Maximum Possible Sum of Products in JavaScript

We are given two arrays say, arr1 and arr2 of positive numbers. The number of values in both the arrays are the same.

We are required to write a function that finds the maximum sum of products of their elements. Each element in arr1 has to be multiplied with exactly one element in arr2 and vice versa such that each element of both the arrays appears exactly once and the sum of product produced is maximum.

Problem Understanding

For example: if,

arr1 = [5,1,3,4,2] and,
arr2 = [8,10,9,7,6]

Then a possible sum of product is ?

5*6 + 1*7 + 3*9 + 4*10 + 2*8 = 30 + 7 + 27 + 40 + 16 = 120

Although, it may not be the largest sum.

Algorithm

To maximize the sum of products, we need to pair the largest elements from both arrays together. This is achieved by:

• Sorting both arrays in descending order
• Multiplying corresponding elements from sorted arrays
• Summing all the products

Example

Following is the code ?

const arr1 = [5,1,3,4,2];
const arr2 = [8,10,9,7,6];

const sorter = (a, b) => b - a;

const greatestProduct = (a1, a2) => {
    if(a1.length !== a2.length){
        return false;
    };
    
    const a1Sorted = a1.slice().sort(sorter);
    const a2Sorted = a2.slice().sort(sorter);
    
    let res = 0;
    for(let i = 0; i < a1.length; i++){
        res += (a1Sorted[i] * a2Sorted[i]);
    };
    
    return res;
};

console.log(greatestProduct(arr1, arr2));

Output

130

How It Works

Let's trace through the algorithm step by step:

const arr1 = [5,1,3,4,2];
const arr2 = [8,10,9,7,6];

// After sorting in descending order:
const a1Sorted = [5,4,3,2,1];
const a2Sorted = [10,9,8,7,6];

console.log("Sorted arr1:", a1Sorted);
console.log("Sorted arr2:", a2Sorted);

// Products: 5*10 + 4*9 + 3*8 + 2*7 + 1*6
console.log("Products: 5*10 + 4*9 + 3*8 + 2*7 + 1*6");
console.log("Result:", 50 + 36 + 24 + 14 + 6);

Sorted arr1: [ 5, 4, 3, 2, 1 ]
Sorted arr2: [ 10, 9, 8, 7, 6 ]
Products: 5*10 + 4*9 + 3*8 + 2*7 + 1*6
Result: 130

Alternative Approach Using Reduce

const maximumProductSum = (arr1, arr2) => {
    if (arr1.length !== arr2.length) return false;
    
    const sorted1 = [...arr1].sort((a, b) => b - a);
    const sorted2 = [...arr2].sort((a, b) => b - a);
    
    return sorted1.reduce((sum, val, index) => sum + val * sorted2[index], 0);
};

const arr1 = [5,1,3,4,2];
const arr2 = [8,10,9,7,6];

console.log("Maximum product sum:", maximumProductSum(arr1, arr2));

Maximum product sum: 130

Conclusion

To find the maximum sum of products, sort both arrays in descending order and multiply corresponding elements. This greedy approach ensures the largest values are paired together for optimal results.