Reverse index value sum of array in JavaScript

Suppose we have an array of numbers like this:

const arr = [3, 6, 7, 3, 1, 4, 4, 3, 6, 7];

This array contains 10 elements, so the index of the last element is 9. We need to write a function that calculates the sum of each element multiplied by its reverse index position.

The reverse index means we multiply each element by (array.length - currentIndex - 1). For our example:

// Element at index 0: 3 * (10-0-1) = 3 * 9 = 27
// Element at index 1: 6 * (10-1-1) = 6 * 8 = 48  
// Element at index 2: 7 * (10-2-1) = 7 * 7 = 49
// ... and so on

Using Array.reduce() Method

The most efficient approach uses the reduce() method to iterate through the array and accumulate the sum:

const arr = [3, 6, 7, 3, 1, 4, 4, 3, 6, 7];

const reverseMultiSum = arr => {
    return arr.reduce((acc, val, ind) => {
        const sum = val * (arr.length - ind - 1);
        return acc + sum;
    }, 0);
};

console.log(reverseMultiSum(arr));

187

Using Traditional For Loop

Here's an alternative approach using a standard for loop:

const arr = [3, 6, 7, 3, 1, 4, 4, 3, 6, 7];

function reverseMultiSumLoop(arr) {
    let total = 0;
    for (let i = 0; i < arr.length; i++) {
        total += arr[i] * (arr.length - i - 1);
    }
    return total;
}

console.log(reverseMultiSumLoop(arr));

187

Step-by-Step Calculation

Let's break down the calculation for better understanding:

const arr = [3, 6, 7, 3, 1, 4, 4, 3, 6, 7];

function reverseMultiSumDetailed(arr) {
    let total = 0;
    console.log("Calculations:");
    
    for (let i = 0; i < arr.length; i++) {
        const reverseIndex = arr.length - i - 1;
        const product = arr[i] * reverseIndex;
        total += product;
        console.log(`Index ${i}: ${arr[i]} * ${reverseIndex} = ${product}`);
    }
    
    console.log(`Total sum: ${total}`);
    return total;
}

reverseMultiSumDetailed(arr);

Calculations:
Index 0: 3 * 9 = 27
Index 1: 6 * 8 = 48
Index 2: 7 * 7 = 49
Index 3: 3 * 6 = 18
Index 4: 1 * 5 = 5
Index 5: 4 * 4 = 16
Index 6: 4 * 3 = 12
Index 7: 3 * 2 = 6
Index 8: 6 * 1 = 6
Index 9: 7 * 0 = 0
Total sum: 187

Comparison

Conclusion

The reverse index value sum multiplies each array element by its position from the end. Both reduce() and traditional loops work well, with reduce() being more functional and concise.