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:
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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.

方法1： 模拟相加

class Solution {public:    int arrangeCoins(int n) {        int level = 1;        for(long sum = 0 ; sum <=n ; ++level){            sum+=level;        }        return max(level-2,0);    }};

方法2：数学公式

class Solution {public:    int arrangeCoins(int n) {        return sqrt(2*static_cast<long>(n)+1/4.0)-1/2.0;    }};