112 lines
3.6 KiB
Java
112 lines
3.6 KiB
Java
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/*This is a java program to find hamilton cycle in graph. In the mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path in an undirected or directed graph that visits each vertex exactly once. A Hamiltonian cycle (or Hamiltonian circuit) is a Hamiltonian path that is a cycle. Determining whether such paths and cycles exist in graphs is the Hamiltonian path problem, which is NP-complete.*/
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import java.util.Arrays;
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import java.util.Scanner;
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public class HamiltonianCycle
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{
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private int V, pathCount;
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private int[] path;
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private int[][] graph;
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/** Function to find cycle **/
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public void findHamiltonianCycle(int[][] g)
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{
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V = g.length;
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path = new int[V];
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Arrays.fill(path, -1);
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graph = g;
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try
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{
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path[0] = 0;
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pathCount = 1;
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solve(0);
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System.out.println("No solution");
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}
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catch (Exception e)
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{
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System.out.println(e.getMessage());
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display();
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}
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}
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/** function to find paths recursively **/
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public void solve(int vertex) throws Exception
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{
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/** solution **/
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if (graph[vertex][0] == 1 && pathCount == V)
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throw new Exception("Solution found");
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/** all vertices selected but last vertex not linked to 0 **/
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if (pathCount == V)
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return;
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for (int v = 0; v < V; v++)
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{
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/** if connected **/
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if (graph[vertex][v] == 1)
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{
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/** add to path **/
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path[pathCount++] = v;
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/** remove connection **/
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graph[vertex][v] = 0;
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graph[v][vertex] = 0;
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/** if vertex not already selected solve recursively **/
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if (!isPresent(v))
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solve(v);
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/** restore connection **/
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graph[vertex][v] = 1;
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graph[v][vertex] = 1;
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/** remove path **/
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path[--pathCount] = -1;
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}
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}
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}
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/** function to check if path is already selected **/
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public boolean isPresent(int v)
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{
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for (int i = 0; i < pathCount - 1; i++)
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if (path[i] == v)
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return true;
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return false;
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}
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/** display solution **/
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public void display()
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{
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System.out.print("\nPath : ");
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for (int i = 0; i <= V; i++)
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System.out.print(path[i % V] + " ");
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System.out.println();
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}
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/** Main function **/
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public static void main(String[] args)
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{
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Scanner scan = new Scanner(System.in);
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/** Make an object of HamiltonianCycle class **/
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HamiltonianCycle hc = new HamiltonianCycle();
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/** Accept number of vertices **/
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System.out.println("Enter number of vertices");
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int V = scan.nextInt();
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/** get graph **/
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System.out.println("Enter adjacency matrix");
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int[][] graph = new int[V][V];
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for (int i = 0; i < V; i++)
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for (int j = 0; j < V; j++)
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graph[i][j] = scan.nextInt();
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hc.findHamiltonianCycle(graph);
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scan.close();
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}
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}
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/*
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Enter number of vertices
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6
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Enter adjacency matrix
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0 1 0 0 0 0
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1 0 1 1 0 0
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0 1 0 0 0 1
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0 1 0 0 1 1
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0 0 0 1 0 1
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0 0 1 1 1 0
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No solution
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