feat: Add Travelling Salesman Problem(Naive Approach) (#1590)

* Add Travelling Salesman Problem(Naive Approach)

* Change header and add reference in Travelling Salesman problem

* feat: Add travelling salesman problem(Naive Approach)

* feat: Add travelling salesman problem.

* Update graph/travelling_salesman_problem.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update graph/travelling_salesman_problem.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update graph/travelling_salesman_problem.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update graph/travelling_salesman_problem.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update graph/travelling_salesman_problem.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* Update graph/travelling_salesman_problem.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* updating DIRECTORY.md

* Update graph/travelling_salesman_problem.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* feat: Add Travelling Salesman Problem

* feat: Add Travelling Salesman Problem

* Update graph/travelling_salesman_problem.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* feat: Add travelling salesman problem

* fix: Hopefully fix Ci errors

* Update graph/travelling_salesman_problem.cpp

Co-authored-by: David Leal <halfpacho@gmail.com>

* clang-format and clang-tidy fixes for 56dc1e90

* feat: Add travelling salesman problem.

* feat: Add travelling salesman problem

Co-authored-by: David Leal <halfpacho@gmail.com>
Co-authored-by: github-actions <${GITHUB_ACTOR}@users.noreply.github.com>

DIRECTORY.md

@@ -122,6 +122,7 @@
   * [Prim](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/prim.cpp)
   * [Topological Sort](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/topological_sort.cpp)
   * [Topological Sort By Kahns Algo](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/topological_sort_by_kahns_algo.cpp)
+  * [Travelling Salesman Problem](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graph/travelling_salesman_problem.cpp)
 
 ## Graphics
   * [Spirograph](https://github.com/TheAlgorithms/C-Plus-Plus/blob/master/graphics/spirograph.cpp)

graph/travelling_salesman_problem.cpp

@@ -0,0 +1,111 @@
+/**
+ * @file
+ * @brief [Travelling Salesman Problem]
+ * (https://en.wikipedia.org/wiki/Travelling_salesman_problem) implementation
+ *
+ * @author [Mayank Mamgain](http://github.com/Mayank17M)
+ *
+ * @details
+ * Travelling salesman problem asks:
+ * Given a list of cities and the distances between each pair of cities, what is
+ * the shortest possible route that visits each city exactly once and returns to
+ * the origin city?
+ * TSP can be modeled as an undirected weighted graph, such that cities are the
+ * graph's vertices, paths are the graph's edges, and a path's distance is the
+ * edge's weight. It is a minimization problem starting and finishing at a
+ * specified vertex after having visited each other vertex exactly once.
+ * This is the naive implementation of the problem.
+ */
+
+#include <algorithm>  /// for std::min
+#include <cassert>    /// for assert
+#include <iostream>   /// for IO operations
+#include <limits>     /// for limits of integral types
+#include <vector>     /// for std::vector
+
+/**
+ * @namespace graph
+ * @brief Graph Algorithms
+ */
+namespace graph {
+/**
+ * @brief Function calculates the minimum path distance that will cover all the
+ * cities starting from the source.
+ *
+ * @param cities matrix representation of cities
+ * @param src Point from where salesman is starting
+ * @param V number of vertices in the graph
+ *
+ */
+int TravellingSalesmanProblem(std::vector<std::vector<uint32_t>> *cities,
+                              int32_t src, uint32_t V) {
+    //// vtx stores the vertexs of the graph
+    std::vector<uint32_t> vtx;
+    for (uint32_t i = 0; i < V; i++) {
+        if (i != src) {
+            vtx.push_back(i);
+        }
+    }
+
+    //// store minimum weight Hamiltonian Cycle.
+    int32_t min_path = 2147483647;
+    do {
+        //// store current Path weight(cost)
+        int32_t curr_weight = 0;
+
+        //// compute current path weight
+        int k = src;
+        for (int i : vtx) {
+            curr_weight += (*cities)[k][i];
+            k = i;
+        }
+        curr_weight += (*cities)[k][src];
+
+        //// update minimum
+        min_path = std::min(min_path, curr_weight);
+
+    } while (next_permutation(vtx.begin(), vtx.end()));
+
+    return min_path;
+}
+}  // namespace graph
+
+/**
+ * @brief Self-test implementations
+ * @returns void
+ */
+static void tests() {
+    std::cout << "Initiatinig Predefined Tests..." << std::endl;
+    std::cout << "Initiating Test 1..." << std::endl;
+    std::vector<std::vector<uint32_t>> cities = {
+        {0, 20, 42, 35}, {20, 0, 30, 34}, {42, 30, 0, 12}, {35, 34, 12, 0}};
+    uint32_t V = cities.size();
+    assert(graph::TravellingSalesmanProblem(&cities, 0, V) == 97);
+    std::cout << "1st test passed..." << std::endl;
+
+    std::cout << "Initiating Test 2..." << std::endl;
+    cities = {{0, 5, 10, 15}, {5, 0, 20, 30}, {10, 20, 0, 35}, {15, 30, 35, 0}};
+    V = cities.size();
+    assert(graph::TravellingSalesmanProblem(&cities, 0, V) == 75);
+    std::cout << "2nd test passed..." << std::endl;
+
+    std::cout << "Initiating Test 3..." << std::endl;
+    cities = {
+        {0, 10, 15, 20}, {10, 0, 35, 25}, {15, 35, 0, 30}, {20, 25, 30, 0}};
+    V = cities.size();
+    assert(graph::TravellingSalesmanProblem(&cities, 0, V) == 80);
+    std::cout << "3rd test passed..." << std::endl;
+}
+
+/**
+ * @brief Main function
+ * @returns 0 on exit
+ */
+int main() {
+    tests();  // run self-test implementations
+    std::vector<std::vector<uint32_t>> cities = {
+        {0, 5, 10, 15}, {5, 0, 20, 30}, {10, 20, 0, 35}, {15, 30, 35, 0}};
+    uint32_t V = cities.size();
+    std::cout << graph::TravellingSalesmanProblem(&cities, 0, V) << std::endl;
+    return 0;
+}