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Count smaller elements on right side using Set in C++ STL
  • Difficulty Level : Medium
  • Last Updated : 14 Jun, 2019

Write a function to count the number of smaller elements on the right of each element in an array. Given an unsorted array arr[] of distinct integers, construct another array countSmaller[] such that countSmaller[i] contains the count of smaller elements on right side of each element arr[i] in the array.

Input : arr[] =  {12, 1, 2, 3, 0, 11, 4}
Output :countSmaller[]  =  {6, 1, 1, 1, 0, 1, 0} 

Input :arr[]={5, 4, 3, 2, 1}
Output :countSmaller[]={4, 3, 2, 1, 0}

In this post an easy implementation of is discussed.

Create an empty Set in C++ STL (Note that Set in C++ STL is implemented Self Balancing Binary Search Tree).

  1. Traverse the array element from i=len-1 to 0 and insert every element in a set.
  2. Find the first element that is lower than A[i] using lower_bound function.
  3. Find the distance between above found element and the beginning of the set using distance function.
  4. Store the distance in another array Lets say CountSmaller.
  5. Print that array .

// CPP program to find count of smaller
// elements on right side using set in C++
// STL.
#include <bits/stdc++.h>
using namespace std;
void countSmallerRight(int A[], int len)
    set<int> s;
    int countSmaller[len];
    for (int i = len - 1; i >= 0; i--) {
        auto it = s.lower_bound(A[i]);
        countSmaller[i] = distance(s.begin(), it);
    for (int i = 0; i < len; i++)
        cout << countSmaller[i] << " ";
// Driver code
int main()
    int A[] = {12, 1, 2, 3, 0, 11, 4};
    int len = sizeof(A) / sizeof(int);
    countSmallerRight(A, len);
    return 0;
6 1 1 1 0 1 0

Note that the above implementation takes worst-case time complexity O(n^2) as the worst case time complexity of distance function is O(n) but the above implementation is very simple and works better than the naive algorithm in the average case.

Above approach works for unique elements but for duplicate elements just replace Set with Multiset.

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