Searching: Given an array, find the largest pair sum

Problem Statement:

You are given a unsorted array of distinct integers, you need to find the largest pair sum

Example:

Input: [1, 4, 3, 2, 5]
Output: 9

Solution 1: Brute force approach

Idea is to use 2 nested loops and then iterate over all the pairs in the array and keep track of the max sum and return the result.

Time Complexity: O(n^2)
Space Complexity: O(1)

Solution 2: Efficient approach

In this approach, we will find the largest and second largest element in the array.

Then return the sum of the 2 elements.

Time Complexity: O(n)
Space Complexity: O(1)

Code Solution

#include <iostream>
#include <vector>
using namespace std;


int solution_2 (vector<int>& arr, int n)
{

    if (n < 2) 
    	return -1; 
  
    int first, second;
    if (arr[0] > arr[1]) 
    {
        first = arr[0];
        second = arr[1];
    }
    else 
    {
        first = arr[1];
        second = arr[0];
    }

    for (int i = 2; i < n; i++) 
    {

        if (arr[i] > first) 
        {
            second = first;
            first = arr[i];
        }

        else if (arr[i] > second)
            second = arr[i];
    }
    return (first + second);
}

int solution_1 (vector<int> &arr, int n)
{
    int maxSum = 0;

    for (int i = 0; i < n - 1; i++) 
    {
        for (int j = i + 1; j < n; j++) 
        {
            int sum = arr[i] + arr[j];
            if (sum > maxSum) {
                maxSum = sum;
            }
        }
    }
    return (maxSum == 0)? -1 :  maxSum;
}

int main()
{
    vector<int> arr = { 1, 4, 3, 2, 5 };
    int n = arr.size();

    cout << "Solution 1 = " << solution_1(arr, n)<<endl;
    cout << "Solution 2 = " << solution_2(arr, n)<<endl;
    return 0;
}

Output

Solution 1 = 9
Solution 2 = 9