Medium Article Snippet

iterative_approach_4.js

const input = [1,3,5,7];

function product(inputArr) {
  const resultArr = new Array(inputArr.length);

  let product = 1;
  for(let i = 0; i < inputArr.length; i++) {
    product *= inputArr[i];

    if (i+1 < inputArr.length) {
      resultArr[i+1] = product;
    }
  }

  product = 1; // reset product
  for(let j = inputArr.length - 1; j >= 0; j--) {
    product *= inputArr[j];

    if (j-1 >= 0) {
      resultArr[j-1] *= product;
    } else {
      resultArr[0] = product;
    }
  }

  return resultArr;
}

console.log(product(input));

Algorithmic Complexity:

Speed: O(2n)
Space: O(n)

Previous Approach: https://gist.github.com/naveedn/00955f4928c1e3d3177eff40967b2fa1

One of the underlying "hacks" that allows us to optimize this function is the fact that multiplication is associative:
( a × b ) × c = a × ( b × c ))

Because we don't care the order in which we multiply the values together, we can speed things up if we create a product of the values before an index, and multiply that with the product of values after an index. No matter what, it will still yield the proper result.