原题链接在这里：https://leetcode.com/problems/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: ¤ ¤ ¤ ¤ ¤ 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.
题解：
1+2+...+x = n, 求和公式(1+x)*x/2 = n, x = (-b + Math.sqrt(b^2 - 4ac))/2a 或者 (-b - Math.sqrt(b^2 - 4ac))/2a.
负值去掉保留正值.
Note: 不能用8*n, 可能overflow. 要用8.0*n自动转化成double型.
Time Complexity: O(1). Space: O(1).
AC Java:
1 public class Solution { 2 public int arrangeCoins(int n) { 3 return (int)((Math.sqrt(8.0*n+1) - 1)/2); 4 } 5 }