Create Hamiltonian Cycle

Author: Skillz619

C++/Algorithms/Backtracking/Hamiltonian Cycle

@@ -0,0 +1,114 @@
+#include <bits/stdc++.h> 
+using namespace std; 
+ 
+ 
+#define V 5 
+ 
+void printSolution(int path[]); 
+ 
+bool isSafe(int v, bool graph[V][V], 
+ int path[], int pos) 
+{ 
+ 
+ if (graph [path[pos - 1]][ v ] == 0) 
+ return false; 
+ 
+ for (int i = 0; i < pos; i++) 
+ if (path[i] == v) 
+ return false; 
+ 
+ return true; 
+} 
+ 
+
+bool hamCycleUtil(bool graph[V][V], 
+ int path[], int pos) 
+{ 
+ 
+ if (pos == V) 
+ { 
+ 
+ if (graph[path[pos - 1]][path[0]] == 1) 
+ return true; 
+ else
+ return false; 
+ } 
+ 
+ 
+ for (int v = 1; v < V; v++) 
+ { 
+ // to Hamiltonian Cycle */
+ if (isSafe(v, graph, path, pos)) 
+ { 
+ path[pos] = v; 
+ 
+ /* recur to construct rest of the path */
+ if (hamCycleUtil (graph, path, pos + 1) == true) 
+ return true; 
+ 
+ /* If adding vertex v doesn't lead to a solution, 
+ then remove it */
+ path[pos] = -1; 
+ } 
+ } 
+ 
+ /* If no vertex can be added to 
+ Hamiltonian Cycle constructed so far, 
+ then return false */
+ return false; 
+} 
+ 
+
+bool hamCycle(bool graph[V][V]) 
+{ 
+ int *path = new int[V]; 
+ for (int i = 0; i < V; i++) 
+ path[i] = -1; 
+ 
+ 
+ path[0] = 0; 
+ if (hamCycleUtil(graph, path, 1) == false ) 
+ { 
+ cout << "\nSolution does not exist"; 
+ return false; 
+ } 
+ 
+ printSolution(path); 
+ return true; 
+} 
+ 
+
+void printSolution(int path[]) 
+{ 
+ cout << "Solution Exists:"
+ " Following is one Hamiltonian Cycle \n"; 
+ for (int i = 0; i < V; i++) 
+ cout << path[i] << " "; 
+
+ cout << path[0] << " "; 
+ cout << endl; 
+} 
+ 
+int main() 
+{ 
+ 
+ bool graph1[V][V] = {{0, 1, 0, 1, 0}, 
+ {1, 0, 1, 1, 1}, 
+ {0, 1, 0, 0, 1}, 
+ {1, 1, 0, 0, 1}, 
+ {0, 1, 1, 1, 0}}; 
+ 
+ hamCycle(graph1); 
+ 
+ 
+ bool graph2[V][V] = {{0, 1, 0, 1, 0}, 
+ {1, 0, 1, 1, 1}, 
+ {0, 1, 0, 0, 1}, 
+ {1, 1, 0, 0, 0}, 
+ {0, 1, 1, 0, 0}}; 
+ 
+ 
+ hamCycle(graph2); 
+ 
+ return 0; 
+}