Create hamiltonian_cycle.cpp

code/graph_algorithms/src/hamiltonian_cycle/hamiltonian_cycles.cpp

@@ -0,0 +1,130 @@
+#include <iostream>
+#include <fstream>
+#include <string>
+#include <vector>
+#include <math.h>
+
+using namespace std;
+
+/**
+    prints all the hamiltonian paths and cycles of the graph
+**/
+void printPathsAndCycles(vector<vector<string> > mN,vector<vector<string> > m1, int n)
+{
+    cout <<"\nThe hamiltonian paths of the graph are : ";
+    vector<string> paths;
+    vector<string> edges;
+    for (int i=0; i<n; i++)
+    {
+        for (int j=0; j<n; j++)
+        {
+            if (mN[i][j] != "0")            // prints the paths from the last mN matrix
+            {
+                cout <<  mN[i][j] <<", " ;
+                paths.push_back(mN[i][j]);
+            }
+
+            if (m1[i][j] != "0")             // stores the edges of the m1 matrix
+            {
+                edges.push_back(m1[i][j]);
+            }
+
+        }
+    }
+    cout <<"\n";
+    string edge1;
+    string edge2;
+    cout <<"\nThe hamiltonian cycles of the graph are : ";
+    for (int i=0; i<paths.size(); i++)
+    {
+        edge2 = paths[i].substr(paths[i].length()-1,1)+paths[i].substr(0,1); // edge that consists of the 1st and the last path nodes
+        for (int j=0; j<edges.size(); j++)
+        {
+            if (edge2.compare(edges[j]) == 0)                         // checks if the there is an edge that connects the path to make a cycle
+            {
+                cout << paths[i] << paths[i].substr(0,1) << ", ";
+            }
+        }
+    }
+}
+
+int main()
+{
+    char c;
+    vector<char> lines;
+    ifstream in ("hamilton.txt"); // opens text file that contains the graph
+    int n=0;
+    if (in.is_open())
+    {
+        while ( in >> c )
+        {
+            lines.push_back(c); // stores graph to memory
+        }
+        in.close();
+    }
+    n = sqrt(lines.size());     // number of nodes of the graph
+    vector<vector<string> > m(n);
+    for (int i=0; i<n; i++)
+    {
+        m[i].resize(n);
+        for (int j=0; j<n; j++)
+        {
+            m[i][j] = lines[i*n+j];  // makes the M matrix
+        }
+    }
+
+    vector<vector<string> > m1(n);
+    for (int i=0; i<n; i++)
+    {
+        m1[i].resize(n);
+        for (int j=0; j<n; j++)
+        {
+            if (m[i][j] != "0")
+            {
+                m1[i][j] = char(65+i) + m[i][j]; // makes the M1 matrix from the M matrix, where 65 is the char 'A'
+            }
+            else
+            {
+                m1[i][j] = m[i][j]; // element of M1 becomes 0, because the element of M is 0
+            }
+        }
+    }
+    vector<vector<string> > temp = m1; // save the starting state of M1 cause it is changed later(M1 becomes the MN-1 matrix)
+    vector<vector<string> > mN(n);
+    for (int i=0; i<n; i++)
+    {
+        mN[i].resize(n);
+        for (int j=0; j<n; j++)
+        {
+            mN[i][j] = "0";
+        }
+    }
+    for (int a=1; a<n-1; a++)       // makes the MN matrices using the M and MN-1 matrices
+    {
+        for (int r=0; r<n; r++)     //
+        {
+            for (int s=0; s<n; s++)
+            {
+                for (int t=0; t<n; t++)
+                {
+                    if (m1[r][t] != "0" && m[t][s] != "0" && m1[r][t].find(m[t][s]) == string::npos )  // MN-1 element cant be 0 , M element cant be 0 and MN-1 cant contain the element from M
+                        mN[r][s] = m1[r][t] + m[t][s];     // MN becomes the "union" of the M and MN-1 matrices
+                }
+            }
+        }
+        if (a!=n-2)                  //  make M1 the MN-1 matrix and empty the MN matrix
+        {
+            m1 = mN;
+            for (int i=0; i<n; i++)
+            {
+                for (int j=0; j<n; j++)
+                {
+                    mN[i][j] = "0";
+                }
+            }
+        }
+
+    }
+
+    printPathsAndCycles(mN,temp,n);       // temp is the saved state of M1 matrix
+}