CodeWars 6kyu. Build a pile of Cubes

Find the largest number of cubes can be piled.

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 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. Being given m can you find the number n of cubes you will have to build?

The parameter of the function findNb (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 + … + 1^3 = m if such a n exists or -1 if there is no such n.

Examples:

findNb(1071225) –> 45
findNb(91716553919377) –> -1
mov rdi, 1071225
call find_nb ; rax <– 45

mov rdi, 91716553919377
call find_nb ; rax <– -1

접근법

Σ k³ (k = 1~n) == ((n * (n+1))/2))**2 가 m보다 작아야 한다.

따라서 n == Math.sqrt(2 * Math.sqrt(m)) 에 근사한 값으로 설정한 후 m보다 커질 때까지 반복한다.

JavaScript Solution

Solution Submit

function findNb(m) {
    let n = parseInt(Math.sqrt(2 * (Math.sqrt(m)))) - 1;
    while ( ((n * (n+1))/2) ** 2 < m ) {
      n++;
    }
    return ((n * (n+1))/2) ** 2 > m ? -1 : n;
}