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Maximum sum of pairwise product in an array with negative allowed in C++ program
In this problem, we are given an array arr[] that contains n integers values (negative values allowed). Our task is to create a program to find the maximum sum of pairwise products in an array with negative allowed.
Problem Description − We need to create pairs using the elements of the array such that the sum of the product of elements of pairs is maximum.
Let’s take an example to understand the problem,
Input
arr[] = {−5, 2, 3, 7, −1, 1, −3, 12}Output
104
Explanation
The pairs to be considered: (−5, −3), (2, 3), (−1, 1), (7, 12) Sum of product = (−5 * −3) + (2 * 3) + (−1 * 1) + (7 * 12) = 15 + 6 − 1 + 84 = 104.
Solution Approach
To solve the problem, we will be finding pairs in such a way that the sum of their products is maximum. To maximize the sum, we need to pair the same pair values together. And making this pairing easy, we need to sort the array and then pair up negatives and positives. Then find if one positive or negative or both values are present in the pair. If a positive/negative value is remaining add it to the pair and if one negative and one positive are present then add their product.
Algorithm
Initialize −
maxSum = 0.
Step 1 −
Sort the array arr[].
Step 2 −
Loop for all negative values of the array. Make pairs, and add their product to maxSum.
Step 3 −
Loop for all positive values of the array. Make pairs, and add their product to maxSum.
Step 4 −
At last check the remaining values.
Step 4.1 −
If one positive value remains, add it to maxSum.
Step 4.1 −
If one negative value remains, add it to maxSum.
Step 4.1 −
If one positive value and one negative value remains, add their product to maxSum.
Step 5 −
Return maxSum.
Example
Program to illustrate the working of our solution,
#include <bits/stdc++.h>
using namespace std;
long calcSumPairProd(int arr[], int n) {
long maxSum = 0;
sort(arr, arr + n);
int i = 0, j = (n − 1);
while (i < n && arr[i] < 0) {
if (i != n − 1 && arr[i + 1] <= 0) {
maxSum = (maxSum + (arr[i] * arr[i + 1]) );
i += 2;
}
else
break;
}
while (j >= 0 && arr[j] > 0) {
if (j != 0 && arr[j − 1] > 0) {
maxSum = (maxSum + (arr[j] * arr[j − 1]) );
j −= 2;
}
else
break;
}
if (j > i)
maxSum = (maxSum + (arr[i] * arr[j]) );
else if (i == j)
maxSum = (maxSum + arr[i]);
return maxSum;
}
int main() {
int arr[] = { −5, 2, 3, 7, −1, 1, −3, 12 };
int n = sizeof(arr) / sizeof(arr[0]);
cout<<"The maximum sum of pairwise product in an array is "<<calcSumPairProd(arr, n);
return 0;
}Output
The maximum sum of pairwise product in an array is 104
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