Tarjan 's off | A C ++ Program to implement Tarjan Offline LCA Algorithm ; number of nodes in input tree ; COLOUR ' WHITE ' is assigned value 1 ; COLOUR ' BLACK ' is assigned value 2 ; A binary tree node has data , pointer to left child and a pointer to right child ; subset [ i ] . parent -- > Holds the parent of node - ' i ' subset [ i ] . rank -- > Holds the rank of node - ' i ' subset [ i ] . ancestor -- > Holds the LCA queries answers subset [ i ] . child -- > Holds one of the child of node - ' i ' if present , else - '0' subset [ i ] . sibling -- > Holds the right - sibling of node - ' i ' if present , else - '0' subset [ i ] . color -- > Holds the colour of node - ' i ' ; Structure to represent a query A query consists of ( L , R ) and we will process the queries offline a / c to Tarjan 's oflline LCA algorithm ; Helper function that allocates a new node with the given data and NULL left and right pointers . ; A utility function to make set ; A utility function to find set of an element i ( uses path compression technique ) ; find root and make root as parent of i ( path compression ) ; A function that does union of two sets of x and y ( uses union by rank ) ; Attach smaller rank tree under root of high rank tree ( Union by Rank ) ; If ranks are same , then make one as root and increment its rank by one ; The main function that prints LCAs . u is root 's data. m is size of q[] ; Make Sets ; Initially , each node 's ancestor is the node  itself. ; This while loop doesn 't run for more than 2 times  as there can be at max. two children of a node ; This is basically an inorder traversal and we preprocess the arrays -> child [ ] and sibling [ ] in " struct ▁ subset " with the tree structure using this function . ; Recur on left child ; Note that the below two lines can also be this - subsets [ node -> data ] . child = node -> right -> data ; subsets [ node -> right -> data ] . sibling = node -> left -> data ; This is because if both left and right children of node - ' i ' are present then we can store any of them in subsets [ i ] . child and correspondingly its sibling ; Recur on right child ; A function to initialise prior to pre - processing and LCA walk ; Initialising the structure with 0 's ; Prints LCAs for given queries q [ 0. . m - 1 ] in a tree with given root ; Allocate memory for V subsets and nodes ; Creates subsets and colors them WHITE ; Preprocess the tree ; Perform a tree walk to process the LCA queries offline ; Driver program to test above functions ; We construct a binary tree : - 1 / \ 2 3 / \ 4 5 ; LCA Queries to answer
#include <bits/stdc++.h> NEW_LINE #define V  5	 NEW_LINE #define WHITE  1	 NEW_LINE #define BLACK  2  NEW_LINE struct Node { int data ; Node * left , * right ; } ; struct subset { int parent , rank , ancestor , child , sibling , color ; } ; struct Query { int L , R ; } ; Node * newNode ( int data ) { Node * node = new Node ; node -> data = data ; node -> left = node -> right = NULL ; return ( node ) ; } void makeSet ( struct subset subsets [ ] , int i ) { if ( i < 1 i > V ) return ; subsets [ i ] . color = WHITE ; subsets [ i ] . parent = i ; subsets [ i ] . rank = 0 ; return ; } int findSet ( struct subset subsets [ ] , int i ) { if ( subsets [ i ] . parent != i ) subsets [ i ] . parent = findSet ( subsets , subsets [ i ] . parent ) ; return subsets [ i ] . parent ; } void unionSet ( struct subset subsets [ ] , int x , int y ) { int xroot = findSet ( subsets , x ) ; int yroot = findSet ( subsets , y ) ; if ( subsets [ xroot ] . rank < subsets [ yroot ] . rank ) subsets [ xroot ] . parent = yroot ; else if ( subsets [ xroot ] . rank > subsets [ yroot ] . rank ) subsets [ yroot ] . parent = xroot ; else { subsets [ yroot ] . parent = xroot ; ( subsets [ xroot ] . rank ) ++ ; } } void lcaWalk ( int u , struct Query q [ ] , int m , struct subset subsets [ ] ) { makeSet ( subsets , u ) ; subsets [ findSet ( subsets , u ) ] . ancestor = u ; int child = subsets [ u ] . child ; while ( child != 0 ) { lcaWalk ( child , q , m , subsets ) ; unionSet ( subsets , u , child ) ; subsets [ findSet ( subsets , u ) ] . ancestor = u ; child = subsets [ child ] . sibling ; } subsets [ u ] . color = BLACK ; for ( int i = 0 ; i < m ; i ++ ) { if ( q [ i ] . L == u ) { if ( subsets [ q [ i ] . R ] . color == BLACK ) { printf ( " LCA ( % d ▁ % d ) ▁ - > ▁ % d STRNEWLINE " , q [ i ] . L , q [ i ] . R , subsets [ findSet ( subsets , q [ i ] . R ) ] . ancestor ) ; } } else if ( q [ i ] . R == u ) { if ( subsets [ q [ i ] . L ] . color == BLACK ) { printf ( " LCA ( % d ▁ % d ) ▁ - > ▁ % d STRNEWLINE " , q [ i ] . L , q [ i ] . R , subsets [ findSet ( subsets , q [ i ] . L ) ] . ancestor ) ; } } } return ; } void preprocess ( Node * node , struct subset subsets [ ] ) { if ( node == NULL ) return ; preprocess ( node -> left , subsets ) ; if ( node -> left != NULL && node -> right != NULL ) { subsets [ node -> data ] . child = node -> left -> data ; subsets [ node -> left -> data ] . sibling = node -> right -> data ; } else if ( ( node -> left != NULL && node -> right == NULL ) || ( node -> left == NULL && node -> right != NULL ) ) { if ( node -> left != NULL && node -> right == NULL ) subsets [ node -> data ] . child = node -> left -> data ; else subsets [ node -> data ] . child = node -> right -> data ; } preprocess ( node -> right , subsets ) ; } void initialise ( struct subset subsets [ ] ) { memset ( subsets , 0 , ( V + 1 ) * sizeof ( struct subset ) ) ; for ( int i = 1 ; i <= V ; i ++ ) subsets [ i ] . color = WHITE ; return ; } void printLCAs ( Node * root , Query q [ ] , int m ) { struct subset * subsets = new subset [ V + 1 ] ; initialise ( subsets ) ; preprocess ( root , subsets ) ; lcaWalk ( root -> data , q , m , subsets ) ; } int main ( ) { Node * root = newNode ( 1 ) ; root -> left = newNode ( 2 ) ; root -> right = newNode ( 3 ) ; root -> left -> left = newNode ( 4 ) ; root -> left -> right = newNode ( 5 ) ; Query q [ ] = { { 5 , 4 } , { 1 , 3 } , { 2 , 3 } } ; int m = sizeof ( q ) / sizeof ( q [ 0 ] ) ; printLCAs ( root , q , m ) ; return 0 ; }