Find distance between two nodes in the given Binary tree for Q queries | C ++ Program to find distance between two nodes using LCA ; log2 ( MAX ) ; Array to store the level of each node ; Vector to store tree ; Pre - Processing to calculate values of lca [ ] [ ] , dist [ ] [ ] ; Using recursion formula to calculate the values of lca [ ] [ ] ; Storing the level of each node ; Using recursion formula to calculate the values of lca [ ] [ ] and dist [ ] [ ] ; Function to find the distance between given nodes u and v ; The node which is present farthest from the root node is taken as v . If u is farther from root node then swap the two ; Finding the ancestor of v which is at same level as u ; Adding distance of node v till its 2 ^ i - th ancestor ; If u is the ancestor of v then u is the LCA of u and v ; Finding the node closest to the root which is not the common ancestor of u and v i . e . a node x such that x is not the common ancestor of u and v but lca [ x ] [ 0 ] is ; Adding the distance of v and u to its 2 ^ i - th ancestor ; Adding the distance of u and v to its first ancestor ; Driver Code ; Number of nodes ; Add edges with their cost ; Initialising lca and dist values with - 1 and 0 respectively ; Perform DFS ; Query 1 : { 1 , 3 } ; Query 2 : { 2 , 3 } ; Query 3 : { 3 , 5 }
#include <bits/stdc++.h> NEW_LINE using namespace std ; #define MAX  1000 NEW_LINE #define log  10  NEW_LINE int level [ MAX ] ; int lca [ MAX ] [ log ] ; int dist [ MAX ] [ log ] ; vector < pair < int , int > > graph [ MAX ] ; void addEdge ( int u , int v , int cost ) { graph [ u ] . push_back ( { v , cost } ) ; graph [ v ] . push_back ( { u , cost } ) ; } void dfs ( int node , int parent , int h , int cost ) { lca [ node ] [ 0 ] = parent ; level [ node ] = h ; if ( parent != -1 ) { dist [ node ] [ 0 ] = cost ; } for ( int i = 1 ; i < log ; i ++ ) { if ( lca [ node ] [ i - 1 ] != -1 ) { lca [ node ] [ i ] = lca [ lca [ node ] [ i - 1 ] ] [ i - 1 ] ; dist [ node ] [ i ] = dist [ node ] [ i - 1 ] + dist [ lca [ node ] [ i - 1 ] ] [ i - 1 ] ; } } for ( auto i : graph [ node ] ) { if ( i . first == parent ) continue ; dfs ( i . first , node , h + 1 , i . second ) ; } } void findDistance ( int u , int v ) { int ans = 0 ; if ( level [ u ] > level [ v ] ) swap ( u , v ) ; for ( int i = log - 1 ; i >= 0 ; i -- ) { if ( lca [ v ] [ i ] != -1 && level [ lca [ v ] [ i ] ] >= level [ u ] ) { ans += dist [ v ] [ i ] ; v = lca [ v ] [ i ] ; } } if ( v == u ) { cout << ans << endl ; } else { for ( int i = log - 1 ; i >= 0 ; i -- ) { if ( lca [ v ] [ i ] != lca [ u ] [ i ] ) { ans += dist [ u ] [ i ] + dist [ v ] [ i ] ; v = lca [ v ] [ i ] ; u = lca [ u ] [ i ] ; } } ans += dist [ u ] [ 0 ] + dist [ v ] [ 0 ] ; cout << ans << endl ; } } int main ( ) { int n = 5 ; addEdge ( 1 , 2 , 2 ) ; addEdge ( 1 , 3 , 3 ) ; addEdge ( 2 , 4 , 5 ) ; addEdge ( 2 , 5 , 7 ) ; for ( int i = 1 ; i <= n ; i ++ ) { for ( int j = 0 ; j < log ; j ++ ) { lca [ i ] [ j ] = -1 ; dist [ i ] [ j ] = 0 ; } } dfs ( 1 , -1 , 0 , 0 ) ; findDistance ( 1 , 3 ) ; findDistance ( 2 , 3 ) ; findDistance ( 3 , 5 ) ; return 0 ; }