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/d4/d8d/jarvis__algorithm_8cpp.html b/d4/d8d/jarvis__algorithm_8cpp.html index 8b3655039..08f8ae1fb 100644 --- a/d4/d8d/jarvis__algorithm_8cpp.html +++ b/d4/d8d/jarvis__algorithm_8cpp.html @@ -137,7 +137,7 @@ FunctionsDetailed 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 index fd2297e32..3bfc24c7e 100644 --- a/d5/d33/gram__schmidt_8cpp.html +++ b/d5/d33/gram__schmidt_8cpp.html @@ -141,7 +141,7 @@ Functions
Takes the input of Linearly Independent Vectors, returns vectors orthogonal to each other.
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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/d3c/namespacedata__structures.html b/d5/d3c/namespacedata__structures.html index 620a3ea12..de98f9aa3 100644 --- a/d5/d3c/namespacedata__structures.html +++ b/d5/d3c/namespacedata__structures.html @@ -124,7 +124,8 @@ constexpr floatDetailed Description
Data Structures algorithms.
-Data-structure algorithms.
+Data-structure algorithms.
+Algorithms with data structures.
+
Backtracking
- Graph Coloring
@@ -106,7 +106,7 @@ Backtracking
- Rat Maze
- Sudoku Solve
-
+
Ciphers
- Caesar Cipher
@@ -115,7 +115,7 @@ Ciphers
Vigenere Cipher
Xor Cipher
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+
Data Structures
- Avltree
@@ -151,7 +151,7 @@ Data Structures
Trie Modern
Trie Tree
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+
Dynamic Programming
- 0 1 Knapsack
@@ -178,13 +178,13 @@ Dynamic Programming
Tree Height
Word Break
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+
Geometry
-
+
Graph
- Breadth First Search
@@ -206,12 +206,12 @@ Graph
Topological Sort
Topological Sort By Kahns Algo
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+
Graphics
-
+
Greedy Algorithms
- Dijkstra
@@ -221,7 +221,7 @@ Greedy Algorithms
Kruskals Minimum Spanning Tree
Prims Minimum Spanning Tree
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+
Hashing
- Chaining
@@ -229,12 +229,12 @@ Hashing
Linear Probing Hash Table
Quadratic Probing Hash Table
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+
Linear Algebra
-
+
Machine Learning
- Adaline Learning
@@ -244,7 +244,7 @@ Machine Learning
Ordinary Least Squares Regressor
Vector Ops
-
+
Math
- Armstrong Number
@@ -285,7 +285,7 @@ Math
Sum Of Binomial Coefficient
Sum Of Digits
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+
Numerical Methods
- Bisection Method
@@ -306,7 +306,7 @@ Numerical Methods
Rungekutta
Successive Approximation
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+
Operations On Datastructures
- Array Left Rotation
@@ -319,7 +319,7 @@ Operations On Datastructures
Selectionsortlinkedlist
Union Of 2 Arrays
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+
Others
- Buzz Number
@@ -341,7 +341,7 @@ Others
Tower Of Hanoi
Vector Important Functions
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+
Probability
- Addition Rule
@@ -349,7 +349,7 @@ Probability
Binomial Dist
Poisson Dist
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+
Range Queries
- Fenwick Tree
@@ -358,7 +358,7 @@ Range Queries
Segtree
Sparse Table
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+
Search
- Binary Search
@@ -373,7 +373,7 @@ Search
Ternary Search
Text Search
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+
Sorting
- Bead Sort
@@ -410,7 +410,7 @@ Sorting
Tim Sort
Wiggle Sort
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+
Strings
- Brute Force String Searching
diff --git a/d5/ddb/bogo__sort_8cpp.html b/d5/ddb/bogo__sort_8cpp.html
index 91a3878d5..d7566a722 100644
--- a/d5/ddb/bogo__sort_8cpp.html
+++ b/d5/ddb/bogo__sort_8cpp.html
@@ -136,7 +136,7 @@ Functions
Backtracking
- Graph Coloring @@ -106,7 +106,7 @@ Backtracking
- Rat Maze
- Sudoku Solve
+
Ciphers
- Caesar Cipher
@@ -115,7 +115,7 @@ Ciphers
+
Data Structures
- Avltree
@@ -151,7 +151,7 @@ Data Structures
+
Dynamic Programming
- 0 1 Knapsack
@@ -178,13 +178,13 @@ Dynamic Programming
+
Geometry
-
+
Graph
- Breadth First Search
@@ -206,12 +206,12 @@ Graph
Graph
- Breadth First Search @@ -206,12 +206,12 @@ Graph
+
Graphics
-
+
Greedy Algorithms
- Dijkstra
@@ -221,7 +221,7 @@ Greedy Algorithms
Greedy Algorithms
- Dijkstra @@ -221,7 +221,7 @@ Greedy Algorithms
+
Hashing
- Chaining
@@ -229,12 +229,12 @@ Hashing
+
Linear Algebra
-
+
Machine Learning
- Adaline Learning
@@ -244,7 +244,7 @@ Machine Learning
Machine Learning
- Adaline Learning @@ -244,7 +244,7 @@ Machine Learning
+
Math
- Armstrong Number
@@ -285,7 +285,7 @@ Math
+
Numerical Methods
- Bisection Method
@@ -306,7 +306,7 @@ Numerical Methods
+
Operations On Datastructures
- Array Left Rotation
@@ -319,7 +319,7 @@ Operations On Datastructures
+
Others
- Buzz Number
@@ -341,7 +341,7 @@ Others
+
Probability
- Addition Rule
@@ -349,7 +349,7 @@ Probability
+
Range Queries
- Fenwick Tree
@@ -358,7 +358,7 @@ Range Queries
+
Search
- Binary Search
@@ -373,7 +373,7 @@ Search
+
Sorting
- Bead Sort
@@ -410,7 +410,7 @@ Sorting
+
Strings
- Brute Force String Searching
diff --git a/d5/ddb/bogo__sort_8cpp.html b/d5/ddb/bogo__sort_8cpp.html
index 91a3878d5..d7566a722 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.
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Algorithm
Shuffle the array untill array is sorted.
diff --git a/d6/d04/classdata__structures_1_1queue__using__array_1_1_queue___array.html b/d6/d04/classdata__structures_1_1queue__using__array_1_1_queue___array.html new file mode 100644 index 000000000..c17b251e0 --- /dev/null +++ b/d6/d04/classdata__structures_1_1queue__using__array_1_1_queue___array.html @@ -0,0 +1,279 @@ + + + + + + + +|
+ Algorithms_in_C++
+ 1.0.0
+
+ Set of algorithms implemented in C++.
+ |
+
Queue_Array class containing the main data and also index of head and tail of the array. + More...
++Public Member Functions | |
| void | enqueue (const int16_t &) |
| Add element to the first of the queue. More... | |
| int | dequeue () |
| Delete element from back of the queue. More... | |
| void | display () const |
| Show all saved data. More... | |
+Private Attributes | |
| +int8_t | front {-1} |
| Index of head of the array. | |
| +int8_t | rear {-1} |
| Index of tail of the array. | |
| +std::array< int16_t, max_size > | arr |
| All stored data. | |
Detailed Description
+Queue_Array class containing the main data and also index of head and tail of the array.
+Member Function Documentation
+ +◆ dequeue()
+ +| int data_structures::queue_using_array::Queue_Array::dequeue | +( | +) | ++ |
Delete element from back of the queue.
+Remove element that is located at the first of the queue.
+- Returns
- data that is deleted if queue is not empty
◆ display()
+ +| void data_structures::queue_using_array::Queue_Array::display | +( | +) | +const | +
Show all saved data.
+Utility function to show all elements in the queue.
+◆ enqueue()
+ +| void data_structures::queue_using_array::Queue_Array::enqueue | +( | +const int16_t & | +ele | ) | ++ |
Add element to the first of the queue.
+Adds new element to the end of the queue.
+- Parameters
-
+
+
+ele to be added to the end of the queue
+
The documentation for this class was generated from the following file:
-
+
- data_structures/queue_using_array.cpp +
-
+
+
- Generated by
1.8.20
+
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.
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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.
|
+ Algorithms_in_C++
+ 1.0.0
+
+ Set of algorithms implemented in C++.
+ |
+
Implementation of Linear Queue using array. +More...
+#include <iostream>+
#include <array>+
+Classes | |
| class | data_structures::queue_using_array::Queue_Array |
| Queue_Array class containing the main data and also index of head and tail of the array. More... | |
+Namespaces | |
| data_structures | |
| Data Structures algorithms. | |
| queue_using_array | |
| Functions for Queue using Array implementation. | |
+Functions | |
| int | main () |
| Main function. More... | |
+Variables | |
| constexpr uint16_t | max_size {10} |
| for std::array More... | |
Detailed Description
+Implementation of Linear Queue using array.
+The Linear Queue is a data structure used for holding a sequence of values, which can be added to the end line (enqueue), removed from head of line (dequeue) and displayed.
++Algorithm
+Values can be added by increasing the rear variable by 1 (which points to the end of the array), then assigning new value to rear's element of the array.
Values can be removed by increasing the front variable by 1 (which points to the first of the array), so it cannot reached any more.
Function Documentation
+ +◆ main()
+ +| int main | +( | +void | +) | ++ |
Main function.
+Allows the user to add and delete values from the queue. Also allows user to display values in the queue.
- Returns
- 0 on exit
Variable Documentation
+ +◆ max_size
+ +
+
|
+ +constexpr | +
for std::array
+for io operations Maximum size of the queue
+ +-
+
+
- Generated by 1.8.20
+
-Public Member Functions | |
| -void | enqueue (int) |
| -int | dequeue () |
| -void | display () |
-Public Attributes | |
| -int * | arr = new int[size] |
-Private Attributes | |
| -int | front |
| -int | rear |
| -int | size |
The documentation for this class was generated from the following file:
-
-
- data_structures/queue_using_array.cpp -
Functions for Queue using Array implementation. +More...
+Detailed Description
+Functions for Queue using Array implementation.
+
