Arranging Coins

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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.

思路：数学公式，一个个减去，然后count即可，break条件就是remain < i

class Solution {
    public int arrangeCoins(int n) {
        if(n <= 0) return 0;
        int count = 0;
        int remain = n;
        for(int i=1; i<=n; i++){
            if(remain >= i){
                count++;
                remain -=i;
            } else {
                break;
            }
        }
        return count;
    }
}

思路2：用binary search，n*(n+1)/2 来判断是否大于N；

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