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.
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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.
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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.
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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.
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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.
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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.
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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/d3/d78/namespacelinear__algebra.html b/d3/d78/namespacelinear__algebra.html new file mode 100644 index 000000000..01a361423 --- /dev/null +++ b/d3/d78/namespacelinear__algebra.html @@ -0,0 +1,113 @@ + + + + + + + +
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+ Algorithms_in_C++
+ 1.0.0
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+ Set of algorithms implemented in C++.
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+linear_algebra Namespace Reference
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+Linear Algebra algorithms. +More...
+Detailed Description
+Linear Algebra algorithms.
+for io operations for assert for fabs for std::array
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diff --git a/d4/d0f/namespacegram__schmidt.html b/d4/d0f/namespacegram__schmidt.html
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+ Algorithms_in_C++
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+ Set of algorithms implemented in C++.
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+gram_schmidt Namespace Reference
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+Functions for Gram Schmidt Orthogonalisation Process +More...
+Detailed Description
+Functions for Gram Schmidt Orthogonalisation Process
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+
diff --git a/d4/d8d/jarvis__algorithm_8cpp.html b/d4/d8d/jarvis__algorithm_8cpp.html
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@@ -137,7 +137,7 @@ Functions
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- Generated by 1.8.20
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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.
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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 new file mode 100644 index 000000000..fd2297e32 --- /dev/null +++ b/d5/d33/gram__schmidt_8cpp.html @@ -0,0 +1,595 @@ + + + + + + + +
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+ 1.0.0
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+ Set of algorithms implemented in C++.
+ |
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+Namespaces |
+Functions
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+gram_schmidt.cpp File Reference
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+Gram Schmidt Orthogonalisation Process +More...
+#include <iostream>+
#include <cassert>+
#include <cmath>+
#include <array>+
+Include dependency graph for gram_schmidt.cpp:
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++Namespaces | |
| linear_algebra | |
| Linear Algebra algorithms. | |
| gram_schmidt | |
| Functions for Gram Schmidt Orthogonalisation Process | |
+Functions | |
| double | linear_algebra::gram_schmidt::dot_product (const std::array< double, 10 > &x, const std::array< double, 10 > &y, const int &c) |
| double | linear_algebra::gram_schmidt::projection (const std::array< double, 10 > &x, const std::array< double, 10 > &y, const int &c) |
| void | linear_algebra::gram_schmidt::display (const int &r, const int &c, const std::array< std::array< double, 10 >, 20 > &B) |
| void | linear_algebra::gram_schmidt::gram_schmidt (int r, const int &c, const std::array< std::array< double, 10 >, 20 > &A, std::array< std::array< double, 10 >, 20 > B) |
| static void | test () |
| int | main () |
| Main Function. More... | |
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)}
+Have defined maximum dimension of vectors to be 10 and number of vectors taken is 20. Please do not give linearly dependent vectors
+ +Function Documentation
+ +◆ display()
+ +
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| void linear_algebra::gram_schmidt::display | +( | +const int & | +r, | +
| + | + | const int & | +c, | +
| + | + | const std::array< std::array< double, 10 >, 20 > & | +B | +
| + | ) | ++ |
+
+Function to print the orthogonalised vector
+- Parameters
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+r number of vectors c dimenaion of vectors B stores orthogonalised vectors
+
- Returns
- void
◆ dot_product()
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| double linear_algebra::gram_schmidt::dot_product | +( | +const std::array< double, 10 > & | +x, | +
| + | + | const std::array< double, 10 > & | +y, | +
| + | + | const int & | +c | +
| + | ) | ++ |
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+Dot product function. Takes 2 vectors along with their dimension as input and returns the dot product.
- Parameters
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+x vector 1 y vector 2 c dimension of the vectors
+
- Returns
- sum
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+Here is the call graph for this function:
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+◆ gram_schmidt()
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| void linear_algebra::gram_schmidt::gram_schmidt | +( | +int | +r, | +
| + | + | const int & | +c, | +
| + | + | const std::array< std::array< double, 10 >, 20 > & | +A, | +
| + | + | std::array< std::array< double, 10 >, 20 > | +B | +
| + | ) | ++ |
+
+Function for the process of Gram Schimdt Process
- Parameters
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+
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+r number of vectors c dimension of vectors A stores input of given LI vectors B stores orthogonalised vectors
+
- Returns
- void
we check whether appropriate dimensions are given or not.
+First vector is copied as it is.
+array to store projections
+First initialised to zero
+to store previous projected array
+to store the factor by which the previous array will change
+projected array created
+we take the projection with all the previous vector and add them.
+subtract total projection vector from the input vector
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137 all_projection[j] = all_projection[j] + temp[j]; ///we take the projection with all the previous vector and add them.
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+Here is the call graph for this function:
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+◆ main()
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| int main | +( | +void | +) | ++ |
+
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+Main Function.
+- Returns
- 0 on exit
a 2-D array for storing all vectors
+a 2-D array for storing orthogonalised vectors
+storing vectors in array A
+Input of vectors is taken
+To check whether vectors are orthogonal or not
+take make the process numerically stable, upper bound for the dot product take 0.1
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+◆ projection()
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| double linear_algebra::gram_schmidt::projection | +( | +const std::array< double, 10 > & | +x, | +
| + | + | const std::array< double, 10 > & | +y, | +
| + | + | const int & | +c | +
| + | ) | ++ |
+
+Projection Function Takes input of 2 vectors along with their dimension and evaluates their projection in temp
+- Parameters
-
+
+
+x Vector 1 y Vector 2 c dimension of each vector
+
- Returns
- factor
The dot product of two vectors is taken
+The norm of the second vector is taken.
+multiply that factor with every element in a 3rd vector, whose initial values are same as the 2nd vector.
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+◆ test()
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+Test Function. Process has been tested for 3 Sample Inputs
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+T fabs(T... args)
double dot_product(const std::array< double, 10 > &x, const std::array< double, 10 > &y, const int &c)
Definition: gram_schmidt.cpp:53
double projection(const std::array< double, 10 > &x, const std::array< double, 10 > &y, const int &c)
Definition: gram_schmidt.cpp:71
STL class.
void gram_schmidt(int r, const int &c, const std::array< std::array< double, 10 >, 20 > &A, std::array< std::array< double, 10 >, 20 > B)
Definition: gram_schmidt.cpp:107
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diff --git a/d5/d33/gram__schmidt_8cpp.js b/d5/d33/gram__schmidt_8cpp.js
new file mode 100644
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@@ -0,0 +1,9 @@
+var gram__schmidt_8cpp =
+[
+ [ "display", "d5/d33/gram__schmidt_8cpp.html#ab6b70f9680752e9fe2ac4e2cce158c40", null ],
+ [ "dot_product", "d5/d33/gram__schmidt_8cpp.html#aed4d308f46ca1d91e348ca260ec1d2fb", null ],
+ [ "gram_schmidt", "d5/d33/gram__schmidt_8cpp.html#aa31ca28f60c880802462335eedc5d91f", null ],
+ [ "main", "d5/d33/gram__schmidt_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4", null ],
+ [ "projection", "d5/d33/gram__schmidt_8cpp.html#a46e459aff5eafffb5ad9ceb129b4d274", null ],
+ [ "test", "d5/d33/gram__schmidt_8cpp.html#aa8dca7b867074164d5f45b0f3851269d", null ]
+];
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+++ b/d5/d88/md__d_i_r_e_c_t_o_r_y.html
@@ -230,6 +230,11 @@ Hashing
-
+
+
- Generated by 1.8.20
+
+Linear Algebra
+-
+
- Gram Schmidt +
Machine Learning
- Adaline Learning @@ -239,7 +244,7 @@ Machine Learning
- Ordinary Least Squares Regressor
- Vector Ops
+
Math
- Armstrong Number
@@ -280,7 +285,7 @@ Math
+
Numerical Methods
- Bisection Method
@@ -301,7 +306,7 @@ Numerical Methods
+
Operations On Datastructures
- Array Left Rotation
@@ -314,7 +319,7 @@ Operations On Datastructures
+
Others
- Buzz Number
@@ -336,7 +341,7 @@ Others
+
Probability
- Addition Rule
@@ -344,7 +349,7 @@ Probability
+
Range Queries
- Fenwick Tree
@@ -353,7 +358,7 @@ Range Queries
+
Search
- Binary Search
@@ -368,7 +373,7 @@ Search
+
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- Bead Sort
@@ -404,7 +409,7 @@ Sorting
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- Brute Force String Searching
diff --git a/d5/ddb/bogo__sort_8cpp.html b/d5/ddb/bogo__sort_8cpp.html
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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.
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+
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 62aa45de4..9453fbcd9 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.
- Author
- Anmol
diff --git a/d8/d95/vector__ops_8hpp_source.html b/d8/d95/vector__ops_8hpp_source.html
index ec9cdbfe0..d04e832cf 100644
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+++ b/d8/d95/vector__ops_8hpp_source.html
@@ -643,6 +643,7 @@ $(document).ready(function(){initNavTree('d8/d95/vector__ops_8hpp_source.html','
STL class.
DenseLayer & operator=(const DenseLayer &layer)=default
+
Functions for checking whether a graph is bipartite or not.
@@ -660,6 +661,7 @@ $(document).ready(function(){initNavTree('d8/d95/vector__ops_8hpp_source.html','
std::vector< std::valarray< T > > operator/(const std::vector< std::valarray< T >> &A, const T &val)Definition: vector_ops.hpp:365
std::vector< T > operator+(std::vector< T > const &A, std::vector< T > const &B)Definition: ordinary_least_squares_regressor.cpp:204
int nn is the number of vertices on right side of Bipartite GraphDefinition: hopcroft_karp.cpp:69
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bool putProber(const Entry &entry, int key)Definition: linear_probing_hash_table.cpp:98
std::valarray< T > pop_front(const std::valarray< T > &A)Definition: vector_ops.hpp:102
An implementation of hash table using double hashing algorithm.
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static bool isCyclicDFS(Graph const &graph)Definition: cycle_check_directed_graph.cpp:212
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Definition: cycle_check_directed_graph.cpp:158
void evaluate(const std::vector< std::vector< std::valarray< double >>> &X, const std::vector< std::vector< std::valarray< double >>> &Y)Definition: neural_network.cpp:606
@@ -806,6 +809,7 @@ $(document).ready(function(){initNavTree('d8/d95/vector__ops_8hpp_source.html','
T at(T... args)
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Neural Network or Multilayer Perceptron.
int64_t mincoins(const T &n, const std::vector< T > &coins, const int16_t &t, std::vector< T > dp)This implementation is for finding minimum number of coins .Definition: coin_change_topdown.cpp:45
void depth_first_search(const std::vector< std::vector< size_t >> &adj, size_t start)initiates depth first search algorithm.Definition: depth_first_search.cpp:99
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bool searchingProber(const Entry &entry, int key)Definition: double_hash_hash_table.cpp:133
T left(T... args)
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std::shared_ptr< struct Node > nextpointer to the next nodeDefinition: chaining.cpp:23
Definition: lowest_common_ancestor.cpp:145
DenseLayer(const int &neurons, const std::string &activation, const std::vector< std::valarray< double >> &kernel)Definition: neural_network.cpp:183
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int lowest_common_ancestor(int u, int v) constQuery the structure to find the lowest common ancestor. Assumes that the provided numbers are valid i...Definition: lowest_common_ancestor.cpp:164
+Functions for Gram Schmidt Orthogonalisation Process
std::vector< int > pair_uvalue of vertex 'u' ranges from 1 to mDefinition: hopcroft_karp.cpp:75
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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
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index 84f7f874b..266d34dd5 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
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file gram_schmidt.cpp Gram Schmidt Orthogonalisation Process
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index 9e22c7070..d9074262b 100644
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index 438ae0d69..ef0ccb8a5 100644
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, linked_list.cpp
, connected_components.cpp
-, gcd_iterative_euclidean.cpp
+, fibonacci_sum.cpp
+, interpolation_search2.cpp
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+, gcd_iterative_euclidean.cpp
, median_search.cpp
-, gcd_of_n_numbers.cpp
, ternary_search.cpp
-, text_search.cpp
, depth_first_search.cpp
-, gcd_recursive_euclidean.cpp
-, bogo_sort.cpp
+, gcd_of_n_numbers.cpp
+, text_search.cpp
, rabin_karp.cpp
, knuth_morris_pratt.cpp
, horspool.cpp
@@ -123,15 +123,15 @@ $(document).ready(function(){initNavTree('globals_func_m.html',''); initResizabl
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, insertion_sort.cpp
, heap_sort.cpp
-, comb_sort.cpp
-, large_factorial.cpp
-, cycle_sort.cpp
, gnome_sort.cpp
+, bogo_sort.cpp
+, gcd_recursive_euclidean.cpp
+, comb_sort.cpp
+, cycle_sort.cpp
, linkedlist_implentation_usingarray.cpp
, dijkstra.cpp
+, large_factorial.cpp
, lcm_sum.cpp
-, least_common_multiple.cpp
-, interpolation_search2.cpp
, interpolation_search.cpp
, hash_search.cpp
, fibonacci_search.cpp
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, modular_inverse_fermat_little_theorem.cpp
, modular_exponentiation.cpp
-, hamiltons_cycle.cpp
-, magic_number.cpp
, miller_rabin.cpp
+, hamiltons_cycle.cpp
+, least_common_multiple.cpp
+, magic_number.cpp
, caesar_cipher.cpp
, queue_using_two_stacks.cpp
, hopcroft_karp.cpp
, is_graph_bipartite.cpp
, skip_list.cpp
-, fibonacci_sum.cpp
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, fibonacci.cpp
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, kohonen_som_trace.cpp
, kohonen_som_topology.cpp
, adaline_learning.cpp
+, gram_schmidt.cpp
, quadratic_probing_hash_table.cpp
, linear_probing_hash_table.cpp
, double_hash_hash_table.cpp
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index 874162f4f..99011104b 100644
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: pascal_triangle.cpp
-- sieve()
-: sieve_of_eratosthenes.cpp
-
- Sieve()
: primes_up_to_billion.cpp
+- sieve()
+: sieve_of_eratosthenes.cpp
+
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, 0_1_knapsack.cpp
, jumpgame.cpp
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-, neural_network.cpp
, merge_insertion_sort.cpp
-, pancake_sort.cpp
, coin_change_topdown.cpp
-, armstrong_number.cpp
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+, pancake_sort.cpp
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+, armstrong_number.cpp
, wiggle_sort.cpp
-, check_amicable_pair.cpp
, horspool.cpp
, vigenere_cipher.cpp
, cut_rod.cpp
+, check_amicable_pair.cpp
, double_factorial.cpp
-, fibonacci.cpp
, palindrome_partitioning.cpp
+, fibonacci.cpp
, fibonacci_sum.cpp
-, lcm_sum.cpp
, caesar_cipher.cpp
, xor_cipher.cpp
, shortest_common_supersequence.cpp
+, lcm_sum.cpp
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-, sum_of_binomial_coefficient.cpp
, word_break.cpp
+, sum_of_binomial_coefficient.cpp
, sum_of_digits.cpp
-, rungekutta.cpp
, trie_tree.cpp
, jarvis_algorithm.cpp
+, rungekutta.cpp
, smallest_circle.cpp
-, median_search.cpp
, is_graph_bipartite.cpp
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@@ -150,8 +151,9 @@ $(document).ready(function(){initNavTree('globals_func_t.html',''); initResizabl
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-: durand_kerner_roots.cpp
+: brent_method_extrema.cpp
, smallest_circle.cpp
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, hill_cipher.cpp
, hamiltons_cycle.cpp
, adaline_learning.cpp
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, large_factorial.cpp
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@@ -174,8 +175,8 @@ $(document).ready(function(){initNavTree('globals_func_t.html',''); initResizabl
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- test_1()
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-, heavy_light_decomposition.cpp
+: heavy_light_decomposition.cpp
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@@ -185,8 +186,8 @@ $(document).ready(function(){initNavTree('globals_func_t.html',''); initResizabl
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- test_3()
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-, heavy_light_decomposition.cpp
+: heavy_light_decomposition.cpp
+, pigeonhole_sort.cpp
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@@ -216,28 +217,28 @@ $(document).ready(function(){initNavTree('globals_func_t.html',''); initResizabl
: postfix_evaluation.cpp
- test_int()
-: shell_sort2.cpp
-, quick_sort_3.cpp
+: quick_sort_3.cpp
+, shell_sort2.cpp
- test_lamniscate()
: kohonen_som_trace.cpp
- tests()
-: sieve_of_eratosthenes.cpp
-, connected_components.cpp
-, comb_sort.cpp
-, breadth_first_search.cpp
+: magic_number.cpp
, insertion_sort.cpp
-, hopcroft_karp.cpp
+, lowest_common_ancestor.cpp
+, double_factorial.cpp
+, comb_sort.cpp
+, dijkstra.cpp
, least_common_multiple.cpp
, complex_numbers.cpp
-, magic_number.cpp
, check_factorial.cpp
+, breadth_first_search.cpp
, number_of_positive_divisors.cpp
-, double_factorial.cpp
, miller_rabin.cpp
-, lowest_common_ancestor.cpp
-, dijkstra.cpp
+, sieve_of_eratosthenes.cpp
+, hopcroft_karp.cpp
+, connected_components.cpp
- TH()
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-, gcd_of_n_numbers.cpp
, ternary_search.cpp
-, text_search.cpp
, depth_first_search.cpp
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+, text_search.cpp
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-, large_factorial.cpp
, cycle_sort.cpp
-, gnome_sort.cpp
, linkedlist_implentation_usingarray.cpp
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-, lcm_sum.cpp
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-, hamiltons_cycle.cpp
-, magic_number.cpp
-, pancake_sort.cpp
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-, miller_rabin.cpp
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+, hamiltons_cycle.cpp
+, least_common_multiple.cpp
+, merge_sort.cpp
+, pancake_sort.cpp
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, caesar_cipher.cpp
, queue_using_two_stacks.cpp
, hopcroft_karp.cpp
+, miller_rabin.cpp
, modular_exponentiation.cpp
-, modular_inverse_fermat_little_theorem.cpp
, is_graph_bipartite.cpp
-, number_of_positive_divisors.cpp
-, interpolation_search2.cpp
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, primes_up_to_billion.cpp
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+, number_of_positive_divisors.cpp
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-: primes_up_to_billion.cpp
-
- sieve()
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+, sum_of_binomial_coefficient.cpp
, sum_of_digits.cpp
-, rungekutta.cpp
, trie_tree.cpp
, jarvis_algorithm.cpp
+, rungekutta.cpp
, smallest_circle.cpp
-, median_search.cpp
, is_graph_bipartite.cpp
+, median_search.cpp
, bogo_sort.cpp
-, cycle_sort.cpp
- test1()
: hill_cipher.cpp
@@ -151,7 +152,8 @@ $(document).ready(function(){initNavTree('globals_t.html',''); initResizable();
- test2()
: smallest_circle.cpp
-, durand_kerner_roots.cpp
+, brent_method_extrema.cpp
+, qr_eigen_values.cpp
, hill_cipher.cpp
, hamiltons_cycle.cpp
, adaline_learning.cpp
@@ -159,10 +161,9 @@ $(document).ready(function(){initNavTree('globals_t.html',''); initResizable();
, kohonen_som_trace.cpp
, large_factorial.cpp
, sum_of_digits.cpp
-, brent_method_extrema.cpp
+, durand_kerner_roots.cpp
, golden_search_extrema.cpp
, lu_decompose.cpp
-, qr_eigen_values.cpp
- test3()
: hamiltons_cycle.cpp
@@ -174,8 +175,8 @@ $(document).ready(function(){initNavTree('globals_t.html',''); initResizable();
, smallest_circle.cpp
- test_1()
-: pigeonhole_sort.cpp
-, heavy_light_decomposition.cpp
+: heavy_light_decomposition.cpp
+, pigeonhole_sort.cpp
- test_2()
: heavy_light_decomposition.cpp
@@ -185,8 +186,8 @@ $(document).ready(function(){initNavTree('globals_t.html',''); initResizable();
: kohonen_som_topology.cpp
- test_3()
-: heavy_light_decomposition.cpp
-, pigeonhole_sort.cpp
+: pigeonhole_sort.cpp
+, heavy_light_decomposition.cpp
- test_3d_classes()
: kohonen_som_trace.cpp
@@ -216,8 +217,8 @@ $(document).ready(function(){initNavTree('globals_t.html',''); initResizable();
: postfix_evaluation.cpp
- test_int()
-: shell_sort2.cpp
-, quick_sort_3.cpp
+: quick_sort_3.cpp
+, shell_sort2.cpp
- test_lamniscate()
: kohonen_som_trace.cpp
@@ -226,21 +227,21 @@ $(document).ready(function(){initNavTree('globals_t.html',''); initResizable();
: brute_force_string_searching.cpp
- tests()
-: hopcroft_karp.cpp
+: sieve_of_eratosthenes.cpp
+, miller_rabin.cpp
, insertion_sort.cpp
+, complex_numbers.cpp
+, lowest_common_ancestor.cpp
+, dijkstra.cpp
+, connected_components.cpp
, number_of_positive_divisors.cpp
-, sieve_of_eratosthenes.cpp
+, check_factorial.cpp
+, hopcroft_karp.cpp
+, magic_number.cpp
, comb_sort.cpp
, least_common_multiple.cpp
-, dijkstra.cpp
-, check_factorial.cpp
-, miller_rabin.cpp
-, double_factorial.cpp
, breadth_first_search.cpp
-, magic_number.cpp
-, lowest_common_ancestor.cpp
-, connected_components.cpp
-, complex_numbers.cpp
+, double_factorial.cpp
- TH()
: tower_of_hanoi.cpp
diff --git a/index.html b/index.html
index 87b189649..c4eefae87 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 acae6b1b5..a73e89a61 100644
--- a/namespacemembers.html
+++ b/namespacemembers.html
@@ -214,12 +214,12 @@ $(document).ready(function(){initNavTree('namespacemembers.html',''); initResiza
- isPossible()
: backtracking
-- issafe()
-: backtracking
-
- isSafe()
: backtracking
+- issafe()
+: backtracking
+
@@ -341,12 +341,12 @@ $(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 ccb35f241..daa5dc1da 100644
--- a/namespacemembers_func.html
+++ b/namespacemembers_func.html
@@ -214,12 +214,12 @@ $(document).ready(function(){initNavTree('namespacemembers_func.html',''); initR
- isPossible()
: backtracking
-- issafe()
-: backtracking
-
- isSafe()
: backtracking
+- issafe()
+: backtracking
+
@@ -332,12 +332,12 @@ $(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 8b47cd3f6..30437e79a 100644
--- a/namespaces.html
+++ b/namespaces.html
@@ -108,52 +108,54 @@ $(document).ready(function(){initNavTree('namespaces.html',''); initResizable();
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 Ngraph Graph algorithms Nheavy_light_decomposition Heavy light decomposition algorithm Nhorspool Functions for Horspool's algorithm Nis_graph_bipartite Functions for checking whether a graph is bipartite or not 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_probing An implementation of hash table using linear probing algorithm Nlinked_list Functions for singly linked list algorithm Nmachine_learning Machine learning algorithms Nmath For std::vector Nmedian_search Functions for Median search algorithm Nmerge_insertion Combined Intersion-Merge sorting algorithm Nmincoins_topdown Functions for minimum coin exchange problem Nmorse Functions for Morse Code 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 Nneural_network Neural Network or Multilayer Perceptron Nnumerical_methods For io operations Nothers Other algorithms 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 Nrange_queries Algorithms and Data Structures that support range queries and updates Nrat_maze Functions for Ngram_schmidt Functions for Gram Schmidt Orthogonalisation Process Ngraph Graph algorithms Nheavy_light_decomposition Heavy light decomposition algorithm Nhorspool Functions for Horspool's algorithm Nis_graph_bipartite Functions for checking whether a graph is bipartite or not 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 Linear Algebra algorithms Nlinear_probing An implementation of hash table using linear probing algorithm Nlinked_list Functions for singly linked list algorithm Nmachine_learning Machine learning algorithms Nmath For std::vector Nmedian_search Functions for Median search algorithm Nmerge_insertion Combined Intersion-Merge sorting algorithm Nmincoins_topdown Functions for minimum coin exchange problem Nmorse Functions for Morse Code 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 Nneural_network Neural Network or Multilayer Perceptron Nnumerical_methods For io operations Nothers Other algorithms 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 Nrange_queries Algorithms and Data Structures that support range queries and updates Nrat_maze Functions for Rat in a Maze algorithm Nrunge_kutta Functions for Runge Kutta fourth order method Nsearch Search algorithms Nshortest_common_supersequence Shortest Common Super Sequence algorithm Nsorting Sorting algorithms Nsparse_table Range queries using sparse-tables Nspirograph Nstatistics Statistical algorithms Nstd STL namespace Nstrand Functions for Strand Sort algorithm Nstring_search String search algorithms Nstrings Algorithms with strings Nutil_functions Various utility functions used in Neural network Nvigenere Functions for vigenère cipher algorithm Nwiggle_sort Functions for Wiggle Sort algorithm Nword_break Functions for Word Break problem NXOR Functions for XOR cipher algorithm Nrunge_kutta Functions for Runge Kutta fourth order method Nsearch Search algorithms Nshortest_common_supersequence Shortest Common Super Sequence algorithm Nsorting Sorting algorithms Nsparse_table Range queries using sparse-tables Nspirograph Nstatistics Statistical algorithms Nstd STL namespace Nstrand Functions for Strand Sort algorithm Nstring_search String search algorithms Nstrings Algorithms with strings Nutil_functions Various utility functions used in Neural network Nvigenere Functions for vigenère cipher algorithm Nwiggle_sort Functions for Wiggle Sort algorithm Nword_break Functions for Word Break problem NXOR Functions for XOR cipher algorithm
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 62aa45de4..9453fbcd9 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.
- Author
- Anmol diff --git a/d8/d95/vector__ops_8hpp_source.html b/d8/d95/vector__ops_8hpp_source.html index ec9cdbfe0..d04e832cf 100644 --- a/d8/d95/vector__ops_8hpp_source.html +++ b/d8/d95/vector__ops_8hpp_source.html @@ -643,6 +643,7 @@ $(document).ready(function(){initNavTree('d8/d95/vector__ops_8hpp_source.html','
- Author
- Anmol diff --git a/db/dca/kadane2_8cpp.html b/db/dca/kadane2_8cpp.html index 84f7f874b..266d34dd5 100644 --- a/db/dca/kadane2_8cpp.html +++ b/db/dca/kadane2_8cpp.html @@ -132,7 +132,7 @@ Functions
- Generated by 1.8.20
+
STL class.
DenseLayer & operator=(const DenseLayer &layer)=default
Functions for checking whether a graph is bipartite or not.
std::vector< std::valarray< T > > operator/(const std::vector< std::valarray< T >> &A, const T &val)
Definition: vector_ops.hpp:365
std::vector< T > operator+(std::vector< T > const &A, std::vector< T > const &B)
Definition: ordinary_least_squares_regressor.cpp:204
int n
n is the number of vertices on right side of Bipartite Graph
Definition: hopcroft_karp.cpp:69
Linear Algebra algorithms.
bool putProber(const Entry &entry, int key)
Definition: linear_probing_hash_table.cpp:98
std::valarray< T > pop_front(const std::valarray< T > &A)
Definition: vector_ops.hpp:102
An implementation of hash table using double hashing algorithm.
std::ostream & operator<<(std::ostream &out, std::vector< std::vector< T >> const &v)
Definition: ordinary_least_squares_regressor.cpp:22
static bool isCyclicDFS(Graph const &graph)
Definition: cycle_check_directed_graph.cpp:212
double dot_product(const std::array< double, 10 > &x, const std::array< double, 10 > &y, const int &c)
Definition: gram_schmidt.cpp:53
Definition: cycle_check_directed_graph.cpp:158
void evaluate(const std::vector< std::vector< std::valarray< double >>> &X, const std::vector< std::vector< std::valarray< double >>> &Y)
Definition: neural_network.cpp:606
T at(T... args)
double projection(const std::array< double, 10 > &x, const std::array< double, 10 > &y, const int &c)
Definition: gram_schmidt.cpp:71
Neural Network or Multilayer Perceptron.
int64_t mincoins(const T &n, const std::vector< T > &coins, const int16_t &t, std::vector< T > dp)
This implementation is for finding minimum number of coins .
Definition: coin_change_topdown.cpp:45
void depth_first_search(const std::vector< std::vector< size_t >> &adj, size_t start)
initiates depth first search algorithm.
Definition: depth_first_search.cpp:99
bool searchingProber(const Entry &entry, int key)
Definition: double_hash_hash_table.cpp:133
T left(T... args)
std::shared_ptr< struct Node > next
pointer to the next node
Definition: chaining.cpp:23
Definition: lowest_common_ancestor.cpp:145
DenseLayer(const int &neurons, const std::string &activation, const std::vector< std::valarray< double >> &kernel)
Definition: neural_network.cpp:183
void spirograph(std::array< std::pair< double, double >, N > *points, double l, double k, double rot)
Definition: spirograph.cpp:70
int lowest_common_ancestor(int u, int v) const
Query the structure to find the lowest common ancestor. Assumes that the provided numbers are valid i...
Definition: lowest_common_ancestor.cpp:164
Functions for Gram Schmidt Orthogonalisation Process
std::vector< int > pair_u
value of vertex 'u' ranges from 1 to m
Definition: hopcroft_karp.cpp:75
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.
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/dir_000001_000012.html b/dir_000001_000013.html similarity index 100% rename from dir_000001_000012.html rename to dir_000001_000013.html diff --git a/dir_4d6e05837bf820fb089a8a8cdf2f42b7_dep.map b/dir_4d6e05837bf820fb089a8a8cdf2f42b7_dep.map index 86d535c46..2c2b7f203 100644 --- a/dir_4d6e05837bf820fb089a8a8cdf2f42b7_dep.map +++ b/dir_4d6e05837bf820fb089a8a8cdf2f42b7_dep.map @@ -1,5 +1,5 @@ diff --git a/dir_4d6e05837bf820fb089a8a8cdf2f42b7_dep.md5 b/dir_4d6e05837bf820fb089a8a8cdf2f42b7_dep.md5 index 98c945800..d660243df 100644 --- a/dir_4d6e05837bf820fb089a8a8cdf2f42b7_dep.md5 +++ b/dir_4d6e05837bf820fb089a8a8cdf2f42b7_dep.md5 @@ -1 +1 @@ -1799d03d2681e4004485de6ae7a1115d \ No newline at end of file +4281c14c6956d44b875c5aa29de893f8 \ No newline at end of file diff --git a/dir_4d6e05837bf820fb089a8a8cdf2f42b7_dep.svg b/dir_4d6e05837bf820fb089a8a8cdf2f42b7_dep.svg index 79aeab1d4..3333bdee9 100644 --- a/dir_4d6e05837bf820fb089a8a8cdf2f42b7_dep.svg +++ b/dir_4d6e05837bf820fb089a8a8cdf2f42b7_dep.svg @@ -32,7 +32,7 @@
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+|
+ Algorithms_in_C++
+ 1.0.0
+
+ Set of algorithms implemented in C++.
+ |
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+
+linear_algebra Directory Reference
+
+
+
++Files | |
| file | gram_schmidt.cpp |
| Gram Schmidt Orthogonalisation Process | |
+
+
+
diff --git a/dir_8c4128baa09a573ad2b8b8c0061a04c9.js b/dir_8c4128baa09a573ad2b8b8c0061a04c9.js
new file mode 100644
index 000000000..7ceb50018
--- /dev/null
+++ b/dir_8c4128baa09a573ad2b8b8c0061a04c9.js
@@ -0,0 +1,4 @@
+var dir_8c4128baa09a573ad2b8b8c0061a04c9 =
+[
+ [ "gram_schmidt.cpp", "d5/d33/gram__schmidt_8cpp.html", "d5/d33/gram__schmidt_8cpp" ]
+];
\ No newline at end of file
diff --git a/files.html b/files.html
index 9e22c7070..d9074262b 100644
--- a/files.html
+++ b/files.html
@@ -157,132 +157,134 @@ solve-a-rat-in-a-maze-c-java-pytho/">Rat in a Maze algorithm
--
+
+
+
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
+
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.