Find Surpasser Count of each element in array

04 Jul, 2022
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]
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++
Java
Python3
C#
PHP
Javascript
// Naive C++ program to find surpasser count of// each element in array#include <bits/stdc++.h>using namespace std; // Function to find surpasser count of each element// in arrayvoid 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;}
// Naive Java program to find surpasser count// of each element in arrayimport 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.
# Naive Python3 program to find# surpasser count of each element in array # Function to find surpasser count of# each element in arraydef 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 arraydef printArray(arr, n):     for i in range(0, n):        print(arr[i], end = " ")     # Driver program to test above functionsarr = [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
// Naive C# program to find surpasser count// of each element in arrayusing 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// Naive PHP program to find// surpasser count of each// element in array // Function to find surpasser// count of each element in arrayfunction findSurpasser($arr, $n){    for ( $i = 0; $i < $n; $i++)    {        // stores surpasser count        // for element arr[i]        $count = 0;        for ( $j = $i + 1; $j < $n; $j++)            if ($arr[$j] > $arr[$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.?>
<script> // Naive Javascript program to find surpasser count// of each element in array     // Function to find surpasser count of    // each element in array    function findSurpasser(arr, n)    {        for (let i = 0; i < n; i++)        {                           // stores surpasser count for            // element arr[i]            let count = 0;            for (let j = i + 1; j < n; j++)                if (arr[j] > arr[i])                    count++;                   document.write(count +" ");        }    }           /* Function to print an array */    function printArray(arr, n)    {        for (let i = 0; i < n; i++)            document.write( arr[i] + " ");                       document.write();    }    // Driver Code             let arr = [ 2, 7, 5, 3, 0, 8, 1 ];        let n = arr.length;               document.write("Given array is " + "<br />");        printArray(arr, n);                 document.write("<br />");               document.write("Surpasser Count of"                               + " array is " + "<br />");        findSurpasser(arr, n);         </script>
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)
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++
Python3
// C++ program to find surpasser count of each element// in array#include <bits/stdc++.h>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 ofthe 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;}
# 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 sorteddef 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 arraydef 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
Given array is 
2 7 5 3 0 8 1 
Surpasser Count of array is 
4 1 1 1 2 0 0 
Time complexity of above solution is O(nlogn).
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