Problem

You have a total of n coins that you want to form in a staircase shape, where every k-th row must have exactly k coins.

Given n, find the total number of full staircase rows that can be formed.

n is a non-negative integer and fits within the range of a 32-bit signed integer.

Example 1:

n = 5

The coins can form the following rows: ¤ ¤ ¤ ¤ ¤

Because the 3rd row is incomplete, we return 2.

Example 2:

n = 8

The coins can form the following rows: ¤ ¤ ¤ ¤ ¤ ¤ ¤ ¤

Because the 4th row is incomplete, we return 3.

Pre analysis

Basically if summation of first kth element such that E (k) <= n , then k is solution https://en.wikipedia.org/wiki/Completing_the_square

Another analysis

Binary search

const arrangeCoins = function (n) {

    if (n == 0 || n == 1) {
        return n;
    }

    let lo = 1;
    let hi = n;

    while (lo < hi) {
        let mid = Math.floor((lo+hi)/2);
        let sum = mid * (mid+1) / 2;

        if (sum > n) {
            hi = mid;
        }

        else {
            lo = mid+1;
        }
    }

    return lo-1;
}