107 lines
2.8 KiB
Java
107 lines
2.8 KiB
Java
package DataStructures.Trees;
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import java.util.ArrayList;
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import java.util.Scanner;
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public class LCA {
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private static Scanner scanner = new Scanner(System.in);
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public static void main(String[] args){
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//The adjacency list representation of a tree:
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ArrayList<ArrayList<Integer>> adj = new ArrayList<>();
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//v is the number of vertices and e is the number of edges
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int v = scanner.nextInt(), e = v-1;
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for(int i=0;i<v;i++){
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adj.add(new ArrayList<Integer>());
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}
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//Storing the given tree as an adjacency list
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int to, from;
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for(int i=0;i<e;i++){
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to = scanner.nextInt();
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from = scanner.nextInt();
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adj.get(to).add(from);
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adj.get(from).add(to);
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}
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//parent[v1] gives parent of a vertex v1
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int[] parent = new int[v];
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//depth[v1] gives depth of vertex v1 with respect to the root
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int[] depth = new int[v];
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//Assuming the tree to be rooted at 0, hence calculating parent and depth of every vertex
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dfs(adj,0,-1,parent,depth);
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//Inputting the two vertices whose LCA is to be calculated
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int v1 = scanner.nextInt(), v2 = scanner.nextInt();
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//Outputting the LCA
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System.out.println(getLCA(v1,v2,depth,parent));
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}
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/**
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* Depth first search to calculate parent and depth of every vertex
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* @param adj The adjacency list representation of the tree
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* @param s The source vertex
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* @param p Parent of source
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* @param parent An array to store parents of all vertices
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* @param depth An array to store depth of all vertices
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*/
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private static void dfs(ArrayList<ArrayList<Integer>> adj, int s, int p, int[] parent, int[] depth){
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for(int adjacent: adj.get(s)){
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if(adjacent!=p){
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parent[adjacent] = s;
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depth[adjacent] = 1 + depth[s];
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dfs(adj,adjacent,s,parent,depth);
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}
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}
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}
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/**
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* Method to calculate Lowest Common Ancestor
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* @param v1 The first vertex
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* @param v2 The second vertex
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* @param depth An array with depths of all vertices
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* @param parent An array with parents of all vertices
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* @return Returns a vertex that is LCA of v1 and v2
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*/
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private static int getLCA(int v1, int v2, int[] depth, int[] parent){
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if(depth[v1] < depth[v2]){
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int temp = v1;
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v1 = v2;
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v2 = temp;
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}
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while(depth[v1]!=depth[v2]){
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v1 = parent[v1];
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}
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if(v1==v2) return v1;
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while(v1!=v2){
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v1 = parent[v1];
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v2 = parent[v2];
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}
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return v1;
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}
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}
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/**
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* Input:
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* 10
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* 0 1
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* 0 2
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* 1 5
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* 5 6
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* 2 4
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* 2 3
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* 3 7
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* 7 9
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* 7 8
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* 9 4
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* Output:
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* 2
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*/ |