Added Hamiltonian_Cycle.cpp

Hamiltonian_Cycle/Hamiltonian_Cycle.cpp

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+/*
+
+Hamiltonian Cycle - Hamiltonian Path in an undirected adjmat is a path
+that visits each vertex exactly once.
+
+A Hamiltonian cycle (or Hamiltonian circuit) is a Hamiltonian Path
+such that there is an edge (in the adjmat) from the last vertex to the
+first vertex of the Hamiltonian Path.
+
+For more information
+Watch "https://www.youtube.com/watch?v=dQr4wZCiJJ4"
+This gives a clear explanation regarding the solution
+
+*/
+
+#include<iostream>
+
+#define NODE 5
+using namespace std;
+
+int path[NODE];
+
+void printcycle() {
+
+    //Prints the first Hamiltonian cycle found
+    cout<<"Hamiltonian Cycle: ";
+
+    for (int i = 0; i < NODE; i++)
+        cout << path[i] << " ";
+
+}
+
+bool isValid(int adjmat[NODE][NODE], int v, int k) {
+
+    if (adjmat [path[k-1]][v] == 0)
+        return false;
+
+    for (int i = 0; i < k; i++)
+        if (path[i] == v)
+            return false;
+
+    return true;
+}
+
+bool cyclepresent(int adjmat[NODE][NODE], int k) {
+
+    if (k == NODE) {
+        if (adjmat[path[k-1]][ path[0] ] == 1 )
+            return true;
+
+        else
+            return false;
+   }
+
+    for (int v = 1; v < NODE; v++) {
+        if (isValid(adjmat, v, k)) {
+            path[k] = v;
+
+            if (cyclepresent (adjmat, k+1) == true)
+                return true;
+
+            path[k] = -1;
+        }
+   }
+    return false;
+}
+
+bool hamilcycle(int adjmat[NODE][NODE]) {
+
+    for (int i = 0; i < NODE; i++)
+        path[i] = -1;
+
+    path[0] = 0;
+
+    if ( cyclepresent(adjmat, 1) == false ) {
+        cout << "Solution does not exist"<<endl;
+        return false;
+    }
+
+    printcycle();
+    return true;
+}
+
+int main() {
+
+
+    cout<<"Enter the connections between the nodes\n";
+    cout<<"Nodes will be marked from 0 to 4\n";
+    cout<<"Enter 0 0 to end the input process\n";
+
+    int x,y;
+    int adjmat[NODE][NODE];
+
+    x=1;
+    y=1;
+    for(int i=0;i<NODE;i++)
+    {
+        for(int j=0;j<NODE;j++)
+        {
+            adjmat[i][j]=0;
+        }
+    }
+    cin>>x>>y;
+    while(x!=0 || y!=0)
+    {
+        adjmat[x][y]=1;
+        adjmat[y][x]=1;
+        cin>>x>>y;
+    }
+
+   hamilcycle(adjmat);
+}
+
+/*
+
+Sample Input
+
+0 1
+0 3
+1 3
+1 4
+1 2
+2 4
+3 4
+0 0
+
+Sample Output
+
+Hamiltonian Cycle: 0 1 2 4 3
+
+*/