[leetcode]441. Arranging Coins

You have a total of n coins that you want to form in a staircase shape, where everyk-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 = 5The coins can form the following rows:¤¤ ¤¤ ¤Because the 3rd row is incomplete, we return 2.

Example 2:

n = 8The coins can form the following rows:¤¤ ¤¤ ¤ ¤¤ ¤Because the 4th row is incomplete, we return 3.

思路：这是一道数学题。x(x+1)/2<=n; 要注意整数的除法为0的情况。

public int arrangeCoins(int n) {        //res*(res+1)/2 <= n        // res*res + res + 1/4 = 2n + 1/4        // res + 1/2 = Math.sqrt(2n + 1/4)        // res = Math.sqrt(2n+1/4)-1/2; //注意这里1/4和1/2都是0，不能这样！                 return (int)(Math.sqrt(2*(long)n + 0.25) - 0.5);    }