Problem:

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.

Summary:

用n枚硬币摆成塔形，求可以摆成的完整的行数。

Analysis:

1.最简单的思路，依次减去递增的每行硬币数，直到n为非整数。

 class Solution {

 public:

     int arrangeCoins(int n) {

         int i = ;

         while (n > ) {

             i++;

             n -= i;

         }

         return n ==  ? i : i - ;

     }

 };

2. 解一元二次方程：x^2 + x = 2 * n 解得：x = sqrt(2 * n + 1 / 4) - 1 /2

但要注意在此处n为32位有符号整型数，2 * n后有可能溢出，故在代码中应做相应处理。

 class Solution {

 public:

     int arrangeCoins(int n) {

         return sqrt((long long) * n + 0.25) - 0.5;

     }

 };