Sum of elements in 1st array such that number of elements less than or equal to them in 2nd array is maximum

Given two unsorted arrays arr1[] and arr2[], the task is to find the sum of elements of arr1[] such that number of elements less than or equal to them in arr2[] is maximum.

Examples:

Input: arr1[] = {1, 2, 3, 4, 7, 9}, arr2[] = {0, 1, 2, 1, 1, 4}
Output: 20
Below table shows the count of elements in arr2[] which are ≤ the elements of arr1[]



arr1[i] Count
1 4
2 5
3 5
4 6
7 6
9 6

Count for 4, 7 and 9 is maximum.
Hence, the resultant sum is 4 + 7 + 9 = 20.

Input:arr1[] = {5, 10, 2, 6, 1, 8, 6, 12}, arr2[] = {6, 5, 11, 4, 2, 3, 7}
Output: 12

Approach: Idea behind efficient solution for the above problem is to use hashing of second array and then finding the cumulative sum of hashed array. After that the count of elements in second array less than or equal to elements of 1st array can easily be calculated. This will give a frequency array which represents the count of elements in second array less than or equal to elements of 1st array from where the sum of elements of first array can be calculated corresponding to maximum frequency in frequency array.

Below is the implementation of the above approach:

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// C++ implementation of the approach
#include <iostream>
using namespace std;
#define MAX 100000
  
// Function to return the required sum
int findSumofEle(int arr1[], int m,
                 int arr2[], int n)
{
    // Creating hash array initially
    // filled with zero
    int hash[MAX] = { 0 };
  
    // Calculate the frequency
    // of elements of arr2[]
    for (int i = 0; i < n; i++)
        hash[arr2[i]]++;
  
    // Running sum of hash array
    // such that hash[i] will give count of
    // elements less than or equal to i in arr2[]
    for (int i = 1; i < MAX; i++)
        hash[i] = hash[i] + hash[i - 1];
  
    // To store the maximum value of
    // the number of elements in arr2[] which are
    // smaller than or equal to some element of arr1[]
    int maximumFreq = 0;
    for (int i = 0; i < m; i++)
        maximumFreq = max(maximumFreq, hash[arr1[i]]);
  
    // Calculate the sum of elements from arr1[]
    // corresponding to maximum frequency
    int sumOfElements = 0;
    for (int i = 0; i < m; i++)
        sumOfElements += (maximumFreq == hash[arr1[i]]) ? arr1[i] : 0;
  
    // Return the required sum
    return sumOfElements;
}
  
// Driver code
int main()
{
    int arr1[] = { 2, 5, 6, 8 };
    int arr2[] = { 4, 10 };
    int m = sizeof(arr1) / sizeof(arr1[0]);
    int n = sizeof(arr2) / sizeof(arr2[0]);
  
    cout << findSumofEle(arr1, m, arr2, n);
  
    return 0;
}
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// Java implementation of the approach
  
class GFG 
{
  
    static int MAX = 100000;
  
    // Function to return the required sum
    static int findSumofEle(int arr1[], int m,
                            int arr2[], int n)
    {
        // Creating hash array initially
        // filled with zero
        int hash[] = new int[MAX];
  
        // Calculate the frequency
        // of elements of arr2[]
        for (int i = 0; i < n; i++) 
        {
            hash[arr2[i]]++;
        }
  
        // Running sum of hash array
        // such that hash[i] will give count of
        // elements less than or equal to i in arr2[]
        for (int i = 1; i < MAX; i++)
        {
            hash[i] = hash[i] + hash[i - 1];
        }
  
        // To store the maximum value of
        // the number of elements in arr2[] which are
        // smaller than or equal to some element of arr1[]
        int maximumFreq = 0;
        for (int i = 0; i < m; i++)
        {
            maximumFreq = Math.max(maximumFreq, hash[arr1[i]]);
        }
  
        // Calculate the sum of elements from arr1[]
        // corresponding to maximum frequency
        int sumOfElements = 0;
        for (int i = 0; i < m; i++)
        {
            sumOfElements += (maximumFreq == hash[arr1[i]]) ? arr1[i] : 0;
        }
  
        // Return the required sum
        return sumOfElements;
    }
  
    // Driver code
    public static void main(String[] args) 
    {
        int arr1[] = {2, 5, 6, 8};
        int arr2[] = {4, 10};
        int m = arr1.length;
        int n = arr2.length;
  
        System.out.println(findSumofEle(arr1, m, arr2, n));
    }
}
  
// This code has been contributed by 29AjayKumar
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# Python 3 implementation of the approach
MAX = 100000
  
# Function to return the required sum
def findSumofEle(arr1, m, arr2, n):
      
    # Creating hash array initially
    # filled with zero
    hash = [0 for i in range(MAX)]
  
    # Calculate the frequency
    # of elements of arr2[]
    for i in range(n):
        hash[arr2[i]] += 1
  
    # Running sum of hash array
    # such that hash[i] will give count of
    # elements less than or equal to i in arr2[]
    for i in range(1, MAX, 1):
        hash[i] = hash[i] + hash[i - 1]
  
    # To store the maximum value of
    # the number of elements in arr2[] 
    # which are smaller than or equal 
    # to some element of arr1[]
    maximumFreq = 0
    for i in range(m):
        maximumFreq = max(maximumFreq, 
                          hash[arr1[i]])
  
    # Calculate the sum of elements from arr1[]
    # corresponding to maximum frequency
    sumOfElements = 0
    for i in range(m):
        if (maximumFreq == hash[arr1[i]]):
            sumOfElements += arr1[i]
  
    # Return the required sum
    return sumOfElements
  
# Driver code
if __name__ == '__main__':
    arr1 = [2, 5, 6, 8]
    arr2 = [4, 10]
    m = len(arr1)
    n = len(arr2) 
    print(findSumofEle(arr1, m, arr2, n))
  
# This code is contributed by
# Surendra_Gangwar
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// C# implementation of the approach
using System;
  
class GFG 
{
  
    static int MAX = 100000;
  
    // Function to return the required sum
    static int findSumofEle(int[] arr1, int m,
                            int[] arr2, int n)
    {
        // Creating hash array initially
        // filled with zero
        int[] hash = new int[MAX];
  
        // Calculate the frequency
        // of elements of arr2[]
        for (int i = 0; i < n; i++) 
        {
            hash[arr2[i]]++;
        }
  
        // Running sum of hash array
        // such that hash[i] will give count of
        // elements less than or equal to i in arr2[]
        for (int i = 1; i < MAX; i++)
        {
            hash[i] = hash[i] + hash[i - 1];
        }
  
        // To store the maximum value of
        // the number of elements in arr2[] which are
        // smaller than or equal to some element of arr1[]
        int maximumFreq = 0;
        for (int i = 0; i < m; i++)
        {
            maximumFreq = Math.Max(maximumFreq, hash[arr1[i]]);
        }
  
        // Calculate the sum of elements from arr1[]
        // corresponding to maximum frequency
        int sumOfElements = 0;
        for (int i = 0; i < m; i++)
        {
            sumOfElements += (maximumFreq == hash[arr1[i]]) ? arr1[i] : 0;
        }
  
        // Return the required sum
        return sumOfElements;
    }
  
    // Driver code
    public static void Main() 
    {
        int[] arr1 = {2, 5, 6, 8};
        int[] arr2 = {4, 10};
        int m = arr1.Length;
        int n = arr2.Length;
  
        Console.WriteLine(findSumofEle(arr1, m, arr2, n));
    }
}
  
// This code has been contributed by Code_Mech.
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<?php
// PHP implementation of the approach
$MAX = 10000;
  
// Function to return the required sum
function findSumofEle($arr1, $m, $arr2, $n)
{
    // Creating hash array initially
    // filled with zero
    $hash = array_fill(0, $GLOBALS['MAX'], 0);
  
    // Calculate the frequency
    // of elements of arr2[]
    for ($i = 0; $i < $n; $i++)
        $hash[$arr2[$i]]++;
  
    // Running sum of hash array
    // such that hash[i] will give count of
    // elements less than or equal to i in arr2[]
    for ($i = 1; $i < $GLOBALS['MAX']; $i++)
        $hash[$i] = $hash[$i] + $hash[$i - 1];
  
    // To store the maximum value of
    // the number of elements in arr2[] which are
    // smaller than or equal to some element of arr1[]
    $maximumFreq = 0;
    for ($i = 0; $i < $m; $i++)
        $maximumFreq = max($maximumFreq
                           $hash[$arr1[$i]]);
  
    // Calculate the sum of elements from arr1[]
    // corresponding to maximum frequency
    $sumOfElements = 0;
    for ($i = 0; $i < $m; $i++)
        $sumOfElements += ($maximumFreq == $hash[$arr1[$i]]) ?
                                                   $arr1[$i] : 0;
  
    // Return the required sum
    return $sumOfElements;
}
  
// Driver code
$arr1 = array( 2, 5, 6, 8 );
$arr2 = array( 4, 10 );
$m = count($arr1);
$n = count($arr2);
  
echo findSumofEle($arr1, $m, $arr2, $n);
  
// This code is contributed by Ryuga
?>
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Output:
19



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