LeetCode 441 Arranging Coins

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:
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¤ ¤
¤ ¤

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

Example 2:

n = 8

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

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

设所求的结果为x,则1+2+3+4+……+x = n，(1+x)x/2=n，(1+x)x =2n, x^2+x-2n = 0; 这是一个方程啊，记得当年的求根公式是x =(-b+sqrt(b^2 - 4ac) )/2  其中a是x^2的系数1，b是x的系数1，c是后面的常数项-2n，则x = -1+sqrt(1+8n); x向下取整即答案；

	public int arrangeCoins(int n) {
		return (int) Math.floor((-1 + Math.sqrt(1 + 8L * n)) / 2.0);
	}