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.

1+2+3...+k <= n   求k的最大值

C++（22ms）：

class Solution {
public:
    int arrangeCoins(int n) {
        int left = 0 ;
        int right = n ;
        while(left <= right){
            int mid = left + (right - left) / 2 ;
            if (0.5 * (1+mid) * mid <= n)
                left = mid + 1;
            else
                right = mid - 1;
        }
        return left - 1 ;
    }
};

java（61ms）：

class Solution {
    public int arrangeCoins(int n) {
        return (int)((-1 + Math.sqrt(1 + 8 * (long)n)) / 2);
    }
}