Sum of two elements whose sum is closest to zero

Given an integer array of N elements. You need to find the maximum sum of two elements such that sum is closest to zero.

Note: In Case if we have two of more ways to form sum of two elements closest to zero return the maximum sum.

Example:

Input: N = 3, arr[] = {-8 -66 -60}
Output: -68
Explanation: Sum of two elements closest to zero is -68 using numbers -60 and -8.

Input: N = 6, arr[] = {-21 -67 -37 -18 4 -65}
Output: -14
Explanation: Sum of two elements closest to zero is -14 using numbers -18 and 4.

Two elements whose sum is closest to zero using Nested Loops:

We use the brute-force method that checks the sum of every possible pair of elements in the array and keeps track of the pair with the minimum absolute sum.

Step-by-step approach:

• Initialize variables min_l and min_r to represent the indices of the pair with the minimum sum.
• Initialize min_sum with the sum of the first two elements (arr[0] + arr[1]).
• Run a loop l from 0 to n-1.
  • Run a loop r from l+1 to n.
    • For each pair of indices (l, r), calculate the sum of the corresponding elements (arr[l] + arr[r]).
    • If the absolute value of the calculated sum is less than the absolute value of min_sum, update min_sum, min_l, and min_r with the current sum and indices.
• After completing the iteration, return the sum of the pair with indices min_l and min_r.

Below is the implementation of the above approach:

C++

// C++ code to find Two elements
// whose sum is closest to zero
#include <bits/stdc++.h>
using namespace std;

// Function to find the two elements whose sum is closest to
// zero
int minAbsSumPair(int arr[], int n)
{
    // Initialize left and right pointers, minimum sum, sum,
    // and minimum left and right indices
    int l, r, min_sum, sum, min_l, min_r;

    // Initialize minimum sum with the sum of the first two
    // elements
    min_l = 0;
    min_r = 1;
    min_sum = arr[0] + arr[1];

    // Loop through the array
    for (l = 0; l < n - 1; l++) {
        // Inner loop to find the element with the minimum
        // sum
        for (r = l + 1; r < n; r++) {
            // Calculate the sum of the current pair
            sum = arr[l] + arr[r];

            // If the absolute value of the current sum is
            // less than the absolute value of the minimum
            // sum
            if (abs(min_sum) > abs(sum)) {
                // Update the minimum sum, minimum left and
                // right indices
                min_sum = sum;
                min_l = l;
                min_r = r;
            }
        }
    }

    // Return the sum of the two elements with the minimum
    // sum
    return arr[min_l] + arr[min_r];
}

// Driver Code
int main()
{
    // Array of elements
    int arr[] = { 1, 60, -10, 70, -80, 85 };

    // Find the two elements with the minimum sum
    int result = minAbsSumPair(arr, 6);

    // Print the result
    cout << result << endl;

    return 0;
}

Java

import java.util.Arrays;

public class Main {
    // Function to find the two elements whose sum is closest to zero
    static int minAbsSumPair(int[] arr) {
        int n = arr.length;

        // Sort the array to simplify the process
        Arrays.sort(arr);

        // Initialize pointers and minimum sum
        int l = 0, r = n - 1;
        int min_sum = Integer.MAX_VALUE;
        int min_l = 0, min_r = 0;

        // Loop through the array
        while (l < r) {
            // Calculate the current sum
            int sum = arr[l] + arr[r];

            // If the absolute value of the current sum is
            // less than the minimum sum found so far
            if (Math.abs(sum) < Math.abs(min_sum)) {
                // Update the minimum sum and indices
                min_sum = sum;
                min_l = l;
                min_r = r;
            }

            // Move pointers based on the sum
            if (sum < 0) {
                l++;
            } else if (sum > 0) {
                r--;
            } else {
                break; // Found a pair with sum zero
            }
        }

        // Return the sum of the two elements with the minimum sum
        return arr[min_l] + arr[min_r];
    }

    // Driver code
    public static void main(String[] args) {
        // Array of elements
        int[] arr = { 1, 60, -10, 70, -80, 85 };

        // Find the two elements with the minimum sum
        int result = minAbsSumPair(arr);

        // Print the result
        System.out.println(result);
    }
}

// This code is contributed by shivamgupta0987654321

Output

5

Time complexity: O(n²)
Auxiliary Space: O(1)

Two elements whose sum is closest to zero using Sorting:

Sort the given array, try two pointer algorithm to find sum closest to zero, we adjust the pointer according to the current sum.

• Sort the given array.
• Initialize two pointers i and j at the beginning and end of the sorted array, respectively.
• Initialize variables sum equal to arr[i] + arr[j] and diff equal to absolute of sum.
• While i is less than j:
  • Calculate the current sum as arr[i] + arr[j].
  • If the current sum is equal to zero, return 0, as this is the closest possible sum.
  • If the absolute value of the current sum is less than the absolute value of diff, update diff and sum with the current sum.
  • If the absolute value of the current sum is equal to the absolute value of diff, update sum to be the maximum of the current sum and the previous sum.
  • If arr[i] + arr[j] is less than 0 then decrement j by 1 else increment i by 1.
• After completing the iteration, return the final sum, which represents the maximum sum of two elements closest to zero.

Below is the implementation of the above approach:

C++

#include <bits/stdc++.h>
using namespace std;

int closestToZero(int arr[], int n)
{

    // sorting the array in ascending order
    sort(arr, arr + n);

    int i = 0, j = n - 1;

    // initializing sum with the first and last elements
    int sum = arr[i] + arr[j];

    // initializing the result with the absolute value of
    // the initial sum
    int diff = abs(sum);

    while (i < j) {

        // if we have zero sum, there's no result better.
        // Hence, we return
        if (arr[i] + arr[j] == 0)
            return 0;

        // if we get a better result, we update the
        // difference
        if (abs(arr[i] + arr[j]) < abs(diff)) {
            diff = (arr[i] + arr[j]);
            sum = arr[i] + arr[j];
        }
        else if (abs(arr[i] + arr[j]) == abs(diff)) {

            // if there are multiple pairs with the same
            // minimum absolute difference, return the pair
            // with the larger sum
            sum = max(sum, arr[i] + arr[j]);
        }

        // if the current sum is greater than zero, we
        // search for a smaller sum
        if (arr[i] + arr[j] > 0)
            j--;
        // else, we search for a larger sum
        else
            i++;
    }
    return sum;
}

// Driver Code
int main()
{
    int arr[] = { 1, 60, -10, 70, -80, 85 };
    int n = sizeof(arr) / sizeof(arr[0]);
    int result = closestToZero(arr, n);

    cout << result;
    return 0;
}

Output

5

Time Complexity: O(nlogn)
Auxiliary Space: O(1)