# Find Surpasser Count of each element in array

A surpasser of an element of an array is a greater element to its right, therefore x[j] is a surpasser of x[i] if i < j and x[i] < x[j]. The surpasser count of an element is the number of surpassers. Given an array of distinct integers, for each element of the array find its surpasser count i.e. count the number of elements to the right that are greater than that element.

Examples :

```Input:  [2, 7, 5, 3, 0, 8, 1]
Output: [4, 1, 1, 1, 2, 0, 0]```
Recommended Practice

Method 1 (Naive): The naive solution would be to run two loops. For each element of the array, we count all elements greater than it to its right. The complexity of this solution is O(n2

Implementation:

## C++

 `// Naive C++ program to find surpasser count of``// each element in array``#include ``using` `namespace` `std;` `// Function to find surpasser count of each element``// in array``void` `findSurpasser(``int` `arr[], ``int` `n)``{``    ``for` `(``int` `i = 0; i < n; i++)``    ``{``        ``// stores surpasser count for element arr[i]``        ``int` `count = 0;``        ``for` `(``int` `j = i + 1; j < n; j++)``            ``if` `(arr[j] > arr[i])``                ``count++;` `        ``cout << count << ``" "``;``    ``}``}` `/* Function to print an array */``void` `printArray(``int` `arr[], ``int` `n)``{``    ``for` `(``int` `i = 0; i < n; i++)``        ``printf``(``"%d "``, arr[i]);``    ``printf``(``"\n"``);``}` `/* Driver program to test above functions */``int` `main()``{``    ``int` `arr[] = { 2, 7, 5, 3, 0, 8, 1 };``    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]);` `    ``printf``(``"Given array is \n"``);``    ``printArray(arr, n);` `    ``printf``(``"Surpasser Count of array is \n"``);``    ``findSurpasser(arr, n);` `    ``return` `0;``}`

## Java

 `// Naive Java program to find surpasser count``// of each element in array``import` `java.io.*;` `class` `GFG {` `    ``// Function to find surpasser count of ``    ``// each element in array``    ``static` `void` `findSurpasser(``int` `arr[], ``int` `n)``    ``{``        ``for` `(``int` `i = ``0``; i < n; i++)``        ``{``            ` `            ``// stores surpasser count for ``            ``// element arr[i]``            ``int` `count = ``0``;``            ``for` `(``int` `j = i + ``1``; j < n; j++)``                ``if` `(arr[j] > arr[i])``                    ``count++;``    ` `            ``System.out.print(count +``" "``);``        ``}``    ``}``    ` `    ``/* Function to print an array */``    ``static` `void` `printArray(``int` `arr[], ``int` `n)``    ``{``        ``for` `(``int` `i = ``0``; i < n; i++)``            ``System.out.print( arr[i] + ``" "``);``            ` `        ``System.out.println();``    ``}``    ` `    ``// Driver program to test above functions``    ``public` `static` `void` `main (String[] args) ``    ``{``        ``int` `arr[] = { ``2``, ``7``, ``5``, ``3``, ``0``, ``8``, ``1` `};``        ``int` `n = arr.length;``    ` `        ``System.out.println(``"Given array is "``);``        ``printArray(arr, n);``    ` `        ``System.out.println(``"Surpasser Count of"``                               ``+ ``" array is "``);``        ``findSurpasser(arr, n);``    ``}``}` `// This code is contributed by Anuj_67.`

## Python3

 `# Naive Python3 program to find ``# surpasser count of each element in array` `# Function to find surpasser count of ``# each element in array``def` `findSurpasser(arr, n):` `    ``for` `i ``in` `range``(``0``, n):``    ` `        ``# stores surpasser count for element``        ``# arr[i]``        ``count ``=` `0``;` `        ``for` `j ``in` `range` `(i ``+` `1``, n):``            ``if` `(arr[j] > arr[i]):``                ``count ``+``=` `1` `        ``print``(count, end ``=` `" "``)`  `# Function to print an array ``def` `printArray(arr, n):` `    ``for` `i ``in` `range``(``0``, n):``        ``print``(arr[i], end ``=` `" "``)``    ` `# Driver program to test above functions ``arr ``=` `[``2``, ``7``, ``5``, ``3``, ``0``, ``8``, ``1` `]``n ``=` `len``(arr)` `print``(``"Given array is"``)``printArray(arr , n)` `print``(``"\nSurpasser Count of array is"``);``findSurpasser(arr , n)` `# This code is contributed by Smitha Dinesh Semwal`

## C#

 `// Naive C# program to find surpasser count``// of each element in array``using` `System;` `class` `GFG {` `    ``// Function to find surpasser count of ``    ``// each element in array``    ``static` `void` `findSurpasser(``int` `[]arr, ``int` `n)``    ``{``        ``for` `(``int` `i = 0; i < n; i++)``        ``{``            ` `            ``// stores surpasser count for ``            ``// element arr[i]``            ``int` `count = 0;``            ``for` `(``int` `j = i + 1; j < n; j++)``                ``if` `(arr[j] > arr[i])``                    ``count++;``    ` `            ``Console.Write(count + ``" "``);``        ``}``    ``}``    ` `    ``/* Function to print an array */``    ``static` `void` `printArray(``int` `[]arr, ``int` `n)``    ``{``        ``for` `(``int` `i = 0; i < n; i++)``            ``Console.Write( arr[i] + ``" "``);``            ` `        ``Console.WriteLine();``    ``}``    ` `    ``// Driver program to test above functions``    ``public` `static` `void` `Main () ``    ``{``        ``int` `[]arr = { 2, 7, 5, 3, 0, 8, 1 };``        ``int` `n = arr.Length;``    ` `        ``Console.WriteLine(``"Given array is "``);``        ``printArray(arr, n);``    ` `        ``Console.WriteLine(``"Surpasser Count of"``                            ``+ ``" array is "``);``        ``findSurpasser(arr, n);``    ``}``}` `// This code is contributed by Anuj_67.`

## PHP

 ` ``\$arr``[``\$i``])``                ``\$count``++;` `        ``echo` `\$count` `, ``" "``;``    ``}``}` `/* Function to print an array */``function` `printArray( ``\$arr``, ``\$n``)``{``    ``for` `( ``\$i` `= 0; ``\$i` `< ``\$n``; ``\$i``++)``        ``echo` `\$arr``[``\$i``],``" "``;``        ``echo` `"\n"``;``}` `// Driver Code``\$arr` `= ``array``( 2, 7, 5, 3, 0, 8, 1 );``\$n` `= ``count``(``\$arr``);` `echo` `"Given array is \n"``;``printArray(``\$arr``, ``\$n``);` `echo` `"Surpasser Count of array is \n"``;``findSurpasser(``\$arr``, ``\$n``);` `// This code is contributed by Anuj_67.``?>`

## Javascript

 ``

Output
```Given array is
2 7 5 3 0 8 1
Surpasser Count of array is
4 1 1 1 2 0 0 ```

Time Complexity : O(n2)

Auxiliary Space: O(1) because using constant space for variables

Method 2 (Uses Merge Sort): For any element of the array, we can easily find out number of elements to the right that are greater than that element if we know number of elements to its right that are less than that element. The idea is to count the number of inversions for each element of the array using merge sort. So, surpasser count of an element at position i will be equal to “n – i – inversion-count” at that position where n is the size of the array.

We have already discussed how to find inversion count of complete array here. We have modified the discussed approach to find number of inversions for each element of the array instead of returning inversion count of whole array. Also, as all elements of the array are distinct, we maintain a map that stores inversion count for each element of the array.

Below is C++ implementation of above idea

## C++

 `// C++ program to find surpasser count of each element``// in array``#include ``using` `namespace` `std;` `/* Function to merge the two haves arr[l..m] and``   ``arr[m+1..r] of array arr[] */``int` `merge(``int` `arr[], ``int` `l, ``int` `m, ``int` `r,``          ``unordered_map<``int``, ``int``> &hm)``{``    ``int` `i, j, k;``    ``int` `n1 = m - l + 1;``    ``int` `n2 = r - m;` `    ``/* create temp arrays */``    ``int` `L[n1], R[n2];` `    ``/* Copy data to temp arrays L[] and R[] */``    ``for` `(i = 0; i < n1; i++)``        ``L[i] = arr[l + i];` `    ``for` `(j = 0; j < n2; j++)``        ``R[j] = arr[m + 1 + j];` `    ``/* Merge the temp arrays back into arr[l..r]*/``    ``i = 0, j = 0, k = l;``    ``int` `c = 0;``    ``while` `(i < n1 && j < n2)``    ``{``        ``if` `(L[i] <= R[j])``        ``{``            ``// increment inversion count of L[i]``            ``hm[L[i]] += c;``            ``arr[k++] = L[i++];``        ``}``        ``else``        ``{``            ``arr[k++] = R[j++];` `            ``// inversion found``            ``c++;``        ``}``    ``}` `    ``/* Copy the remaining elements of L[], if``    ``there are any */``    ``while` `(i < n1)``    ``{``        ``hm[L[i]] += c;``        ``arr[k++] = L[i++];``    ``}` `    ``/* Copy the remaining elements of R[], if``    ``there are any */``    ``while` `(j < n2)``        ``arr[k++] = R[j++];``}` `/* l is for left index and r is right index of``the sub-array of arr to be sorted */``int` `mergeSort(``int` `arr[], ``int` `l, ``int` `r,``              ``unordered_map<``int``, ``int``> &hm)``{``    ``if` `(l < r)``    ``{``        ``int` `m = l + (r - l) / 2;``        ``mergeSort(arr, l, m, hm);``        ``mergeSort(arr, m + 1, r, hm);``        ``merge(arr, l, m, r, hm);``    ``}``}` `/* Function to print an array */``void` `printArray(``int` `arr[], ``int` `n)``{``    ``for` `(``int` `i = 0; i < n; i++)``        ``printf``(``"%d "``, arr[i]);``    ``printf``(``"\n"``);``}` `void` `findSurpasser(``int` `arr[], ``int` `n)``{``    ``// To store inversion count for elements``    ``unordered_map<``int``, ``int``> hm;` `    ``// To store copy of array``    ``int` `dup[n];``    ``memcpy``(dup, arr, n*``sizeof``(arr[0]));` `    ``// Sort the copy and store inversion count``    ``// for each element.``    ``mergeSort(dup, 0, n - 1, hm);` `    ``printf``(``"Surpasser Count of array is \n"``);``    ``for` `(``int` `i = 0; i < n; i++)``        ``printf``(``"%d "``, (n - 1) - i - hm[arr[i]]);``}` `/* Driver program to test above functions */``int` `main()``{``    ``int` `arr[] = { 2, 7, 5, 3, 0, 8, 1 };``    ``int` `n = ``sizeof``(arr) / ``sizeof``(arr[0]);` `    ``printf``(``"Given array is \n"``);``    ``printArray(arr, n);` `    ``findSurpasser(arr, n);` `    ``return` `0;``}`

## Java

 `// Java program to find surpasser count of each element``// in array``import` `java.util.Arrays;``import` `java.util.HashMap;``import` `java.util.Map;` `public` `class` `Surpasser {` `    ``/* Function to merge the two haves arr[l..m] and``    ``arr[m+1..r] of array arr[] */``    ``public` `static` `void` `merge(``int``[] arr, ``int` `l, ``int` `m, ``int` `r, Map hm) {``        ``int` `n1 = m - l + ``1``;``        ``int` `n2 = r - m;``        ``/* create temp arrays */``        ``int``[] L = ``new` `int``[n1];``        ``int``[] R = ``new` `int``[n2];``        ` `        ``/* Copy data to temp arrays L[] and R[] */``        ``for` `(``int` `i = ``0``; i < n1; i++) {``            ``L[i] = arr[l + i];``        ``}``        ``for` `(``int` `j = ``0``; j < n2; j++) {``            ``R[j] = arr[m + ``1` `+ j];``        ``}``        ` `        ``/* Merge the temp arrays back into arr[l..r]*/``        ``int` `i = ``0``, j = ``0``, k = l;``        ``int` `c = ``0``;``        ``while` `(i < n1 && j < n2) {``            ``if` `(L[i] <= R[j]) {``                ``// increment inversion count of L[i]``                ``hm.put(L[i], hm.getOrDefault(L[i], ``0``) + c);``                ``arr[k++] = L[i++];``            ``} ``else` `{``                ``// inversion found``                ``arr[k++] = R[j++];``                ``c++;``            ``}``        ``}``        ` `        ``/* Copy the remaining elements of L[], if``        ``there are any */``        ``while` `(i < n1) {``            ``hm.put(L[i], hm.getOrDefault(L[i], ``0``) + c);``            ``arr[k++] = L[i++];``        ``}``        ``/* Copy the remaining elements of R[], if``        ``there are any */``        ``while` `(j < n2) {``            ``arr[k++] = R[j++];``        ``}``    ``}``    ` `    ``/* l is for left index and r is right index of``    ``the sub-array of arr to be sorted */``    ``public` `static` `void` `mergeSort(``int``[] arr, ``int` `l, ``int` `r, Map hm) {``        ``if` `(l < r) {``            ``int` `m = l + (r - l) / ``2``;``            ``mergeSort(arr, l, m, hm);``            ``mergeSort(arr, m + ``1``, r, hm);``            ``merge(arr, l, m, r, hm);``        ``}``    ``}``    ` `    ``/* Function to print an array */``    ``public` `static` `void` `findSurpasser(``int``[] arr,``int` `n)``    ``{``        ``// To store inversion count for elements``        ``Map hm = ``new` `HashMap<>();``        ` `        ``// To store copy of array``        ``int``[] dup = arr.clone();``        ` `        ``// Sort the copy and store inversion count``        ``// for each element.``        ``mergeSort(dup, ``0``, n - ``1``, hm);` `        ``System.out.println(``"Surpasser Count of array is: "``);``        ``for` `(``int` `i = ``0``; i < n; i++) {``            ``if``(hm.containsKey(arr[i]))``            ``System.out.print((n - ``1``) - i - hm.get(arr[i]) + ``" "``);``            ``else``            ``System.out.print((n - ``1``) - i + ``" "``);``        ``}``        ``System.out.println();``    ``}``    ` `    ``/* Driver program to test above functions */``    ``public` `static` `void` `main(String[] args) {``        ``int``[] arr = {``2``, ``7``, ``5``, ``3``, ``0``, ``8``, ``1``};``        ``int` `n = arr.length;` `        ``System.out.println(``"Given array is: "` `+ Arrays.toString(arr));` `        ``findSurpasser(arr, n);``    ``}``}` `// This code is contributed by Aman Kumar`

## Python3

 `# Python program to find surpasser count of each element``# in array` `#  Function to merge the two haves arr[l..m] and``# arr[m+1..r] of array arr[] ``def` `merge(arr, l, m, r, hm):` `    ``n1 ``=` `m ``-` `l ``+` `1``    ``n2 ``=` `r ``-` `m` `    ``# create temp arrays``    ``L``=` `[``0` `for` `i ``in` `range``(n1)]``    ``R ``=` `[``0` `for` `i ``in` `range``(n2)]` `    ``# Copy data to temp arrays L[] and R[]``    ``for` `i ``in` `range``(n1):``        ``L[i] ``=` `arr[l ``+` `i]` `    ``for` `j ``in` `range``(n2):``        ``R[j] ``=` `arr[m ``+` `1` `+` `j]` `    ``#  Merge the temp arrays back into arr[l..r]``    ``i,j,k,c ``=` `0``,``0``,l,``0``    ``while` `(i < n1 ``and` `j < n2):``        ``if` `(L[i] <``=` `R[j]):``            ``# increment inversion count of L[i]``            ``if``(L[i] ``in` `hm):``                ``hm[L[i]] ``+``=` `c``            ``else` `:``                ``hm[L[i]] ``=` `c``            ``arr[k] ``=` `L[i]``            ``k ``+``=` `1``            ``i ``+``=` `1``        ``else``:``            ``arr[k] ``=` `R[j]` `            ``# inversion found``            ``c ``+``=` `1``            ``k ``+``=` `1``            ``j ``+``=` `1` `    ``# Copy the remaining elements of L[], if``    ``# there are any``    ``while` `(i < n1):``        ``if``(L[i] ``in` `hm):``            ``hm[L[i]] ``+``=` `c``        ``else` `:``            ``hm[L[i]] ``=` `c``        ``arr[k] ``=` `L[i]``        ``k ``+``=` `1``        ``i ``+``=` `1` `    ``# Copy the remaining elements of R[], if``    ``# there are any ``    ``while` `(j < n2):``        ``arr[k] ``=` `R[j]``        ``k ``+``=` `1``        ``j ``+``=` `1` `# l is for left index and r is right index of``# the sub-array of arr to be sorted``def` `mergeSort(arr,l,r,hm):``    ``if` `(l < r):``        ``m ``=` `l ``+` `(r ``-` `l) ``/``/` `2``        ``mergeSort(arr, l, m, hm)``        ``mergeSort(arr, m ``+` `1``, r, hm)``        ``merge(arr, l, m, r, hm)` `#  Function to print an array ``def` `printArray(arr,n):` `    ``for` `i ``in` `range``(n):``        ``print``(arr[i],end ``=` `" "``)``    ``print``("")` `def` `findSurpasser(arr, n):``    ``# To store inversion count for elements``    ``hm ``=` `{}` `    ``# To store copy of array``    ``dup ``=` `arr[:]` `    ``# Sort the copy and store inversion count``    ``# for each element.``    ``mergeSort(dup, ``0``, n ``-` `1``, hm)` `    ``print``(``"Surpasser Count of array is "``)``    ``for` `i ``in` `range``(n):``        ``print``((n ``-` `1``) ``-` `i ``-` `(hm[arr[i]] ``if` `arr[i] ``in` `hm ``else` `0``),end ``=` `" "``)` `# Driver program to test above functions ` `arr ``=` `[ ``2``, ``7``, ``5``, ``3``, ``0``, ``8``, ``1` `]``n ``=` `len``(arr)` `print``(``"Given array is "``)``printArray(arr, n)` `findSurpasser(arr, n)` `# This code is contributed by shinjanpatra`

## Javascript

 ``

## C#

 `// C++ program to find surpasser count of each element``// in array``using` `System;``using` `System.Collections.Generic;` `public` `class` `Surpasser {` `    ``/* Function to merge the two haves arr[l..m] and``    ``arr[m+1..r] of array arr[] */``    ``public` `static` `void` `Merge(``int``[] arr, ``int` `l, ``int` `m, ``int` `r,``                             ``Dictionary<``int``, ``int``> hm)``    ``{``        ``int` `n1 = m - l + 1;``        ``int` `n2 = r - m;``        ``/* create temp arrays */``        ``int``[] L = ``new` `int``[n1];``        ``int``[] R = ``new` `int``[n2];` `        ``/* Copy data to temp arrays L[] and R[] */``        ``for` `(``int` `x = 0; x < n1; x++) {``            ``L[x] = arr[l + x];``        ``}``        ``for` `(``int` `y = 0; y < n2; y++) {``            ``R[y] = arr[m + 1 + y];``        ``}` `        ``/* Merge the temp arrays back into arr[l..r]*/``        ``int` `i = 0, j = 0, k = l;``        ``int` `c = 0;``        ``while` `(i < n1 && j < n2) {``            ``if` `(L[i] <= R[j]) {``                ``// increment inversion count of L[i]``                ``if` `(hm.ContainsKey(L[i])) {``                    ``hm[L[i]] += c;``                ``}``                ``else` `{``                    ``hm.Add(L[i], c);``                ``}``                ``arr[k++] = L[i++];``            ``}``            ``else` `{``                ``// inversion found``                ``arr[k++] = R[j++];``                ``c++;``            ``}``        ``}` `        ``/* Copy the remaining elements of L[], if``        ``there are any */``        ``while` `(i < n1) {``            ``if` `(hm.ContainsKey(L[i])) {``                ``hm[L[i]] += c;``            ``}``            ``else` `{``                ``hm.Add(L[i], c);``            ``}``            ``arr[k++] = L[i++];``        ``}``        ``/* Copy the remaining elements of R[], if``        ``there are any */``        ``while` `(j < n2) {``            ``arr[k++] = R[j++];``        ``}``    ``}` `    ``/* l is for left index and r is right index of``   ``the sub-array of arr to be sorted */``    ``public` `static` `void` `MergeSort(``int``[] arr, ``int` `l, ``int` `r,``                                 ``Dictionary<``int``, ``int``> hm)``    ``{``        ``if` `(l < r) {``            ``int` `m = l + (r - l) / 2;``            ``MergeSort(arr, l, m, hm);``            ``MergeSort(arr, m + 1, r, hm);``            ``Merge(arr, l, m, r, hm);``        ``}``    ``}` `    ``/* Function to print an array */``    ``public` `static` `void` `FindSurpasser(``int``[] arr, ``int` `n)``    ``{``        ``// To store inversion count for elements``        ``Dictionary<``int``, ``int``> hm``            ``= ``new` `Dictionary<``int``, ``int``>();` `        ``// To store copy of array``        ``int``[] dup = (``int``[])arr.Clone();` `        ``// Sort the copy and store inversion count``        ``// for each element.``        ``MergeSort(dup, 0, n - 1, hm);` `        ``Console.Write(``"Surpasser Count of array is: \n"``);``        ``for` `(``int` `i = 0; i < n; i++) {``            ``if` `(hm.ContainsKey(arr[i])) {``                ``Console.Write((n - 1) - i - hm[arr[i]]``                              ``+ ``" "``);``            ``}``            ``else` `{``                ``Console.Write((n - 1) - i + ``" "``);``            ``}``        ``}``        ``Console.WriteLine();``    ``}` `    ``/* Driver program to test above functions */``    ``public` `static` `void` `Main(``string``[] args)``    ``{``        ``int``[] arr = { 2, 7, 5, 3, 0, 8, 1 };``        ``int` `n = arr.Length;` `        ``Console.WriteLine(``"Given array is: \n"``                          ``+ ``string``.Join(``" "``, arr));` `        ``FindSurpasser(arr, n);``    ``}``}``// This code is contributed by prajwal kandekar`

Output
```Given array is
2 7 5 3 0 8 1
Surpasser Count of array is
4 1 1 1 2 0 0 ```

Time Complexity: O(nlogn)
Auxiliary Space: O(n)

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