To identify loop in the graph, We are going to use Find and Union technic with Path Compression. We are going to create subject of each vertex and we will represent one element of that subset as a parent, So next time we will take two vertex will check the parent of each, if both has same parent then loop found.
See Utility for graph to get Graph and Node class
Lets see below two graphs,
Find same algorithm without using path compression
Find algorithm below.
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package com.omt.learn.geekforgeek.greedy; import java.util.HashMap; import java.util.Map; import com.omt.learn.algo.util.graph.Graph; import com.omt.learn.algo.util.graph.Node; import com.omt.learn.algo.util.graph.State; public class FindCycleInGraphUnionFindPathComp { public static void main(String[] args) { System.out.println("Is Cycle Found:" + isCycleInGraph(generateLoopGraph())); System.out.println("Is Cycle Found:" + isCycleInGraph(generateNonLoopGraph())); } public static boolean isCycleInGraph(Graph graph) { Map<Node, Node> subSet = new HashMap<Node, Node>(); for (Node n : graph.getVertices()) { if (n.getAdjacent() != null && !n.getAdjacent().isEmpty()) { n.setState(State.VISITED); for (Node to : n.getAdjacent()) { if (to.isVisited()) { continue; } Node n1 = find(subSet, n); Node n2 = find(subSet, to); if (n1 == n2) { prettyPrintMap(subSet); return true; } else { union(subSet, n, to); } } } } prettyPrintMap(subSet); return false; } public static Node find(Map<Node, Node> subSet, Node n) { if (subSet.get(n) == null) { return n; } return find(subSet, subSet.get(n)); } public static void union(Map<Node, Node> subSet, Node from, Node to) { Node n1 = find(subSet, from); Node n2 = find(subSet, to); //Below code is for PATH COMPRESSION if (n1.getNodeId() < n2.getNodeId()) { subSet.put(n2, n1); } else if (n1.getNodeId() > n2.getNodeId()) { subSet.put(n1, n2); } else { n1.setNodeId(n1.getNodeId() + 1); subSet.put(n1, n2); } } public static Graph generateLoopGraph() { Graph graph = new Graph(); Node a = new Node("A"); // 0 Node b = new Node("B"); // 1 Node c = new Node("C"); // 2 Node d = new Node("D"); // 3 Node e = new Node("E"); // 4 Node f = new Node("F"); // 5 Node g = new Node("G"); // 6 Node h = new Node("H"); // 7 Node i = new Node("I"); // 8 a.addAdjacent(b); a.addAdjacent(c); b.addAdjacent(d); b.addAdjacent(a); d.addAdjacent(b); d.addAdjacent(e); d.addAdjacent(f); e.addAdjacent(d); e.addAdjacent(f); e.addAdjacent(g); f.addAdjacent(e); f.addAdjacent(d); f.addAdjacent(g); g.addAdjacent(e); g.addAdjacent(f); c.addAdjacent(a); c.addAdjacent(h); h.addAdjacent(c); graph.addVertex(a); graph.addVertex(b); graph.addVertex(c); graph.addVertex(d); graph.addVertex(e); graph.addVertex(f); graph.addVertex(g); graph.addVertex(h); graph.addVertex(i); return graph; } public static Graph generateNonLoopGraph() { Graph graph = new Graph(); Node a = new Node("A"); // 0 Node b = new Node("B"); // 1 Node c = new Node("C"); // 2 Node d = new Node("D"); // 3 Node e = new Node("E"); // 4 Node f = new Node("F"); // 5 Node g = new Node("G"); // 6 Node h = new Node("H"); // 7 Node i = new Node("I"); // 8 a.addAdjacent(b); a.addAdjacent(c); b.addAdjacent(d); b.addAdjacent(a); d.addAdjacent(b); d.addAdjacent(f); e.addAdjacent(i); e.addAdjacent(g); f.addAdjacent(d); f.addAdjacent(g); g.addAdjacent(e); g.addAdjacent(f); c.addAdjacent(a); c.addAdjacent(h); h.addAdjacent(c); i.addAdjacent(e); graph.addVertex(a); graph.addVertex(b); graph.addVertex(c); graph.addVertex(h); graph.addVertex(d); graph.addVertex(f); graph.addVertex(g); graph.addVertex(e); graph.addVertex(i); return graph; } public static void prettyPrintMap(Map<Node, Node> subSet) { for (Node key : subSet.keySet()) { System.out.println(key.getVertex() + "->" + subSet.get(key).getVertex()); } } } |
Output of above algorithm
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F->A H->A D->A C->A E->A B->A Is Cycle Found:true F->A I->A D->A B->A C->A H->A E->A G->A Is Cycle Found:false |
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