Cloning of a LinkedList and a Binary Tree with random pointers has already been discussed. The idea behind cloning a graph is pretty much similar.
The idea is to do a BFS traversal of the graph and while visiting a node make a clone node of it (a copy of original node). If a node is encountered which is already visited then it already has a clone node.
How to keep track of the visited/cloned nodes?
A HashMap/Map is required in order to maintain all the nodes which have already been created.
Key stores: Reference/Address of original Node
Value stores: Reference/Address of cloned Node
A copy of all the graph nodes has been made, how to connect clone nodes?
While visiting the neighboring vertices of a node u get the corresponding cloned node for u , let’s call that cloneNodeU , now visit all the neighboring nodes for u and for each neighbor find the corresponding clone node(if not found create one) and then push into the neighboring vector of cloneNodeU node.
How to verify if the cloned graph is a correct?
Do a BFS traversal before and after the cloning of graph. In BFS traversal display the value of a node along with its address/reference.
Compare the order in which nodes are displayed, if the values are same but the address/reference is different for both the traversals than the cloned graph is correct.
C++
// A C++ program to Clone an Undirected Graph #include<bits/stdc++.h> using namespace std; struct GraphNode { int val; //A neighbour vector which contains addresses to //all the neighbours of a GraphNode vector<GraphNode*> neighbours; }; // A function which clones a Graph and // returns the address to the cloned // src node GraphNode *cloneGraph(GraphNode *src) { //A Map to keep track of all the //nodes which have already been created map<GraphNode*, GraphNode*> m; queue<GraphNode*> q; // Enqueue src node q.push(src); GraphNode *node; // Make a clone Node node = new GraphNode(); node->val = src->val; // Put the clone node into the Map m[src] = node; while (!q.empty()) { //Get the front node from the queue //and then visit all its neighbours GraphNode *u = q.front(); q.pop(); vector<GraphNode *> v = u->neighbours; int n = v.size(); for (int i = 0; i < n; i++) { // Check if this node has already been created if (m[v[i]] == NULL) { // If not then create a new Node and // put into the HashMap node = new GraphNode(); node->val = v[i]->val; m[v[i]] = node; q.push(v[i]); } // add these neighbours to the cloned graph node m[u]->neighbours.push_back(m[v[i]]); } } // Return the address of cloned src Node return m[src]; } // Build the desired graph GraphNode *buildGraph() { /* Note : All the edges are Undirected Given Graph: 1--2 | | 4--3 */ GraphNode *node1 = new GraphNode(); node1->val = 1; GraphNode *node2 = new GraphNode(); node2->val = 2; GraphNode *node3 = new GraphNode(); node3->val = 3; GraphNode *node4 = new GraphNode(); node4->val = 4; vector<GraphNode *> v; v.push_back(node2); v.push_back(node4); node1->neighbours = v; v.clear(); v.push_back(node1); v.push_back(node3); node2->neighbours = v; v.clear(); v.push_back(node2); v.push_back(node4); node3->neighbours = v; v.clear(); v.push_back(node3); v.push_back(node1); node4->neighbours = v; return node1; } // A simple bfs traversal of a graph to // check for proper cloning of the graph void bfs(GraphNode *src) { map<GraphNode*, bool> visit; queue<GraphNode*> q; q.push(src); visit[src] = true; while (!q.empty()) { GraphNode *u = q.front(); cout << "Value of Node " << u->val << "
"; cout << "Address of Node " <<u << "
"; q.pop(); vector<GraphNode *> v = u->neighbours; int n = v.size(); for (int i = 0; i < n; i++) { if (!visit[v[i]]) { visit[v[i]] = true; q.push(v[i]); } } } cout << endl; } // Driver program to test above function int main() { GraphNode *src = buildGraph(); cout << "BFS Traversal before cloning
"; bfs(src); GraphNode *newsrc = cloneGraph(src); cout << "BFS Traversal after cloning
"; bfs(newsrc); return 0; } |
Java
// Java program to Clone an Undirected Graph import java.util.*; // GraphNode class represents each // Node of the Graph class GraphNode { int val; // A neighbour Vector which contains references to // all the neighbours of a GraphNode Vector<GraphNode> neighbours; public GraphNode(int val) { this.val = val; neighbours = new Vector<GraphNode>(); } } class Graph { // A method which clones the graph and // returns the reference of new cloned source node public GraphNode cloneGraph(GraphNode source) { Queue<GraphNode> q = new LinkedList<GraphNode>(); q.add(source); // An HashMap to keep track of all the // nodes which have already been created HashMap<GraphNode,GraphNode> hm = new HashMap<GraphNode,GraphNode>(); //Put the node into the HashMap hm.put(source,new GraphNode(source.val)); while (!q.isEmpty()) { // Get the front node from the queue // and then visit all its neighbours GraphNode u = q.poll(); // Get corresponding Cloned Graph Node GraphNode cloneNodeU = hm.get(u); if (u.neighbours != null) { Vector<GraphNode> v = u.neighbours; for (GraphNode graphNode : v) { // Get the corresponding cloned node // If the node is not cloned then we will // simply get a null GraphNode cloneNodeG = hm.get(graphNode); // Check if this node has already been created if (cloneNodeG == null) { q.add(graphNode); // If not then create a new Node and // put into the HashMap cloneNodeG = new GraphNode(graphNode.val); hm.put(graphNode,cloneNodeG); } // add the 'cloneNodeG' to neighbour // vector of the cloneNodeG cloneNodeU.neighbours.add(cloneNodeG); } } } // Return the reference of cloned source Node return hm.get(source); } // Build the desired graph public GraphNode buildGraph() { /* Note : All the edges are Undirected Given Graph: 1--2 | | 4--3 */ GraphNode node1 = new GraphNode(1); GraphNode node2 = new GraphNode(2); GraphNode node3 = new GraphNode(3); GraphNode node4 = new GraphNode(4); Vector<GraphNode> v = new Vector<GraphNode>(); v.add(node2); v.add(node4); node1.neighbours = v; v = new Vector<GraphNode>(); v.add(node1); v.add(node3); node2.neighbours = v; v = new Vector<GraphNode>(); v.add(node2); v.add(node4); node3.neighbours = v; v = new Vector<GraphNode>(); v.add(node3); v.add(node1); node4.neighbours = v; return node1; } // BFS traversal of a graph to // check if the cloned graph is correct public void bfs(GraphNode source) { Queue<GraphNode> q = new LinkedList<GraphNode>(); q.add(source); HashMap<GraphNode,Boolean> visit = new HashMap<GraphNode,Boolean>(); visit.put(source,true); while (!q.isEmpty()) { GraphNode u = q.poll(); System.out.println("Value of Node " + u.val); System.out.println("Address of Node " + u); if (u.neighbours != null) { Vector<GraphNode> v = u.neighbours; for (GraphNode g : v) { if (visit.get(g) == null) { q.add(g); visit.put(g,true); } } } } System.out.println(); } } // Driver code class Main { public static void main(String args[]) { Graph graph = new Graph(); GraphNode source = graph.buildGraph(); System.out.println("BFS traversal of a graph before cloning"); graph.bfs(source); GraphNode newSource = graph.cloneGraph(source); System.out.println("BFS traversal of a graph after cloning"); graph.bfs(newSource); } } |
Output in Java:
BFS traversal of a graph before cloning Value of Node 1 Address of Node [email protected] Value of Node 2 Address of Node [email protected] Value of Node 4 Address of Node [email protected] Value of Node 3 Address of Node [email protected] BFS traversal of a graph after cloning Value of Node 1 Address of Node [email protected] Value of Node 2 Address of Node [email protected] Value of Node 4 Address of Node [email protected] Value of Node 3 Address of Node [email protected]
Output in C++:
BFS Traversal before cloning Value of Node 1 Address of Node 0x24ccc20 Value of Node 2 Address of Node 0x24ccc50 Value of Node 4 Address of Node 0x24cccb0 Value of Node 3 Address of Node 0x24ccc80 BFS Traversal after cloning Value of Node 1 Address of Node 0x24cd030 Value of Node 2 Address of Node 0x24cd0e0 Value of Node 4 Address of Node 0x24cd170 Value of Node 3 Address of Node 0x24cd200
Clone an undirected graph with multiple connected components
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