build-a-pile-of-cubes.md

Build a pile of Cubes ^{6 Kyu}

^{LINK TO THE KATA - MATHEMATICS ALGORITHMS}

Description

Your task is to construct a building which will be a pile of n cubes. The cube at the bottom will have a volume of $n^3$, the cube above will have a volume of $(n-1)^3$, and so on until the top which will have a volume of $1^3$.

You are given the total volume m of the building. Can you find the number n of cubes you will have to build?

The parameter of the function (find_nb, find-nb, findNb, ...) will be an integer m, and you have to return the integer n such as: $n^3 + (n-1)^3 + (n-2)^3 + ... + 1^3 = m$ if such a n exists or -1 if there is no such n.

Examples:

findNb(1071225) --> 45

findNb(91716553919377) --> -1

Solution

const findNb = totalVolume => {
  let currentVolumeSum = 0
  let numberOfCubes = 0

  while (currentVolumeSum < totalVolume) {
    numberOfCubes++
    currentVolumeSum += Math.pow(numberOfCubes, 3)
  }

  return currentVolumeSum === totalVolume ? numberOfCubes : -1
}