題目：

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.

解釋： 因為是連續求和，所以想到mid*(mid+1)/2，然後可以通過二分查詢的方式找到mid。 python程式碼：

class Solution(object):
    def arrangeCoins(self, n):
        """
        :type n: int
        :rtype: int
        """
 

        if n <=0:
            return 0
        if n==1:
            return 1
        left=1
        right=n
        while left<=right:
            mid=(left+right)/2
            temp=(mid*(mid+1))/2
            if temp==n:
                return mid
            elif temp>n:
                right=
 
mid-1
            else:
                left=mid+1
        return left-1        

c++程式碼：

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

總結： c++用乘法的時候會超出範圍，所以注意要改變數值型別，注意，mid的資料型別一定要改成long，不然答案是錯的，可能是因為如果mid是int型別的，那麼它相乘的結果預設是用int儲存的，即使轉化為long型別，如果tmp過大，還是會變成負數，答案錯誤。