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

Last Updated : 29 Aug, 2022

Given two unsorted arrays arr1[] and arr2[], the task is to find the sum of elements of arr1[] such that the 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: The idea behind an efficient solution for the above problem is to use hashing of the second array and then find the cumulative sum of a hashed array. After that, the count of elements in the 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 the second array less than or equal to elements of 1st array from where the sum of elements of the first array can be calculated corresponding to the maximum frequency in the frequency array.

Below is the implementation of the above approach:

C++

   // 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;
}
 
  

Java

   // 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
 
  

Python3

   # 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
 
  

C#

   // 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.
 
  

PHP

   <?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
?>
 
  

Javascript

   <script>
 
// Javascript implementation of the approach
 
// Function to return the required sum
function findSumofEle(arr1, m, arr2, n)
{
    let MAX = 100000;
     
    // Creating hash array initially
    // filled with zero
    let hash = new Array(MAX);
     
    for(let i = 0; i < MAX; i++) 
        hash[i] = 0;
 
    // Calculate the frequency
    // of elements of arr2[]
    for(let 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(let 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[]
    let maximumFreq = 0;
    for(let i = 0; i < m; i++)
    {
        maximumFreq = Math.max(maximumFreq,
                               hash[arr1[i]]);
    }
 
    // Calculate the sum of elements from arr1[]
    // corresponding to maximum frequency
    let sumOfElements = 0;
    for(let i = 0; i < m; i++)
    {
        if (maximumFreq == hash[arr1[i]])
           sumOfElements += arr1[i];
    }
     
    // Return the required sum
    return sumOfElements;
}
 
// Driver code
let arr1 = [ 2, 5, 6, 8 ];
let arr2 = [ 4, 10 ];
let m = arr1.length;
let n = arr2.length;
 
document.write(findSumofEle(arr1, m, arr2, n));
 
// This code is contributed by mohit kumar 29
 
</script>
 
  

Output

Time Complexity: O(MAX)
Auxiliary Space: O(MAX), since MAX extra space has been taken.

Another efficient approach: Using Standard Template Library (STL)
In this approach, we will first sort the 2nd array. Then we will iterate in the first array and for each element in the first array, we will find the count of smaller elements in arr2 using lower_bound STL in O(log(n)) time. If the count of such elements is maximum then we can say that the corresponding element in arr1 will be in the answer. In this way, we keep on iterating in the 1st array and try to find the elements with the maximum count in the 2nd array and we will add those elements to the answer. The time complexity of this approach is O(n*log(n)+m*log(n)) and hence it is better than the previous approach for small values of n and m. Also, the auxiliary space in this approach is O(1) which is better than the previous approach.

Below is the implementation of the above approach:

C++

   // C++ implementation of the approach
#include <bits/stdc++.h>
using namespace std;
 
// Function to return the required sum
int findSumofEle(int arr1[], int m, int arr2[], int n)
{
    // Variable to store the 
    // maximum count of numbers
    // which are smaller than 
    // any element
    int maxi=INT_MIN;
    // Variable to store the answer
    int ans=0;
    sort(arr2,arr2+n);
    for(int i=0;i<m;i++)
    {
        // find the index of first element 
        // in arr2 which is greater than 
        // current element in arr1
        int y = lower_bound(arr2,arr2+n,arr1[i]+1)-arr2;
        // subtracting 1 to get the count of all smaller 
        // elements
        y=y-1;
        // if the count of all such element 
        // is highest for this element in arr1
        // then it will be the answer
        if(y>maxi)
        {
            maxi=y;
            ans=arr1[i];
        }
        // if count of all such element is 
        // equal to highest for this element
        // in arr1 then add this element also in answer
        else if(y==maxi)
        {
            ans+=arr1[i];
        }
    }
    // Return the answer
    return ans;
}
 
// Driver code
int main()
{
    int arr1[] = {5, 10, 2, 6, 1, 8, 6, 12};
    int arr2[] = { 6, 5, 11, 4, 2, 3, 7};
    int m = sizeof(arr1) / sizeof(arr1[0]);
    int n = sizeof(arr2) / sizeof(arr2[0]);
 
    cout << findSumofEle(arr1, m, arr2, n);
 
    return 0;
}
 
// This code is contributed by Pushpesh Raj
 
  

Java

   // Java implementation of the approach
import java.util.*;
 
class GFG {
  static int lower_bound(int[] arr, int elem)
  {
    for (int i = 0; i < arr.length; i++)
      if (elem <= arr[i])
        return i;
    return arr.length;
  }
 
  // Function to return the required sum
  static int findSumofEle(int[] arr1, int m, int[] arr2,
                          int n)
  {
    // Variable to store the
    // maximum count of numbers
    // which are smaller than
    // any element
    int maxi = Integer.MIN_VALUE;
 
    // Variable to store the answer
    int ans = 0;
    Arrays.sort(arr2);
    for (int i = 0; i < m; i++)
    {
 
      // find the index of first element
      // in arr2 which is greater than
      // current element in arr1
      int y = lower_bound(arr2, arr1[i] + 1);
 
      // subtracting 1 to get the count of all smaller
      // elements
      y = y - 1;
 
      // if the count of all such element
      // is highest for this element in arr1
      // then it will be the answer
      if (y > maxi) {
        maxi = y;
        ans = arr1[i];
      }
 
      // if count of all such element is
      // equal to highest for this element
      // in arr1 then add this element also in answer
      else if (y == maxi) {
        ans += arr1[i];
      }
    }
 
    // Return the answer
    return ans;
  }
 
  // Driver code
  public static void main(String[] args)
  {
    int[] arr1 = { 5, 10, 2, 6, 1, 8, 6, 12 };
    int[] arr2 = { 6, 5, 11, 4, 2, 3, 7 };
    int m = arr1.length;
    int n = arr2.length;
 
    System.out.println(findSumofEle(arr1, m, arr2, n));
  }
}
 
// This code is contributed by phasing17
 
  

Python3

   # Python3 implementation of the approach
def lower_bound(arr, n, elem):
    for i in range(n):
        if (arr[i] >= elem):
            return i;
    return n;
     
# function to return the required sum
def findSumofEle(arr1, m, arr2, n):
 
    # Variable to store the 
    # maximum count of numbers
    # which are smaller than 
    # any element
    maxi= -1000000;
    # Variable to store the answer
    ans=0;
    arr2.sort();
     
    for i in range(m):
     
        # find the index of first element 
        # in arr2 which is greater than 
        # current element in arr1
        y = lower_bound(arr2, n, arr1[i]+1);
         
        # subtracting 1 to get the count of all smaller 
        # elements
        y = y - 1;
         
        # if the count of all such element 
        # is highest for this element in arr1
        # then it will be the answer
        if(y > maxi):
            maxi = y;
            ans = arr1[i];
         
        # if count of all such element is 
        # equal to highest for this element
        # in arr1 then add this element also in answer
        elif(y==maxi):
            ans+=arr1[i];
     
     
    # Return the answer
    return ans;
 
# Driver code
arr1 = [5, 10, 2, 6, 1, 8, 6, 12];
arr2 = [ 6, 5, 11, 4, 2, 3, 7];
m = len(arr1);
n = len(arr2)
 
print(findSumofEle(arr1, m, arr2, n));
 
# This code is contributed by phasing17
 
  

C#

   // C# implementation of the approach
 
using System;
using System.Collections.Generic;
 
class GFG
{
    static int lower_bound(int[] arr, int elem)
    {
        for (int i = 0; i < arr.Length; i++)
            if (elem <= arr[i])
                return i;
        return arr.Length;
    }
    // Function to return the required sum
    static int findSumofEle(int[] arr1, int m, int[] arr2, int n)
    {
        // Variable to store the 
        // maximum count of numbers
        // which are smaller than 
        // any element
        int maxi= Int32.MinValue;
        // Variable to store the answer
        int ans=0;
        Array.Sort(arr2);
        for(int i=0;i<m;i++)
        {
            // find the index of first element 
            // in arr2 which is greater than 
            // current element in arr1
            int y = lower_bound(arr2, arr1[i]+1);
            // subtracting 1 to get the count of all smaller 
            // elements
            y=y-1;
            // if the count of all such element 
            // is highest for this element in arr1
            // then it will be the answer
            if(y>maxi)
            {
                maxi=y;
                ans=arr1[i];
            }
            // if count of all such element is 
            // equal to highest for this element
            // in arr1 then add this element also in answer
            else if(y==maxi)
            {
                ans+=arr1[i];
            }
        }
        // Return the answer
        return ans;
    }
     
    // Driver code
    public static void Main(string[] args)
    {
        int[] arr1 = {5, 10, 2, 6, 1, 8, 6, 12};
        int[] arr2 = { 6, 5, 11, 4, 2, 3, 7};
        int m = arr1.Length;
        int n = arr2.Length;
     
        Console.WriteLine(findSumofEle(arr1, m, arr2, n));
     
    }
}
 
// This code is contributed by phasing17
 
  

Javascript

   // JavaScript implementation of the approach
function lower_bound(arr, n, elem)
{
    for (var i = 0; i < n; i++)
        if (arr[i] >= elem)
            return i;
    return n;
     
}
 
// Function to return the required sum
function findSumofEle(arr1, m, arr2, n)
{
    // Variable to store the 
    // maximum count of numbers
    // which are smaller than 
    // any element
    let maxi= -1000000;
    // Variable to store the answer
    let ans=0;
    arr2.sort();
     
    for(var i=0;i<m;i++)
    {
        // find the index of first element 
        // in arr2 which is greater than 
        // current element in arr1
        var y = lower_bound(arr2, n, arr1[i]+1);
         
        // subtracting 1 to get the count of all smaller 
        // elements
        y = y - 1;
         
        // if the count of all such element 
        // is highest for this element in arr1
        // then it will be the answer
        if(y > maxi)
        {
            maxi = y;
            ans = arr1[i];
        }
         
        // if count of all such element is 
        // equal to highest for this element
        // in arr1 then add this element also in answer
        else if(y==maxi)
        {
            ans+=arr1[i];
        }
    }
     
    // Return the answer
    return ans;
}
 
// Driver code
let arr1 = [5, 10, 2, 6, 1, 8, 6, 12];
let arr2 = [ 6, 5, 11, 4, 2, 3, 7];
let m = arr1.length;
let n = arr2.length;
 
console.log(findSumofEle(arr1, m, arr2, n));
 
// This code is contributed by phasing17
 
  

Output

Time Complexity: O(n*log(n)+m*log(n)) where m and n are size of the array.
Auxiliary Space: O(1)

Choose two elements from the given array such that their sum is not present in any of the arrays

Shivam.Pradhan

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