441.Arranging Coins

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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:
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.

我的解法

解题思路

比较笨的办法，不断将n减去行数。

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class Solution {
public:
    int arrangeCoins(int n) {
        int i = 1;
        while (n > 0){
            if (n < i)
                return --i;
            n -= i++;
        }
        return --i;
    }
};

执行用时 :12 ms, 在所有 C++ 提交中击败了52.52%的用户
内存消耗 :7.2 MB, 在所有 C++ 提交中击败了100.00%的用户

其实可以直接用等差数列求和来求解

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class Solution {
public:
    int arrangeCoins(int n) {
        return floor(-0.5+sqrt((double)2*n+0.25));
    }
};

执行用时 :4 ms, 在所有 C++ 提交中击败了89.51%的用户
内存消耗 :7.5 MB, 在所有 C++ 提交中击败了100.00%的用户