Count smaller elements on right side and greater elements on left side using Binary Index Tree | C ++ implementation of the approach ; Function to return the sum of arr [ 0. . index ] This function assumes that the array is preprocessed and partial sums of array elements are stored in BITree [ ] ; Traverse ancestors of BITree [ index ] ; Add current element of BITree to sum ; Move index to parent node in getSum View ; Updates a node in Binary Index Tree ( BITree ) at given index in BITree . The given value ' val ' is added to BITree [ i ] and all of its ancestors in tree . ; Traverse all ancestors and add ' val ' ; Add ' val ' to current node of BI Tree ; Update index to that of parent in update View ; Converts an array to an array with values from 1 to n and relative order of smaller and greater elements remains same . For example , { 7 , - 90 , 100 , 1 } is converted to { 3 , 1 , 4 , 2 } ; Create a copy of arrp [ ] in temp and sort the temp array in increasing order ; Traverse all array elements ; lower_bound ( ) Returns pointer to the first element greater than or equal to arr [ i ] ; Function to find smaller_right array ; Convert arr [ ] to an array with values from 1 to n and relative order of smaller and greater elements remains same . For example , { 7 , - 90 , 100 , 1 } is converted to { 3 , 1 , 4 , 2 } ; Create a BIT with size equal to maxElement + 1 ( Extra one is used so that elements can be directly be used as index ) ; To store smaller elements in right side and greater elements on left side ; Traverse all elements from right . ; Get count of elements smaller than arr [ i ] ; Add current element to BIT ; Print smaller_right array ; Find all left side greater elements ; Get count of elements greater than arr [ i ] ; Add current element to BIT ; Print greater_left array ; Driver code ; Function call
#include <bits/stdc++.h> NEW_LINE using namespace std ; int getSum ( int BITree [ ] , int index ) { while ( index > 0 ) { sum += BITree [ index ] ; index -= index & ( - index ) ; } return sum ; } void updateBIT ( int BITree [ ] , int n , int index , int val ) { while ( index <= n ) { BITree [ index ] += val ; index += index & ( - index ) ; } } void convert ( int arr [ ] , int n ) { int temp [ n ] ; for ( int i = 0 ; i < n ; i ++ ) temp [ i ] = arr [ i ] ; sort ( temp , temp + n ) ; for ( int i = 0 ; i < n ; i ++ ) { arr [ i ] = lower_bound ( temp , temp + n , arr [ i ] ) - temp + 1 ; } } void findElements ( int arr [ ] , int n ) { convert ( arr , n ) ; int BIT [ n + 1 ] ; for ( int i = 1 ; i <= n ; i ++ ) BIT [ i ] = 0 ; int smaller_right [ n ] , greater_left [ n ] ; for ( int i = n - 1 ; i >= 0 ; i -- ) { smaller_right [ i ] = getSum ( BIT , arr [ i ] - 1 ) ; updateBIT ( BIT , n , arr [ i ] , 1 ) ; } cout << " Smaller ▁ right : ▁ " ; for ( int i = 0 ; i < n ; i ++ ) cout << smaller_right [ i ] << " ▁ " ; cout << endl ; for ( int i = 1 ; i <= n ; i ++ ) BIT [ i ] = 0 ; for ( int i = 0 ; i < n ; i ++ ) { greater_left [ i ] = i - getSum ( BIT , arr [ i ] ) ; updateBIT ( BIT , n , arr [ i ] , 1 ) ; } cout << " Greater ▁ left : ▁ " ; for ( int i = 0 ; i < n ; i ++ ) cout << greater_left [ i ] << " ▁ " ; } int main ( ) { int arr [ ] = { 12 , 1 , 2 , 3 , 0 , 11 , 4 } ; int n = sizeof ( arr ) / sizeof ( arr [ 0 ] ) ; findElements ( arr , n ) ; return 0 ; }