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Description
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:
¤
¤ ¤
¤ ¤ ¤
¤ ¤
Because the 4th row is incomplete, we return 3.
分析
- 一种数学解法O(1)，充分利用了等差数列的性质，我们建立等式, n = (1 + x) * x / 2, 我们用一元二次方程的求根公式可以得到 x = (-1 + sqrt(8 * n + 1)) / 2, 然后取整后就是能填满的行数.
- 还可以一行一行的累加，或者二分搜索，看来我还是太肤浅了。
- 数学在有些时候能够收到奇效
代码
class Solution {
public:
int arrangeCoins(int n) {
return int(-1+sqrt(1+8*(long)n))/2;
}
};