This is a java program to find longest path in DAG.
Here is the source code of the Java Program to Find the Longest Path in a DAG. The Java program is successfully compiled and run on a Windows system. The program output is also shown below.
package com.maixuanviet.hardgraph; import java.util.Scanner; import java.util.Vector; class Node { int name; // node ID, started from 0 to n-1 Vector<Integer> preds; // predecessors (String) Vector<Integer> neibs; // neighbors (String) Vector<Integer> backs; // backward edges -node is end vertex (Integer) Vector<Integer> fors; // forward edges -node is start vertex (Integer) int pNode; // previous node on the augmenting path int pEdge; // from which edge this node comes on the augmenting // path public Node(int id) { name = id; backs = new Vector<Integer>(); fors = new Vector<Integer>(); pNode = -1; pEdge = -1; } } class Edge { int name; // edge ID, started from 0 to n-1 int start; // start vertex of this edge int end; // end vertex of this edge int direct; // forwards (+1) or backwards (-1) on augmenting path // if 0 then not part of augmenting path int capacity; // capacity int flow; // current flow public Edge(int id) { name = id; start = -1; end = -1; direct = 0; // default is neither capacity = 0; flow = 0; } public String toString() { return name + ": s=" + start + " e=" + end + " d=" + direct; } } public class LongestPathinDAG { int n; // number of nodes int target; // destination node int minLength; // the minimal length of each path Node[] v; // used to store Nodes Edge[] e; // used to store Edges int[] path; // used to store temporary path int length = 0; // length of the path int distance = 0; // distance of the path int[] bestPath; // used to store temporary path int bestLength = 0; // length of the longest path int bestDistance = -1000000; // distance of the longest path int[] visited; // used to mark a node as visited if set as // 1 public LongestPathinDAG() { Scanner sc = new Scanner(System.in); System.out.println("Enter the number of vertices: "); n = sc.nextInt(); System.out.println("Enter the number of edges: "); int m = sc.nextInt(); v = new Node[n]; e = new Edge[m]; System.out.println(n + " nodes and " + m + " edges."); for (int i = 0; i < n; i++) v[i] = new Node(i); int i = 0; while (i < e.length) { Edge edge = new Edge(i); int sVal = sc.nextInt(); edge.start = sVal;// sc.nextInt(); int eVal = sc.nextInt(); edge.end = eVal;// sc.nextInt(); edge.capacity = sc.nextInt(); System.out.println(" edge: " + edge.start + " - " + edge.end + " : " + edge.capacity); edge.flow = 0; e[i] = edge; v[sVal].fors.add(i); v[eVal].backs.add(i); i++; if (i == m) break; } visited = new int[v.length]; path = new int[v.length]; bestPath = new int[v.length]; sc.close(); } /* * this function looks for a longest path starting from being to end, * using the backtrack depth-first search. */ public boolean findLongestPath(int begin, int end, int minLen) { /* * compute a longest path from begin to end */ target = end; bestDistance = -100000000; minLength = minLen; dfsLongestPath(begin); if (bestDistance == -100000000) return false; else return true; } private void dfsLongestPath(int current) { visited[current] = 1; path[length++] = current; if (current == target && length >= minLength) { if (distance > bestDistance) { for (int i = 0; i < length; i++) bestPath[i] = path[i]; bestLength = length; bestDistance = distance; } } else { Vector<Integer> fors = v[current].fors; for (int i = 0; i < fors.size(); i++) { Integer edge_obj = (Integer) fors.elementAt(i); int edge = edge_obj.intValue(); if (visited[e[edge].end] == 0) { distance += e[edge].capacity; dfsLongestPath(e[edge].end); distance -= e[edge].capacity; } } } visited[current] = 0; length--; } public String toString() { String output = "v" + bestPath[0]; for (int i = 1; i < bestLength; i++) output = output + " -> v" + bestPath[i]; return output; } public static void main(String arg[]) { LongestPathinDAG lp = new LongestPathinDAG(); /* * find a longest path from vertex 0 to vertex n-1. */ if (lp.findLongestPath(0, lp.n - 1, 1)) System.out.println("Longest Path is " + lp + " and the distance is " + lp.bestDistance); else System.out.println("No path from v0 to v" + (lp.n - 1)); /* * find a longest path from vertex 3 to vertex 5. */ if (lp.findLongestPath(3, 5, 1)) System.out.println("Longest Path is " + lp + " and the distance is " + lp.bestDistance); else System.out.println("No path from v3 to v5"); /* * find a longest path from vertex 5 to vertex 3. */ if (lp.findLongestPath(lp.n - 1, 3, 1)) System.out.println("Longest Path is " + lp + " and the distance is " + lp.bestDistance); else System.out.println("No path from v5 to v3"); } }
Output:
$ javac LongestPathinDAG.java $ java LongestPathinDAG Enter the number of vertices: 6 Enter the number of edges: 7 6 nodes and 7 edges. 0 1 2 edge: 0 - 1 : 2 1 2 3 edge: 1 - 2 : 3 1 3 4 edge: 1 - 3 : 4 3 4 5 edge: 3 - 4 : 5 4 5 6 edge: 4 - 5 : 6 5 3 7 edge: 5 - 3 : 7 5 2 8 edge: 5 - 2 : 8 Longest Path is v0 -> v1 -> v3 -> v4 -> v5 and the distance is 17 Longest Path is v3 -> v4 -> v5 and the distance is 11 Longest Path is v5 -> v3 and the distance is 7
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