441. Arranging Coins

题目

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.

题目大意

你总共有 n 枚硬币，你需要将它们摆成一个阶梯形状，第 k 行就必须正好有 k 枚硬币。给定一个数字 n，找出可形成完整阶梯行的总行数。n 是一个非负整数，并且在32位有符号整型的范围内。

解题思路

• n 个硬币，按照递增的方式排列搭楼梯，第一层一个，第二层二个，……第 n 层需要 n 个硬币。问硬币 n 能够搭建到第几层？
• 这一题有 2 种解法，第一种解法就是解方程求出 X，(1+x)x/2 = n，即 x = floor(sqrt(2*n+1/4) - 1/2)，第二种解法是模拟。