The longest path algorithm is used to find the maximum length of a given graph. The maximum length may be measured by the maximum number of edges or the sum of the weights in a weighted graph. Following is a sample java code to find the Longest Path. It has two classes. CreateMatrix.java class to create the matrix and LongestPath.java to find the Longest Path to the created matrix.

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/********************* LongestPathAlgo.java ********************/ class LongestPathAlgo { public static void main(String[] args) { int length = 13;//length of the 2-D array int adjMatrix[][] = new int[length][length]; CreateMatrix cm = new CreateMatrix(); cm.createMatrix(length); adjMatrix = cm.readMatrix(adjMatrix); long starttime = System.nanoTime(); LongestPathAlgo lpa = new LongestPathAlgo(); boolean visited[] = new boolean[adjMatrix.length]; lpa.initialize(adjMatrix, visited); int max = lpa.longestPath(0, visited, adjMatrix); long runtime = System.nanoTime()-starttime; System.out.println("Runtime =" + runtime +" nano seconds"); System.out.println("Longest Path Length = "+max); } public void initialize(int adjMatrix[][], boolean visited[]) { for (int u = 0; u < adjMatrix.length; u++) { visited[u] = false; } } int longestPath(int vertex, boolean visited[], int adjMatrix[][]) { int dist, max = 0; visited[vertex] = true; for (int u = 0; u < adjMatrix[vertex].length; u++) { if (adjMatrix[vertex][u] != -1) { if (!visited[u]) { dist = adjMatrix[vertex][u] + longestPath(u, visited, adjMatrix); if (dist > max) { max = dist; } } } } visited[vertex] = false; return max; } }

/********************* CreateMatrix.java ********************/ import java.io.BufferedReader; import java.io.BufferedWriter; import java.io.File; import java.io.FileReader; import java.io.FileWriter; import java.io.IOException; public class CreateMatrix { public void createMatrix(int length) { Random ran = new Random(); FileWriter fw; try { File file = new File("matrix.txt"); fw = new FileWriter(file); BufferedWriter bw = new BufferedWriter(fw); for (int i = 0; i < length; i++) { for (int j = 0; j < length; j++) { if (i == j) { bw.write("" + -1); } else { bw.write("" + (i+j)); } bw.write("@"); } bw.newLine(); } for (int i = 0; i < length; i++) { } bw.close(); fw.close(); } catch (IOException ex) { System.out.println("File Not Found"); } } public int[][] readMatrix(int adjMatrix[][]) { try { File file = new File("matrix.txt"); FileReader fr = new FileReader(file); BufferedReader br = new BufferedReader(fr); int i = 0; while (br.ready()) { String line = br.readLine(); String array[] = line.split("@"); for (int j = 0; j < adjMatrix.length; j++) { adjMatrix[i][j] = Integer.parseInt(array[j]); } i++; } } catch (Exception e) { System.out.println("Error " + e); } return adjMatrix; } }