html
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+ Algorithms_in_C++
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+
+ Set of algorithms implemented in C++.
+
+
+
+
+
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+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+divide_and_conquer Namespace Reference
+
+
+
+
+
+
+
+ - Generated by 1.9.1
+
+
+
+
diff --git a/de/d41/namespacekaratsuba__algorithm.html b/de/d41/namespacekaratsuba__algorithm.html
new file mode 100644
index 000000000..e7be124e5
--- /dev/null
+++ b/de/d41/namespacekaratsuba__algorithm.html
@@ -0,0 +1,112 @@
+
+
+
+
+
+
+
+Algorithms_in_C++: karatsuba_algorithm Namespace Reference
+
+
+
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+
+
+
+
+
+
+
+
+
+
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+
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+
+ Algorithms_in_C++
+ 1.0.0
+
+ Set of algorithms implemented in C++.
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+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+karatsuba_algorithm Namespace Reference
+
+
+
+Functions for the Karatsuba algorithm for fast multiplication
+More...
+Detailed Description
+Functions for the Karatsuba algorithm for fast multiplication
+
+
+
+
+
+
+ - Generated by 1.9.1
+
+
+
+
diff --git a/df/d66/vector__cross__product_8cpp.html b/df/d66/vector__cross__product_8cpp.html
index 52b7c4fe9..346554810 100644
--- a/df/d66/vector__cross__product_8cpp.html
+++ b/df/d66/vector__cross__product_8cpp.html
@@ -145,7 +145,7 @@ Functions
The direction ratios (DR) are calculated as follows: 1st DR, J: (b * z) - (c * y) 2nd DR, A: -((a * z) - (c * x)) 3rd DR, N: (a * y) - (b * x)
Therefore, the direction ratios of the cross product are: J, A, N The following C++ Program calculates the direction ratios of the cross products of two vector. The program uses a function, cross() for doing so. The direction ratios for the first and the second vector has to be passed one by one seperated by a space character.
Magnitude of a vector is the square root of the sum of the squares of the direction ratios.
-
+
Example:
An example of a running instance of the executable program:
Pass the first Vector: 1 2 3
Pass the second Vector: 4 5 6 The cross product is: -3 6 -3 Magnitude: 7.34847
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+Algorithms_in_C++: divide_and_conquer Directory Reference
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+
+
+
+
+
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+
+
+
+
+
+
+
+ Algorithms_in_C++
+ 1.0.0
+
+ Set of algorithms implemented in C++.
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+divide_and_conquer Directory Reference
+
+
+
+
+Files
file karatsuba_algorithm_for_fast_multiplication.cpp Implementation of the Karatsuba algorithm for fast multiplication
+
+
+
+
+
+
+ - Generated by 1.9.1
+
+
+
+
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@@ -0,0 +1,4 @@
+var dir_93bc990c5cceb745f78af6949e9ef947 =
+[
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+];
\ No newline at end of file
diff --git a/files.html b/files.html
index bb23d379f..4f03426e4 100644
--- a/files.html
+++ b/files.html
@@ -143,194 +143,196 @@ solve-a-rat-in-a-maze-c-java-pytho/"
- ► dynamic_programming ► geometry ► graph ► graphics ► greedy_algorithms ► hashing ► linear_algebra ► machine_learning ► math ► numerical_methods ► operations_on_datastructures ► others ► probability ► range_queries ► search ► sorting ► strings ► divide_and_conquer ► dynamic_programming ► geometry ► graph ► graphics ► greedy_algorithms ► hashing ► linear_algebra ► machine_learning ► math ► numerical_methods ► operations_on_datastructures ► others ► probability ► range_queries ► search ► sorting ► strings
diff --git a/files_dup.js b/files_dup.js
index 1c7b2311f..927c6694b 100644
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[ "data_structures", "dir_2e746e9d06bf2d8ff842208bcc6ebcfc.html", "dir_2e746e9d06bf2d8ff842208bcc6ebcfc" ],
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index d419feb46..2037df291 100644
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@@ -123,12 +123,12 @@ $(document).ready(function(){initNavTree('globals_func_i.html',''); initResizabl
- is_square()
: ordinary_least_squares_regressor.cpp
-- IsPrime()
-: primality_test.cpp
-
- isPrime()
: modular_inverse_fermat_little_theorem.cpp
+- IsPrime()
+: primality_test.cpp
+
- it_ternary_search()
: ternary_search.cpp
diff --git a/globals_func_m.html b/globals_func_m.html
index ec78c7e50..73acfcea5 100644
--- a/globals_func_m.html
+++ b/globals_func_m.html
@@ -127,6 +127,7 @@ $(document).ready(function(){initNavTree('globals_func_m.html',''); initResizabl
, trie_modern.cpp
, trie_tree.cpp
, trie_using_hashmap.cpp
+, karatsuba_algorithm_for_fast_multiplication.cpp
, 0_1_knapsack.cpp
, abbreviation.cpp
, coin_change_topdown.cpp
diff --git a/globals_func_t.html b/globals_func_t.html
index bcfe1e6bc..075a37744 100644
--- a/globals_func_t.html
+++ b/globals_func_t.html
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, sparse_table.cpp
, trie_tree.cpp
, trie_using_hashmap.cpp
+, karatsuba_algorithm_for_fast_multiplication.cpp
, 0_1_knapsack.cpp
, abbreviation.cpp
, coin_change_topdown.cpp
diff --git a/globals_i.html b/globals_i.html
index e0a80ea03..0e3b0d811 100644
--- a/globals_i.html
+++ b/globals_i.html
@@ -127,14 +127,14 @@ $(document).ready(function(){initNavTree('globals_i.html',''); initResizable();
- is_square()
: ordinary_least_squares_regressor.cpp
-- IsPrime()
-: primality_test.cpp
+
- isPrime()
+: modular_inverse_fermat_little_theorem.cpp
- isprime
: prime_factorization.cpp
-- isPrime()
-: modular_inverse_fermat_little_theorem.cpp
+
- IsPrime()
+: primality_test.cpp
- it_ternary_search()
: ternary_search.cpp
diff --git a/globals_m.html b/globals_m.html
index cff3f1311..dc05172a4 100644
--- a/globals_m.html
+++ b/globals_m.html
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, trie_modern.cpp
, trie_tree.cpp
, trie_using_hashmap.cpp
+, karatsuba_algorithm_for_fast_multiplication.cpp
, 0_1_knapsack.cpp
, abbreviation.cpp
, coin_change_topdown.cpp
diff --git a/globals_t.html b/globals_t.html
index a96384888..9a9a89dcd 100644
--- a/globals_t.html
+++ b/globals_t.html
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, sparse_table.cpp
, trie_tree.cpp
, trie_using_hashmap.cpp
+, karatsuba_algorithm_for_fast_multiplication.cpp
, 0_1_knapsack.cpp
, abbreviation.cpp
, coin_change_topdown.cpp
diff --git a/index.html b/index.html
index 1f62bb9e6..eddd83466 100644
--- a/index.html
+++ b/index.html
@@ -96,10 +96,10 @@ $(document).ready(function(){initNavTree('index.html',''); initResizable(); });
-
+
Overview
The repository is a collection of open-source implementation of a variety of algorithms implemented in C++ and licensed under MIT License. The algorithms span a variety of topics from computer science, mathematics and statistics, data science, machine learning, engineering, etc.. The implementations and the associated documentation are meant to provide a learning resource for educators and students. Hence, one may find more than one implementation for the same objective but using a different algorithm strategies and optimizations.
-
+
Features
- The repository provides implementations of various algorithms in one of the most fundamental general purpose languages - C++.
@@ -110,12 +110,12 @@ Features
- Self-checks within programs ensure correct implementations with confidence.
- Modular implementations and OpenSource licensing enable the functions to be utilized conveniently in other applications.
-
+
Documentation
Online Documentation is generated from the repository source codes directly. The documentation contains all resources including source code snippets, details on execution of the programs, diagrammatic representation of program flow, and links to external resources where necessary. The documentation also introduces interactive source code with links to documentation for C++ STL library functions used. Click on Files menu to see the list of all the files documented with the code.
Documentation of Algorithms in C++ by The Algorithms Contributors is licensed under CC BY-SA 4.0
-
+
Contributions
As a community developed and maintained repository, we welcome new un-plagiarized quality contributions. Please read our Contribution Guidelines.
diff --git a/namespacemembers.html b/namespacemembers.html
index 76cc12229..0138c4e4e 100644
--- a/namespacemembers.html
+++ b/namespacemembers.html
@@ -223,12 +223,12 @@ $(document).ready(function(){initNavTree('namespacemembers.html',''); initResiza
- isPossible()
: backtracking
-- isSafe()
-: backtracking
-
- issafe()
: backtracking
+- isSafe()
+: backtracking
+
@@ -366,12 +366,12 @@ $(document).ready(function(){initNavTree('namespacemembers.html',''); initResiza
- quadraticProbe()
: quadratic_probing
-- quickSort()
-: sorting
-
- quicksort()
: sorting
+- quickSort()
+: sorting
+
diff --git a/namespacemembers_func.html b/namespacemembers_func.html
index c2c007a17..0c64c200b 100644
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- isPossible()
: backtracking
-- isSafe()
-: backtracking
-
- issafe()
: backtracking
+- isSafe()
+: backtracking
+
@@ -354,12 +354,12 @@ $(document).ready(function(){initNavTree('namespacemembers_func.html',''); initR
- quadraticProbe()
: quadratic_probing
-- quickSort()
-: sorting
-
- quicksort()
: sorting
+- quickSort()
+: sorting
+
diff --git a/namespaces.html b/namespaces.html
index 30f1fb490..d06908f98 100644
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diff --git a/search/variables_f.js b/search/variables_f.js
index 3c943184b..f3d8f5cab 100644
--- a/search/variables_f.js
+++ b/search/variables_f.js
@@ -1,5 +1,5 @@
var searchData=
[
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Detailed Description
Implementation of Bogosort algorithm
In computer science, bogosort (also known as permutation sort, stupid sort, slowsort, shotgun sort, random sort, monkey sort, bobosort or shuffle sort) is a highly inefficient sorting algorithm based on the generate and test paradigm. Two versions of this algorithm exist: a deterministic version that enumerates all permutations until it hits a sorted one, and a randomized version that randomly permutes its input.Randomized version is implemented here.
-
+
Algorithm
Shuffle the array untill array is sorted.
diff --git a/d6/d10/cut__rod_8cpp.html b/d6/d10/cut__rod_8cpp.html index 6d78b405a..19ba0d116 100644 --- a/d6/d10/cut__rod_8cpp.html +++ b/d6/d10/cut__rod_8cpp.html @@ -136,7 +136,7 @@ FunctionsDetailed Description
Implementation of cutting a rod problem.
Given a rod of length n inches and an array of prices that contains prices of all pieces of size<=n. Determine the maximum profit obtainable by cutting up the rod and selling the pieces.
-
+
Algorithm
The idea is to break the given rod into every smaller piece as possible and then check profit for each piece, by calculating maximum profit for smaller pieces we will build the solution for larger pieces in bottom-up manner.
a's lowercase letters.a.
+
Algorithm
The idea is in the problem statement itself: iterate through characters of string a and b (for character indexes i and j respectively):
- If
a[i]andb[j]are equal, then move to next position
diff --git a/d8/d90/iterative__tree__traversals_8cpp.html b/d8/d90/iterative__tree__traversals_8cpp.html
index 3e6d60baa..6b5f02a15 100644
--- a/d8/d90/iterative__tree__traversals_8cpp.html
+++ b/d8/d90/iterative__tree__traversals_8cpp.html
@@ -158,13 +158,13 @@ Functions
- Depth first search diff --git a/da/d52/minimum__edit__distance_8cpp.html b/da/d52/minimum__edit__distance_8cpp.html index 51128f6bc..ec8c27c78 100644 --- a/da/d52/minimum__edit__distance_8cpp.html +++ b/da/d52/minimum__edit__distance_8cpp.html @@ -137,7 +137,7 @@ Functions
- If the last characters of two strings are the same, Ignore the characters and get the count for the remaining string. So, we get the solution for lengths m-1 and n-1 in a DP array. diff --git a/da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html b/da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html new file mode 100644 index 000000000..de3b3ec97 --- /dev/null +++ b/da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html @@ -0,0 +1,425 @@ + + + + + + + +
- Parameters
-
+
+
+first the input string 1 second the input string 2
+ - Returns
- the concatenated string
- Parameters
-
+
+
+str1 the input string 1 str2 the input string 2
+ - Returns
- the multiplicative number value
- Returns
- void
- Generated by 1.9.1
+
- Author
- Anmol diff --git a/db/dca/kadane2_8cpp.html b/db/dca/kadane2_8cpp.html index 8eb7970bc..a8d85a1c6 100644 --- a/db/dca/kadane2_8cpp.html +++ b/db/dca/kadane2_8cpp.html @@ -132,7 +132,7 @@ Functions
- See also
- here for simple number exponentiation algorithm or explaination here.
- Generated by 1.9.1
+
- Generated by 1.9.1
+
- Generated by 1.9.1
+
- is_square() : ordinary_least_squares_regressor.cpp -
- IsPrime() -: primality_test.cpp -
- isPrime() : modular_inverse_fermat_little_theorem.cpp +
- IsPrime() +: primality_test.cpp +
- it_ternary_search() : ternary_search.cpp diff --git a/globals_func_m.html b/globals_func_m.html index ec78c7e50..73acfcea5 100644 --- a/globals_func_m.html +++ b/globals_func_m.html @@ -127,6 +127,7 @@ $(document).ready(function(){initNavTree('globals_func_m.html',''); initResizabl , trie_modern.cpp , trie_tree.cpp , trie_using_hashmap.cpp +, karatsuba_algorithm_for_fast_multiplication.cpp , 0_1_knapsack.cpp , abbreviation.cpp , coin_change_topdown.cpp diff --git a/globals_func_t.html b/globals_func_t.html index bcfe1e6bc..075a37744 100644 --- a/globals_func_t.html +++ b/globals_func_t.html @@ -113,6 +113,7 @@ $(document).ready(function(){initNavTree('globals_func_t.html',''); initResizabl , sparse_table.cpp , trie_tree.cpp , trie_using_hashmap.cpp +, karatsuba_algorithm_for_fast_multiplication.cpp , 0_1_knapsack.cpp , abbreviation.cpp , coin_change_topdown.cpp diff --git a/globals_i.html b/globals_i.html index e0a80ea03..0e3b0d811 100644 --- a/globals_i.html +++ b/globals_i.html @@ -127,14 +127,14 @@ $(document).ready(function(){initNavTree('globals_i.html',''); initResizable();
- is_square() : ordinary_least_squares_regressor.cpp -
- IsPrime() -: primality_test.cpp +
- isPrime() +: modular_inverse_fermat_little_theorem.cpp
- isprime : prime_factorization.cpp -
- isPrime() -: modular_inverse_fermat_little_theorem.cpp +
- IsPrime() +: primality_test.cpp
- it_ternary_search()
: ternary_search.cpp
diff --git a/globals_m.html b/globals_m.html
index cff3f1311..dc05172a4 100644
--- a/globals_m.html
+++ b/globals_m.html
@@ -127,6 +127,7 @@ $(document).ready(function(){initNavTree('globals_m.html',''); initResizable();
, trie_modern.cpp
, trie_tree.cpp
, trie_using_hashmap.cpp
+, karatsuba_algorithm_for_fast_multiplication.cpp
, 0_1_knapsack.cpp
, abbreviation.cpp
, coin_change_topdown.cpp
diff --git a/globals_t.html b/globals_t.html
index a96384888..9a9a89dcd 100644
--- a/globals_t.html
+++ b/globals_t.html
@@ -113,6 +113,7 @@ $(document).ready(function(){initNavTree('globals_t.html',''); initResizable();
, sparse_table.cpp
, trie_tree.cpp
, trie_using_hashmap.cpp
+, karatsuba_algorithm_for_fast_multiplication.cpp
, 0_1_knapsack.cpp
, abbreviation.cpp
, coin_change_topdown.cpp
diff --git a/index.html b/index.html
index 1f62bb9e6..eddd83466 100644
--- a/index.html
+++ b/index.html
@@ -96,10 +96,10 @@ $(document).ready(function(){initNavTree('index.html',''); initResizable(); });
diff --git a/namespacemembers.html b/namespacemembers.html index 76cc12229..0138c4e4e 100644 --- a/namespacemembers.html +++ b/namespacemembers.html @@ -223,12 +223,12 @@ $(document).ready(function(){initNavTree('namespacemembers.html',''); initResiza
- +
Overview
The repository is a collection of open-source implementation of a variety of algorithms implemented in C++ and licensed under MIT License. The algorithms span a variety of topics from computer science, mathematics and statistics, data science, machine learning, engineering, etc.. The implementations and the associated documentation are meant to provide a learning resource for educators and students. Hence, one may find more than one implementation for the same objective but using a different algorithm strategies and optimizations.
-+
Features
- The repository provides implementations of various algorithms in one of the most fundamental general purpose languages - C++. @@ -110,12 +110,12 @@ Features
- Self-checks within programs ensure correct implementations with confidence.
- Modular implementations and OpenSource licensing enable the functions to be utilized conveniently in other applications.
-+
Documentation
Online Documentation is generated from the repository source codes directly. The documentation contains all resources including source code snippets, details on execution of the programs, diagrammatic representation of program flow, and links to external resources where necessary. The documentation also introduces interactive source code with links to documentation for C++ STL library functions used. Click on Files menu to see the list of all the files documented with the code.
Documentation of Algorithms in C++ by The Algorithms Contributors is licensed under CC BY-SA 4.0
-
+
Contributions
As a community developed and maintained repository, we welcome new un-plagiarized quality contributions. Please read our Contribution Guidelines.
- isPossible() : backtracking -
- isSafe() -: backtracking -
- issafe() : backtracking +
- isSafe() +: backtracking + @@ -366,12 +366,12 @@ $(document).ready(function(){initNavTree('namespacemembers.html',''); initResiza
- quadraticProbe() : quadratic_probing -
- quickSort() -: sorting -
- quicksort() : sorting +
- quickSort() +: sorting + diff --git a/namespacemembers_func.html b/namespacemembers_func.html index c2c007a17..0c64c200b 100644 --- a/namespacemembers_func.html +++ b/namespacemembers_func.html @@ -223,12 +223,12 @@ $(document).ready(function(){initNavTree('namespacemembers_func.html',''); initR
- isPossible() : backtracking -
- isSafe() -: backtracking -
- issafe() : backtracking +
- isSafe() +: backtracking + @@ -354,12 +354,12 @@ $(document).ready(function(){initNavTree('namespacemembers_func.html',''); initR
- quadraticProbe() : quadratic_probing -
- quickSort() -: sorting -
- quicksort() : sorting +
- quickSort() +: sorting + diff --git a/namespaces.html b/namespaces.html index 30f1fb490..d06908f98 100644 --- a/namespaces.html +++ b/namespaces.html @@ -140,153 +140,155 @@ $(document).ready(function(){initNavTree('namespaces.html',''); initResizable();
Detailed Description
Iterative version of Preorder, Postorder, and preorder Traversal of the Tree
-
+
Iterative Preorder Traversal of a tree
Create a Stack that will store the Node of Tree. Push the root node into the stack. Save the root into the variabe named as current, and pop and elemnt from the stack. Store the data of current into the result array, and start traversing from it. Push both the child node of the current node into the stack, first right child then left child. Repeat the same set of steps untill the Stack becomes empty. And return the result array as the preorder traversal of a tree.
-
+
Iterative Postorder Traversal of a tree
Create a Stack that will store the Node of Tree. Push the root node into the stack. Save the root into the variabe named as current, and pop and elemnt from the stack. Store the data of current into the result array, and start traversing from it. Push both the child node of the current node into the stack, first left child then right child. Repeat the same set of steps untill the Stack becomes empty. Now reverse the result array and then return it to the calling function as a postorder traversal of a tree.
-
+
Iterative Inorder Traversal of a tree
Create a Stack that will store the Node of Tree. Push the root node into the stack. Save the root into the variabe named as current. Now iterate and take the current to the extreme left of the tree by traversing only to its left. Pop the elemnt from the stack and assign it to the current. Store the data of current into the result array. Repeat the same set of steps until the Stack becomes empty or the current becomes NULL. And return the result array as the inorder traversal of a tree.
Function Documentation
diff --git a/d8/d99/connected__components__with__dsu_8cpp.html b/d8/d99/connected__components__with__dsu_8cpp.html index 20a095355..947a3d0d0 100644 --- a/d8/d99/connected__components__with__dsu_8cpp.html +++ b/d8/d99/connected__components__with__dsu_8cpp.html @@ -156,7 +156,7 @@ uint32_tDetailed Description
The Disjoint union is the technique to find connected component in graph efficiently.
-
+
Algorithm
In Graph, if you have to find out the number of connected components, there are 2 options
Detailed Description
Implementation of Minimum Edit Distance using Dynamic Programing.
Given two strings str1 & str2 and we have to calculate the minimum number of operations (Insert, Remove, Replace) required to convert str1 to str2.
-
+
Algorithm
We will solve this problem using Naive recursion. But as we are approaching with a DP solution. So, we will take a DP array to store the solution of all sub-problems so that we don't have to perform recursion again and again. Now to solve the problem, We can traverse all characters from either right side of the strings or left side. Suppose we will do it from the right side. So, there are two possibilities for every pair of characters being traversed.
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+ Algorithms_in_C++
+ 1.0.0
+
+ Set of algorithms implemented in C++.
+ |
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+Namespaces |
+Functions
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+karatsuba_algorithm_for_fast_multiplication.cpp File Reference
+
+
+
+
+
+
+
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+
+Implementation of the Karatsuba algorithm for fast multiplication +More...
+#include <cassert>+
#include <cstring>+
#include <iostream>+
#include <vector>+
+Include dependency graph for karatsuba_algorithm_for_fast_multiplication.cpp:
+
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++Namespaces | |
| divide_and_conquer | |
| for std::vector | |
| karatsuba_algorithm | |
| Functions for the Karatsuba algorithm for fast multiplication | |
+Functions | |
| std::string | divide_and_conquer::karatsuba_algorithm::addStrings (std::string first, std::string second) |
| Helper function for the main function, that implements Karatsuba's algorithm for fast multiplication. More... | |
| int64_t | divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm (std::string str1, std::string str2) |
| The main function implements Karatsuba's algorithm for fast multiplication. More... | |
| static void | test () |
| Self-test implementations. More... | |
| int | main () |
| Main function. More... | |
Detailed Description
+Implementation of the Karatsuba algorithm for fast multiplication
+Given two strings in binary notation we want to multiply them and return the value Simple approach is to multiply bits one by one which will give the time complexity of around O(n^2). To make it more efficient we will be using Karatsuba' algorithm to find the product which will solve the problem O(nlogn) of time.
+Function Documentation
+ +◆ addStrings()
+ +
+
+
+
+
+
+
| std::string divide_and_conquer::karatsuba_algorithm::addStrings | +( | +std::string | +first, | +
| + | + | std::string | +second | +
| + | ) | ++ |
+
+
+Helper function for the main function, that implements Karatsuba's algorithm for fast multiplication.
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T at(T... args)
T max(T... args)
T size(T... args)
T to_string(T... args)
+Here is the call graph for this function:
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+◆ karatsuba_algorithm()
+ +
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| int64_t divide_and_conquer::karatsuba_algorithm::karatsuba_algorithm | +( | +std::string | +str1, | +
| + | + | std::string | +str2 | +
| + | ) | ++ |
+
+
+The main function implements Karatsuba's algorithm for fast multiplication.
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Functions for the Karatsuba algorithm for fast multiplication
T substr(T... args)
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+◆ main()
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diff --git a/da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.js b/da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.js
new file mode 100644
index 000000000..dd00fedc3
--- /dev/null
+++ b/da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.js
@@ -0,0 +1,7 @@
+var karatsuba__algorithm__for__fast__multiplication_8cpp =
+[
+ [ "addStrings", "da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#a7d1dbae365c7746295d3322e6f7f80b6", null ],
+ [ "karatsuba_algorithm", "da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#a7a890d2f26855ada3b9f1d43aec70a86", null ],
+ [ "main", "da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4", null ],
+ [ "test", "da/dd3/karatsuba__algorithm__for__fast__multiplication_8cpp.html#aa8dca7b867074164d5f45b0f3851269d", null ]
+];
\ No newline at end of file
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diff --git a/db/d16/0__1__knapsack_8cpp.html b/db/d16/0__1__knapsack_8cpp.html
index c0cfe26cd..81c519815 100644
--- a/db/d16/0__1__knapsack_8cpp.html
+++ b/db/d16/0__1__knapsack_8cpp.html
@@ -136,7 +136,7 @@ Functions
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Detailed Description
Implementation of 0-1 Knapsack Problem
Given weights and values of n items, put these items in a knapsack of capacity W to get the maximum total value in the knapsack. In other words, given two integer arrays val[0..n-1] and wt[0..n-1] which represent values and weights associated with n items respectively. Also given an integer W which represents knapsack capacity, find out the maximum value subset of val[] such that sum of the weights of this subset is smaller than or equal to W. You cannot break an item, either pick the complete item or don’t pick it (0-1 property)
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Algorithm
The idea is to consider all subsets of items and calculate the total weight and value of all subsets. Consider the only subsets whose total weight is smaller than W. From all such subsets, pick the maximum value subset.
Detailed Description
Implementation of Kadane Algorithm
Kadane algorithm is used to find the maximum sum subarray in an array and maximum sum subarray problem is the task of finding a contiguous subarray with the largest sum
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Algorithm
The simple idea of the algorithm is to search for all positive contiguous segments of the array and keep track of maximum sum contiguous segment among all positive segments(curr_sum is used for this) Each time we get a positive sum we compare it with max_sum and update max_sum if it is greater than curr_sum
diff --git a/dd/d47/namespacemath.html b/dd/d47/namespacemath.html index 2050416db..17df5d494 100644 --- a/dd/d47/namespacemath.html +++ b/dd/d47/namespacemath.html @@ -146,7 +146,7 @@ FunctionsMathematical algorithms
Given a recurrence relation; evaluate the value of nth term. For e.g., For fibonacci series, recurrence series is f(n) = f(n-1) + f(n-2) where f(0) = 0 and f(1) = 1. Note that the method used only demonstrates recurrence relation with one variable (n), unlike nCr problem, since it has two (n, r)
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Algorithm
This problem can be solved using matrix exponentiation method.
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+ Algorithms_in_C++
+ 1.0.0
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+ Set of algorithms implemented in C++.
+ |
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+
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+divide_and_conquer Namespace Reference
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diff --git a/de/d41/namespacekaratsuba__algorithm.html b/de/d41/namespacekaratsuba__algorithm.html
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+ 1.0.0
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+ Set of algorithms implemented in C++.
+ |
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+karatsuba_algorithm Namespace Reference
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+Functions for the Karatsuba algorithm for fast multiplication +More...
+Detailed Description
+Functions for the Karatsuba algorithm for fast multiplication
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diff --git a/df/d66/vector__cross__product_8cpp.html b/df/d66/vector__cross__product_8cpp.html
index 52b7c4fe9..346554810 100644
--- a/df/d66/vector__cross__product_8cpp.html
+++ b/df/d66/vector__cross__product_8cpp.html
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The direction ratios (DR) are calculated as follows: 1st DR, J: (b * z) - (c * y) 2nd DR, A: -((a * z) - (c * x)) 3rd DR, N: (a * y) - (b * x)
Therefore, the direction ratios of the cross product are: J, A, N The following C++ Program calculates the direction ratios of the cross products of two vector. The program uses a function, cross() for doing so. The direction ratios for the first and the second vector has to be passed one by one seperated by a space character.
Magnitude of a vector is the square root of the sum of the squares of the direction ratios.
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Example:
An example of a running instance of the executable program:
Pass the first Vector: 1 2 3
Pass the second Vector: 4 5 6 The cross product is: -3 6 -3 Magnitude: 7.34847
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+
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+ Algorithms_in_C++
+ 1.0.0
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+ Set of algorithms implemented in C++.
+ |
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+
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+
+
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+
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+
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+divide_and_conquer Directory Reference
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++Files | |
| file | karatsuba_algorithm_for_fast_multiplication.cpp |
| Implementation of the Karatsuba algorithm for fast multiplication | |
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+
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vector vector