题目描述:

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:

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n = 5

The coins can form the following rows:
¤
¤ ¤
¤ ¤

Because the 3rd row is incomplete, we return 2.

Example 2:

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n = 8

The coins can form the following rows:
¤
¤ ¤
¤ ¤ ¤
¤ ¤

Because the 4th row is incomplete, we return 3.

等差数列的问题, 前m行共有 $$ \frac{m(m+1)}{2} $$ 个硬币, 共有n个硬币, 那么应该找出最大的m满足 $$ \frac{m(m+1)}{2} \le n \rightarrow m^2+m-2n \le 0 $$ 因为m是正整数, 所以 $$ m \le \frac{-1+\sqrt{1+8n}}{2} $$

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class Solution {
public:
    int arrangeCoins(int n) {
        return (sqrt((long long)n * 8 + 1) - 1.0) / 2;
    }
};