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:
¤
¤ ¤
¤ ¤

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.

public class Solution {
    public int arrangeCoins(int n) {
        int a=1;
        for(int i=n;i>0;i--){
            a=(int)Math.sqrt(i*2);
            if(i*2%a==0&&i*2%(a+1)==0)
                break;
        }
        return a;
    }
}

　　上面的代码会超时，使用下面的代码:

public class Solution {
    public int arrangeCoins(int n) {
        return (int) Math.floor((-1 + Math.sqrt(1+8*(long)n))/2.0);//Math.floor（n）取小于等于n的最大整数返回double型
    }
}

leetcode-441. Arranging Coins