From ac34907793e2a02c50ea7e7688f68652f8ef4c5b Mon Sep 17 00:00:00 2001 From: github-actions <${GITHUB_ACTOR}@users.noreply.github.com> Date: Tue, 24 Jan 2023 19:59:00 +0000 Subject: [PATCH] Documentation for f093837c78c4abaefa372ceaedea14cf06b933e0 --- d2/d90/namespacegreedy__algorithms.html | 119 +++++ ...oruvkas__minimum__spanning__tree_8cpp.html | 505 ++++++++++++++++++ .../boruvkas__minimum__spanning__tree_8cpp.js | 8 + ...311b22324cf09926726e4ce1309af8b_cgraph.map | 4 + ...311b22324cf09926726e4ce1309af8b_cgraph.md5 | 1 + ...311b22324cf09926726e4ce1309af8b_cgraph.svg | 44 ++ ...83bb8ccf42aaf7375a83e91490eda1e_cgraph.map | 4 + ...83bb8ccf42aaf7375a83e91490eda1e_cgraph.md5 | 1 + ...83bb8ccf42aaf7375a83e91490eda1e_cgraph.svg | 36 ++ ...4c615fc66b72e0adbcbcb99aabb1a59_cgraph.map | 6 + ...4c615fc66b72e0adbcbcb99aabb1a59_cgraph.md5 | 1 + ...4c615fc66b72e0adbcbcb99aabb1a59_cgraph.svg | 82 +++ ...5de0f5e70e83164dbd1b4c515565e84_cgraph.map | 3 + ...5de0f5e70e83164dbd1b4c515565e84_cgraph.md5 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| 12 +- navtreeindex2.js | 144 ++--- navtreeindex3.js | 46 +- navtreeindex4.js | 56 +- navtreeindex5.js | 138 ++--- navtreeindex6.js | 88 +-- navtreeindex7.js | 172 +++--- navtreeindex8.js | 116 ++-- navtreeindex9.js | 68 +-- search/all_11.js | 4 +- search/all_14.js | 8 +- search/all_15.js | 233 ++++---- search/all_3.js | 45 +- search/all_7.js | 125 ++--- search/all_8.js | 48 +- search/all_a.js | 16 +- search/all_e.js | 6 +- search/files_2.js | 11 +- search/functions_13.js | 8 +- search/functions_14.js | 169 +++--- search/functions_2.js | 21 +- search/functions_6.js | 142 ++--- search/functions_9.js | 12 +- search/functions_d.js | 2 +- search/namespaces_1.js | 3 +- search/namespaces_5.js | 3 +- 67 files changed, 2774 insertions(+), 1634 deletions(-) create mode 100644 d2/d90/namespacegreedy__algorithms.html create mode 100644 d4/d6c/boruvkas__minimum__spanning__tree_8cpp.html create mode 100644 d4/d6c/boruvkas__minimum__spanning__tree_8cpp.js create mode 100644 d4/d6c/boruvkas__minimum__spanning__tree_8cpp_a2311b22324cf09926726e4ce1309af8b_cgraph.map create mode 100644 d4/d6c/boruvkas__minimum__spanning__tree_8cpp_a2311b22324cf09926726e4ce1309af8b_cgraph.md5 create mode 100644 d4/d6c/boruvkas__minimum__spanning__tree_8cpp_a2311b22324cf09926726e4ce1309af8b_cgraph.svg create mode 100644 d4/d6c/boruvkas__minimum__spanning__tree_8cpp_a483bb8ccf42aaf7375a83e91490eda1e_cgraph.map create mode 100644 d4/d6c/boruvkas__minimum__spanning__tree_8cpp_a483bb8ccf42aaf7375a83e91490eda1e_cgraph.md5 create mode 100644 d4/d6c/boruvkas__minimum__spanning__tree_8cpp_a483bb8ccf42aaf7375a83e91490eda1e_cgraph.svg create mode 100644 d4/d6c/boruvkas__minimum__spanning__tree_8cpp_a94c615fc66b72e0adbcbcb99aabb1a59_cgraph.map create mode 100644 d4/d6c/boruvkas__minimum__spanning__tree_8cpp_a94c615fc66b72e0adbcbcb99aabb1a59_cgraph.md5 create mode 100644 d4/d6c/boruvkas__minimum__spanning__tree_8cpp_a94c615fc66b72e0adbcbcb99aabb1a59_cgraph.svg create mode 100644 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Algorithms_in_C++ 1.0.0 +
+
Set of algorithms implemented in C++.
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greedy_algorithms Namespace Reference
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Greedy Algorithms. +More...

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Detailed Description

+

Greedy Algorithms.

+

for IO operations for std::vector for assert for INT_MAX

+
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Set of algorithms implemented in C++.
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boruvkas_minimum_spanning_tree.cpp File Reference
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+ +

[Borůvkas Algorithm](https://en.wikipedia.org/wiki/Borůvka's_algorithm) to find the Minimum Spanning Tree +More...

+
#include <iostream>
+#include <vector>
+#include <cassert>
+#include <climits>
+
+Include dependency graph for boruvkas_minimum_spanning_tree.cpp:
+
+
+
+
+
+ + + + + + + +

+Namespaces

namespace  greedy_algorithms
 Greedy Algorithms.
 
namespace  boruvkas_minimum_spanning_tree
 Functions for the [Borůvkas Algorithm](https://en.wikipedia.org/wiki/Borůvka's_algorithm) implementation.
 
+ + + + + + + + + + + + + + + + +

+Functions

int greedy_algorithms::boruvkas_minimum_spanning_tree::findParent (std::vector< std::pair< int, int > > parent, const int v)
 Recursively returns the vertex's parent at the root of the tree.
 
std::vector< std::vector< int > > greedy_algorithms::boruvkas_minimum_spanning_tree::boruvkas (std::vector< std::vector< int > > adj)
 the implementation of boruvka's algorithm
 
int greedy_algorithms::boruvkas_minimum_spanning_tree::test_findGraphSum (std::vector< std::vector< int > > adj)
 counts the sum of edges in the given tree
 
static void tests ()
 Self-test implementations.
 
int main ()
 Main function.
 
+

Detailed Description

+

[Borůvkas Algorithm](https://en.wikipedia.org/wiki/Borůvka's_algorithm) to find the Minimum Spanning Tree

+
Author
Jason Nardoni
+

Boruvka's algorithm is a greepy algorithm to find the MST by starting with small trees, and combining them to build bigger ones.

    +
  1. Creates a group for every vertex.
  2. +
  3. looks through each edge of every vertex for the smallest weight. Keeps track of the smallest edge for each of the current groups.
  4. +
  5. Combine each group with the group it shares its smallest edge, adding the smallest edge to the MST.
  6. +
  7. Repeat step 2-3 until all vertices are combined into a single group.
  8. +
+

It assumes that the graph is connected. Non-connected edges can be represented using 0 or INT_MAX

+

Function Documentation

+ +

◆ boruvkas()

+ +
+
+ + + + + + + + +
std::vector< std::vector< int > > greedy_algorithms::boruvkas_minimum_spanning_tree::boruvkas (std::vector< std::vector< int > > adj)
+
+ +

the implementation of boruvka's algorithm

+
Parameters
+ + +
adja graph adjancency matrix stored as 2d vectors.
+
+
+
Returns
the MST as 2d vectors
+
57 {
+
58
+
59 size_t size = adj.size();
+
60 size_t total_groups = size;
+
61
+
62 if (size <= 1) {
+
63 return adj;
+
64 }
+
65
+
66 // Stores the current Minimum Spanning Tree. As groups are combined, they are added to the MST
+
67 std::vector<std::vector<int>> MST(size, std::vector<int>(size, INT_MAX));
+
68 for (int i = 0; i < size; i++) {
+
69 MST[i][i] = 0;
+
70 }
+
71
+
72 // Step 1: Create a group for each vertex
+
73
+
74 // Stores the parent of the vertex and its current depth, both initialized to 0
+ +
76
+
77 for (int i = 0; i < size; i++) {
+
78 parent[i].first = i; // Sets parent of each vertex to itself, depth remains 0
+
79 }
+
80
+
81 // Repeat until all are in a single group
+
82 while (total_groups > 1) {
+
83
+
84 std::vector<std::pair<int,int>> smallest_edge(size, std::make_pair(-1, -1)); //Pairing: start node, end node
+
85
+
86 // Step 2: Look throught each vertex for its smallest edge, only using the right half of the adj matrix
+
87 for (int i = 0; i < size; i++) {
+
88 for (int j = i+1; j < size; j++) {
+
89
+
90 if (adj[i][j] == INT_MAX || adj[i][j] == 0) { // No connection
+
91 continue;
+
92 }
+
93
+
94 // Finds the parents of the start and end points to make sure they arent in the same group
+
95 int parentA = findParent(parent, i);
+
96 int parentB = findParent(parent, j);
+
97
+
98 if (parentA != parentB) {
+
99
+
100 // Grabs the start and end points for the first groups current smallest edge
+
101 int start = smallest_edge[parentA].first;
+
102 int end = smallest_edge[parentA].second;
+
103
+
104 // If there is no current smallest edge, or the new edge is smaller, records the new smallest
+
105 if (start == -1 || adj [i][j] < adj[start][end]) {
+
106 smallest_edge[parentA].first = i;
+
107 smallest_edge[parentA].second = j;
+
108 }
+
109
+
110 // Does the same for the second group
+
111 start = smallest_edge[parentB].first;
+
112 end = smallest_edge[parentB].second;
+
113
+
114 if (start == -1 || adj[j][i] < adj[start][end]) {
+
115 smallest_edge[parentB].first = j;
+
116 smallest_edge[parentB].second = i;
+
117 }
+
118 }
+
119 }
+
120 }
+
121
+
122 // Step 3: Combine the groups based off their smallest edge
+
123
+
124 for (int i = 0; i < size; i++) {
+
125
+
126 // Makes sure the smallest edge exists
+
127 if (smallest_edge[i].first != -1) {
+
128
+
129 // Start and end points for the groups smallest edge
+
130 int start = smallest_edge[i].first;
+
131 int end = smallest_edge[i].second;
+
132
+
133 // Parents of the two groups - A is always itself
+
134 int parentA = i;
+
135 int parentB = findParent(parent, end);
+
136
+
137 // Makes sure the two nodes dont share the same parent. Would happen if the two groups have been
+
138 //merged previously through a common shortest edge
+
139 if (parentA == parentB) {
+
140 continue;
+
141 }
+
142
+
143 // Tries to balance the trees as much as possible as they are merged. The parent of the shallower
+
144 //tree will be pointed to the parent of the deeper tree.
+
145 if (parent[parentA].second < parent[parentB].second) {
+
146 parent[parentB].first = parentA; //New parent
+
147 parent[parentB].second++; //Increase depth
+
148 }
+
149 else {
+
150 parent[parentA].first = parentB;
+
151 parent[parentA].second++;
+
152 }
+
153 // Add the connection to the MST, using both halves of the adj matrix
+
154 MST[start][end] = adj[start][end];
+
155 MST[end][start] = adj[end][start];
+
156 total_groups--; // one fewer group
+
157 }
+
158 }
+
159 }
+
160 return MST;
+
161}
+
int findParent(std::vector< std::pair< int, int > > parent, const int v)
Recursively returns the vertex's parent at the root of the tree.
Definition: boruvkas_minimum_spanning_tree.cpp:44
+
T end(T... args)
+
T make_pair(T... args)
+
T size(T... args)
+ +
+Here is the call graph for this function:
+
+
+
+
+ +
+
+ +

◆ findParent()

+ +
+
+ + + + + + + + + + + + + + + + + + +
int greedy_algorithms::boruvkas_minimum_spanning_tree::findParent (std::vector< std::pair< int, int > > parent,
const int v 
)
+
+ +

Recursively returns the vertex's parent at the root of the tree.

+
Parameters
+ + + +
parentthe array that will be checked
vvertex to find parent of
+
+
+
Returns
the parent of the vertex
+
44 {
+
45 if (parent[v].first != v) {
+
46 parent[v].first = findParent(parent, parent[v].first);
+
47 }
+
48
+
49 return parent[v].first;
+
50}
+
+Here is the call graph for this function:
+
+
+
+
+ +
+
+ +

◆ main()

+ +
+
+ + + + + + + + +
int main (void )
+
+ +

Main function.

+
Returns
0 on exit
+
219 {
+
220 tests(); // run self-test implementations
+
221 return 0;
+
222}
+
static void tests()
Self-test implementations.
Definition: boruvkas_minimum_spanning_tree.cpp:190
+
+Here is the call graph for this function:
+
+
+
+
+ +
+
+ +

◆ test_findGraphSum()

+ +
+
+ + + + + + + + +
int greedy_algorithms::boruvkas_minimum_spanning_tree::test_findGraphSum (std::vector< std::vector< int > > adj)
+
+ +

counts the sum of edges in the given tree

+
Parameters
+ + +
adj2D vector adjacency matrix
+
+
+
Returns
the int size of the tree
+
168 {
+
169
+
170 size_t size = adj.size();
+
171 int sum = 0;
+
172
+
173 //Moves through one side of the adj matrix, counting the sums of each edge
+
174 for (int i = 0; i < size; i++) {
+
175 for (int j = i + 1; j < size; j++) {
+
176 if (adj[i][j] < INT_MAX) {
+
177 sum += adj[i][j];
+
178 }
+
179 }
+
180 }
+
181 return sum;
+
182}
+
T sum(const std::vector< std::valarray< T > > &A)
Definition: vector_ops.hpp:232
+
+Here is the call graph for this function:
+
+
+
+
+ +
+
+ +

◆ tests()

+ +
+
+ + + + + +
+ + + + + + + +
static void tests ()
+
+static
+
+ +

Self-test implementations.

+
Returns
void
+
190 {
+
191 std::cout << "Starting tests...\n\n";
+ +
193 {0, 5, INT_MAX, 3, INT_MAX} ,
+
194 {5, 0, 2, INT_MAX, 5} ,
+
195 {INT_MAX, 2, 0, INT_MAX, 3} ,
+
196 {3, INT_MAX, INT_MAX, 0, INT_MAX} ,
+
197 {INT_MAX, 5, 3, INT_MAX, 0} ,
+
198 };
+ +
200 assert(greedy_algorithms::boruvkas_minimum_spanning_tree::test_findGraphSum(MST) == 13);
+
201 std::cout << "1st test passed!" << std::endl;
+
202
+
203 graph = {
+
204 { 0, 2, 0, 6, 0 },
+
205 { 2, 0, 3, 8, 5 },
+
206 { 0, 3, 0, 0, 7 },
+
207 { 6, 8, 0, 0, 9 },
+
208 { 0, 5, 7, 9, 0 }
+
209 };
+ +
211 assert(greedy_algorithms::boruvkas_minimum_spanning_tree::test_findGraphSum(MST) == 16);
+
212 std::cout << "2nd test passed!" << std::endl;
+
213}
+ +
std::vector< std::vector< int > > boruvkas(std::vector< std::vector< int > > adj)
the implementation of boruvka's algorithm
Definition: boruvkas_minimum_spanning_tree.cpp:57
+
T endl(T... args)
+
Graph Algorithms.
+
+Here is the call graph for this function:
+
+
+
+
+ +
+
+
+
+ + + + diff --git a/d4/d6c/boruvkas__minimum__spanning__tree_8cpp.js b/d4/d6c/boruvkas__minimum__spanning__tree_8cpp.js new file mode 100644 index 000000000..110a32e9e --- /dev/null +++ b/d4/d6c/boruvkas__minimum__spanning__tree_8cpp.js @@ -0,0 +1,8 @@ +var boruvkas__minimum__spanning__tree_8cpp = +[ + [ "boruvkas", "d4/d6c/boruvkas__minimum__spanning__tree_8cpp.html#a94c615fc66b72e0adbcbcb99aabb1a59", null ], + [ "findParent", "d4/d6c/boruvkas__minimum__spanning__tree_8cpp.html#a95de0f5e70e83164dbd1b4c515565e84", null ], + [ "main", "d4/d6c/boruvkas__minimum__spanning__tree_8cpp.html#ae66f6b31b5ad750f1fe042a706a4e3d4", null ], + [ "test_findGraphSum", "d4/d6c/boruvkas__minimum__spanning__tree_8cpp.html#a2311b22324cf09926726e4ce1309af8b", null ], + [ "tests", "d4/d6c/boruvkas__minimum__spanning__tree_8cpp.html#a483bb8ccf42aaf7375a83e91490eda1e", null ] +]; \ No newline at end of file diff --git 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a/d4/d6c/boruvkas__minimum__spanning__tree_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.map b/d4/d6c/boruvkas__minimum__spanning__tree_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.map new file mode 100644 index 000000000..aa55430a8 --- /dev/null +++ b/d4/d6c/boruvkas__minimum__spanning__tree_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.map @@ -0,0 +1,5 @@ + + + + + diff --git a/d4/d6c/boruvkas__minimum__spanning__tree_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.md5 b/d4/d6c/boruvkas__minimum__spanning__tree_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.md5 new file mode 100644 index 000000000..369853fe2 --- /dev/null +++ b/d4/d6c/boruvkas__minimum__spanning__tree_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.md5 @@ -0,0 +1 @@ +013a17a951e53e3d590014cf6fe5eaa9 \ No newline at end of file diff --git a/d4/d6c/boruvkas__minimum__spanning__tree_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg b/d4/d6c/boruvkas__minimum__spanning__tree_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg new file mode 100644 index 000000000..405ff6b1f --- /dev/null +++ b/d4/d6c/boruvkas__minimum__spanning__tree_8cpp_ae66f6b31b5ad750f1fe042a706a4e3d4_cgraph.svg @@ -0,0 +1,51 @@ + + + + + + +main + + +Node1 + + +main + + + + + +Node2 + + +tests + + + + + +Node1->Node2 + + + + + +Node3 + + +std::endl + + + + + +Node2->Node3 + + + + + diff --git a/d8/d64/namespaceboruvkas__minimum__spanning__tree.html b/d8/d64/namespaceboruvkas__minimum__spanning__tree.html new file mode 100644 index 000000000..b2c2afb9b --- /dev/null +++ b/d8/d64/namespaceboruvkas__minimum__spanning__tree.html @@ -0,0 +1,118 @@ + + + + + + + +Algorithms_in_C++: boruvkas_minimum_spanning_tree Namespace Reference + + + + + + + + + + + + + + + +
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Algorithms_in_C++ 1.0.0 +
+
Set of algorithms implemented in C++.
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boruvkas_minimum_spanning_tree Namespace Reference
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Functions for the [Borůvkas Algorithm](https://en.wikipedia.org/wiki/Borůvka's_algorithm) implementation. +More...

+

Detailed Description

+

Functions for the [Borůvkas Algorithm](https://en.wikipedia.org/wiki/Borůvka's_algorithm) implementation.

+
+
+ + + + diff --git a/dc/d5d/boruvkas__minimum__spanning__tree_8cpp__incl.map b/dc/d5d/boruvkas__minimum__spanning__tree_8cpp__incl.map new file mode 100644 index 000000000..58b606656 --- /dev/null +++ b/dc/d5d/boruvkas__minimum__spanning__tree_8cpp__incl.map @@ -0,0 +1,7 @@ + + + + + + + diff --git a/dc/d5d/boruvkas__minimum__spanning__tree_8cpp__incl.md5 b/dc/d5d/boruvkas__minimum__spanning__tree_8cpp__incl.md5 new file mode 100644 index 000000000..13238dbd6 --- /dev/null +++ b/dc/d5d/boruvkas__minimum__spanning__tree_8cpp__incl.md5 @@ -0,0 +1 @@ +9d12a74c1dc8880000ebe84ff8b45fed \ No newline at end of file diff --git a/dc/d5d/boruvkas__minimum__spanning__tree_8cpp__incl.svg b/dc/d5d/boruvkas__minimum__spanning__tree_8cpp__incl.svg new file mode 100644 index 000000000..0099f4aa2 --- /dev/null +++ b/dc/d5d/boruvkas__minimum__spanning__tree_8cpp__incl.svg @@ -0,0 +1,82 @@ + + + + + + +greedy_algorithms/boruvkas_minimum_spanning_tree.cpp + + +Node1 + + +greedy_algorithms/boruvkas +_minimum_spanning_tree.cpp + + + + + +Node2 + + +iostream + + + + + +Node1->Node2 + + + + + +Node3 + + +vector + + + + + +Node1->Node3 + + + + + +Node4 + + +cassert + + + + + +Node1->Node4 + + + + + +Node5 + + +climits + + + + + +Node1->Node5 + + + + + diff --git a/dir_0eaa691bd54ab0922ca7f50599de6d22.html b/dir_0eaa691bd54ab0922ca7f50599de6d22.html index 0bc7f7280..07680ccb7 100644 --- a/dir_0eaa691bd54ab0922ca7f50599de6d22.html +++ b/dir_0eaa691bd54ab0922ca7f50599de6d22.html @@ -103,6 +103,9 @@ $(document).ready(function(){initNavTree('dir_0eaa691bd54ab0922ca7f50599de6d22.h + + + diff --git a/dir_0eaa691bd54ab0922ca7f50599de6d22.js b/dir_0eaa691bd54ab0922ca7f50599de6d22.js index a4ccbbdee..93bbe0324 100644 --- a/dir_0eaa691bd54ab0922ca7f50599de6d22.js +++ b/dir_0eaa691bd54ab0922ca7f50599de6d22.js @@ -1,4 +1,5 @@ var dir_0eaa691bd54ab0922ca7f50599de6d22 = [ + [ "boruvkas_minimum_spanning_tree.cpp", "d4/d6c/boruvkas__minimum__spanning__tree_8cpp.html", "d4/d6c/boruvkas__minimum__spanning__tree_8cpp" ], [ "jumpgame.cpp", "df/d64/jumpgame_8cpp.html", "df/d64/jumpgame_8cpp" ] ]; \ No newline at end of file diff --git a/files.html b/files.html index c0e3b0809..526cea670 100644 --- a/files.html +++ b/files.html @@ -196,7 +196,8 @@ solve-a-rat-in-a-maze-c-java-pytho/" target="_blank">Rat in a Maze algorithm - + + diff --git a/globals_func_m.html b/globals_func_m.html index dd1c1361a..f043ce718 100644 --- a/globals_func_m.html +++ b/globals_func_m.html @@ -100,7 +100,7 @@ $(document).ready(function(){initNavTree('globals_func_m.html',''); initResizabl  

- m -

diff --git a/globals_m.html b/globals_m.html index c4da5776c..ee9603c54 100644 --- a/globals_m.html +++ b/globals_m.html @@ -100,7 +100,7 @@ $(document).ready(function(){initNavTree('globals_m.html',''); initResizable();
Here is a list of all documented file members with links to the documentation:

- m -

- - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + + +

Files

file  boruvkas_minimum_spanning_tree.cpp
 [Borůvkas Algorithm](https://en.wikipedia.org/wiki/Borůvka's_algorithm) to find the Minimum Spanning Tree
 
file  jumpgame.cpp
 Implementation of an algorithm to solve the jumping game problem.
 
  graphics
  greedy_algorithms
  hashing
 Nbidirectional_dijkstraFunctions for [Bidirectional Dijkstra Shortest Path] (https://www.coursera.org/learn/algorithms-on-graphs/lecture/7ml18/bidirectional-dijkstra) algorithm
 NbinomialFunctions for Binomial coefficients implementation
 Nbit_manipulationFor IO operations
 NcaesarFunctions for Caesar cipher algorithm
 NciphersAlgorithms for encryption and decryption
 Ncircular_linked_listFunctions for the Circular Linked List implementation
 Ncount_bits_flipFunctions for the count bits flip implementation
 Ncount_of_set_bitsFunctions for the count sets bits implementation
 Ncount_of_trailing_ciphers_in_factorial_nFunctions for the Count the number of ciphers in n! implementation
 Ncut_rodImplementation of cutting a rod problem
 Ncycle_detectionFunctions for the Floyd's Cycle Detection algorithm
 Ncycle_sortFunctions for Cycle sort algorithm
 Ndata_structuresFor IO operations
 Ndepth_first_searchFunctions for Depth First Search algorithm
 Ndisjoint_unionFunctions for Disjoint union implementation
 Ndivide_and_conquerFor std::vector
 Ndnf_sortFunctions for the DNF sort implementation
 Ndouble_hashingAn implementation of hash table using double hashing algorithm
 NdpFor std::vector
 Ndynamic_programmingDynamic Programming algorithms
 Nfalse_positionFunctions for [False Position] (https://en.wikipedia.org/wiki/Regula_falsi) method
 Nfibonacci_sumFunctions for the sum of the Fibonacci Sequence: \(\mathrm{F}(n) + +
 Nboruvkas_minimum_spanning_treeFunctions for the [Borůvkas Algorithm](https://en.wikipedia.org/wiki/Borůvka's_algorithm) implementation
 NcaesarFunctions for Caesar cipher algorithm
 NciphersAlgorithms for encryption and decryption
 Ncircular_linked_listFunctions for the Circular Linked List implementation
 Ncount_bits_flipFunctions for the count bits flip implementation
 Ncount_of_set_bitsFunctions for the count sets bits implementation
 Ncount_of_trailing_ciphers_in_factorial_nFunctions for the Count the number of ciphers in n! implementation
 Ncut_rodImplementation of cutting a rod problem
 Ncycle_detectionFunctions for the Floyd's Cycle Detection algorithm
 Ncycle_sortFunctions for Cycle sort algorithm
 Ndata_structuresFor IO operations
 Ndepth_first_searchFunctions for Depth First Search algorithm
 Ndisjoint_unionFunctions for Disjoint union implementation
 Ndivide_and_conquerFor std::vector
 Ndnf_sortFunctions for the DNF sort implementation
 Ndouble_hashingAn implementation of hash table using double hashing algorithm
 NdpFor std::vector
 Ndynamic_programmingDynamic Programming algorithms
 Nfalse_positionFunctions for [False Position] (https://en.wikipedia.org/wiki/Regula_falsi) method
 Nfibonacci_sumFunctions for the sum of the Fibonacci Sequence: \(\mathrm{F}(n) + \mathrm{F}(n+1) + .. + \mathrm{F}(m)\)
 Nfind_non_repeating_integerFunctions to find the non repeating integer in an array of repeating integers. Single Number
 Ngeometric_distFunctions for the Geometric Distribution algorithm implementation
 NgeometryFor std::vector
 Ngram_schmidtFunctions for Gram Schmidt Orthogonalisation Process
 NgraphGraph Algorithms
 Ngraph_coloringFunctions for the Graph Coloring algorithm,
 Nground_to_ground_projectile_motionFunctions for the Ground to ground projectile motion equation
 Nhamming_distanceFunctions for Hamming distance implementation
 NhashingHashing algorithms
 Nheavy_light_decompositionHeavy light decomposition algorithm
 NhorspoolFunctions for Horspool's algorithm
 Nhouse_robberFunctions for the House Robber algorithm
 Ninorder_successor_of_bstFunctions for the Inorder successor of a binary search tree implementation
 Ninterpolation_searchFunctions for the Recursive version of Inorder, Preorder, and Postorder Traversal of the Tree algorithm implementation
 NinversionFunctions for counting inversions using Merge Sort algorithm
 Nis_graph_bipartiteFunctions for checking whether a graph is bipartite or not
 Niterative_tree_traversalsFunctions for the Traversal of the Tree algorithm
 NjarvisFunctions for Jarvis’s algorithm
 NkadaneFunctions for Kadane algorithm
 Nkaratsuba_algorithmFunctions for the Karatsuba algorithm for fast multiplication implementation
 NKnapsackImplementation of 0-1 Knapsack problem
 Nknight_tourFunctions for the Knight's tour algorithm
 NlayersThis namespace contains layers used in MLP
 Nlinear_probingAn implementation of hash table using linear probing algorithm
 Nlinear_recurrence_matrixFunctions for Linear Recurrence Matrix implementation
 Nlinked_listFunctions for singly linked list algorithm
 Nlist_arrayFunctions for Dynamic Array algorithm
 Nlru_cacheImplementation of the LRU caching algorithm
 Nmachine_learningA* search algorithm
 Nmagic_sequenceFunctions for the Magic sequence implementation
 NmanacherFunctions for Manacher's Algorithm implementation
 NmathFor IO operations
 NMD5Functions for the MD5 algorithm implementation
 Nmedian_searchFunctions for Median search algorithm
 Nmerge_insertionCombined Intersion-Merge sorting algorithm
 Nmidpoint_ruleFunctions for the Midpoint Integral method implementation
 Nmincoins_topdownFunctions for minimum coin exchange problem
 NMinimumImplementation of Minimum Edit Distance algorithm
 Nmodular_divisionFunctions for Modular Division implementation
 Nmonte_carloFunctions for the Monte Carlo Integration implementation
 NmorseFunctions for [Morse Code] (https://en.wikipedia.org/wiki/Morse_code)
 Nn_bonacciFunctions for the N-bonacci implementation
 Nn_queensFunctions for Eight Queens puzzle
 Nn_queens_all_solutionsFunctions for the Eight Queens puzzle with all solutions
 Nn_queens_optimizedFunctions for Eight Queens puzzle optimized
 Nncr_modulo_pFunctions for nCr modulo p implementation
 Nneural_networkNeural Network or Multilayer Perceptron
 Nnumerical_methodsFor assert
 Noperations_on_datastructuresFor std::vector
 NothersFor vector
 Npalindrome_partitioningFunctions for Palindrome Partitioning algorithm
 Npancake_sortFunctions for Pancake sort algorithm
 NphysicsFor IO operations
 Npostfix_expressionFunctions for Postfix Expression algorithm
 Nprefix_sum_arrayRange sum queries using prefix-sum-array
 NprobabilityProbability algorithms
 Nqr_algorithmFunctions to compute QR decomposition of any rectangular matrix
 Nquadratic_probingAn implementation of hash table using quadratic probing algorithm
 Nqueue_using_arrayFunctions for [Queue using Array] (https://www.geeksforgeeks.org/array-implementation-of-queue-simple/) implementation
 Nquick_sortFunctions for the Quick sort implementation in C++
 Nradix_sortFunctions for Radix sort algorithm
 Nrandom_pivot_quick_sortFunctions for the Random Pivot Quick Sort implementation
 Nrange_queriesAlgorithms and Data Structures that support range queries and updates
 Nrat_mazeFunctions for  Nfind_non_repeating_integerFunctions to find the non repeating integer in an array of repeating integers. Single Number
 Ngeometric_distFunctions for the Geometric Distribution algorithm implementation
 NgeometryFor std::vector
 Ngram_schmidtFunctions for Gram Schmidt Orthogonalisation Process
 NgraphGraph Algorithms
 Ngraph_coloringFunctions for the Graph Coloring algorithm,
 Ngreedy_algorithmsGreedy Algorithms
 Nground_to_ground_projectile_motionFunctions for the Ground to ground projectile motion equation
 Nhamming_distanceFunctions for Hamming distance implementation
 NhashingHashing algorithms
 Nheavy_light_decompositionHeavy light decomposition algorithm
 NhorspoolFunctions for Horspool's algorithm
 Nhouse_robberFunctions for the House Robber algorithm
 Ninorder_successor_of_bstFunctions for the Inorder successor of a binary search tree implementation
 Ninterpolation_searchFunctions for the Recursive version of Inorder, Preorder, and Postorder Traversal of the Tree algorithm implementation
 NinversionFunctions for counting inversions using Merge Sort algorithm
 Nis_graph_bipartiteFunctions for checking whether a graph is bipartite or not
 Niterative_tree_traversalsFunctions for the Traversal of the Tree algorithm
 NjarvisFunctions for Jarvis’s algorithm
 NkadaneFunctions for Kadane algorithm
 Nkaratsuba_algorithmFunctions for the Karatsuba algorithm for fast multiplication implementation
 NKnapsackImplementation of 0-1 Knapsack problem
 Nknight_tourFunctions for the Knight's tour algorithm
 NlayersThis namespace contains layers used in MLP
 Nlinear_probingAn implementation of hash table using linear probing algorithm
 Nlinear_recurrence_matrixFunctions for Linear Recurrence Matrix implementation
 Nlinked_listFunctions for singly linked list algorithm
 Nlist_arrayFunctions for Dynamic Array algorithm
 Nlru_cacheImplementation of the LRU caching algorithm
 Nmachine_learningA* search algorithm
 Nmagic_sequenceFunctions for the Magic sequence implementation
 NmanacherFunctions for Manacher's Algorithm implementation
 NmathFor IO operations
 NMD5Functions for the MD5 algorithm implementation
 Nmedian_searchFunctions for Median search algorithm
 Nmerge_insertionCombined Intersion-Merge sorting algorithm
 Nmidpoint_ruleFunctions for the Midpoint Integral method implementation
 Nmincoins_topdownFunctions for minimum coin exchange problem
 NMinimumImplementation of Minimum Edit Distance algorithm
 Nmodular_divisionFunctions for Modular Division implementation
 Nmonte_carloFunctions for the Monte Carlo Integration implementation
 NmorseFunctions for [Morse Code] (https://en.wikipedia.org/wiki/Morse_code)
 Nn_bonacciFunctions for the N-bonacci implementation
 Nn_queensFunctions for Eight Queens puzzle
 Nn_queens_all_solutionsFunctions for the Eight Queens puzzle with all solutions
 Nn_queens_optimizedFunctions for Eight Queens puzzle optimized
 Nncr_modulo_pFunctions for nCr modulo p implementation
 Nneural_networkNeural Network or Multilayer Perceptron
 Nnumerical_methodsFor assert
 Noperations_on_datastructuresFor std::vector
 NothersFor vector
 Npalindrome_partitioningFunctions for Palindrome Partitioning algorithm
 Npancake_sortFunctions for Pancake sort algorithm
 NphysicsFor IO operations
 Npostfix_expressionFunctions for Postfix Expression algorithm
 Nprefix_sum_arrayRange sum queries using prefix-sum-array
 NprobabilityProbability algorithms
 Nqr_algorithmFunctions to compute QR decomposition of any rectangular matrix
 Nquadratic_probingAn implementation of hash table using quadratic probing algorithm
 Nqueue_using_arrayFunctions for [Queue using Array] (https://www.geeksforgeeks.org/array-implementation-of-queue-simple/) implementation
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 Ntree_234Functions for 2–3–4 tree
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 NvigenereFunctions for vigenère cipher algorithm
 Nwave_sortFunctions for the Wave sort implementation
 Nwiggle_sortFunctions for Wiggle Sort algorithm
 Nwildcard_matchingFunctions for the Wildcard Matching problem
 Nwindowed_medianFunctions for the Windowed Median algorithm implementation
 Nword_breakFunctions for Word Break problem
 NXORFunctions for XOR cipher algorithm
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