Add Travelling Salesman Problem(Naive Approach)

graph/travelling_salesman_problem.cpp

@@ -0,0 +1,45 @@
+// Travelling salesman problem states that:
+// 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?
+// This is the naive approach to solve this problem.
+
+#include <bits/stdc++.h>
+using namespace std;
+
+int TravellingSalesmanProblem(vector<vector<int>> cities, int src, int V) {
+    vector<int> vtx;
+    for (int i = 0; i < V; i++) {
+        if (i != src) {
+            vtx.push_back(i);
+        }
+    }
+
+    // store minimum weight Hamiltonian Cycle.
+    int min_path = INT_MAX;
+    do {
+        // store current Path weight(cost)
+        int curr_weight = 0;
+
+        // compute current path weight
+        int k = src;
+        for (int i = 0; i < vtx.size(); i++) {
+            curr_weight += cities[k][vtx[i]];
+            k = vtx[i];
+        }
+        curr_weight += cities[k][src];
+
+        // update minimum
+        min_path = min(min_path, curr_weight);
+
+    } while (next_permutation(vtx.begin(), vtx.end()));
+
+    return min_path;
+}
+
+int main() {
+    vector<vector<int>> cities = {
+        {0, 20, 42, 35}, {20, 0, 30, 34}, {42, 30, 0, 12}, {35, 34, 12, 0}};
+    int V = cities.size();
+    cout << TravellingSalesmanProblem(cities, 0, V);
+}