LeetCode 441. 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: ¤ ¤ ¤ ¤ ¤ 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.
题目标签：Math
题目给了我们 coins 的总数， n， 让我们找出可以组成几行，返回 行数。
首先来看一下规律：
1 x 1 * 2 / 2 = 1
2 x x 2 * 3 / 2 = 3
3 x x x 3 * 4 / 2 = 6
4 x x x x 4 * 5 / 2 = 10
5 x x x x x 5 * 6 / 2 = 15
可以利用公式 x * (x + 1) / 2 来算出， 某一行累积的总 coins 数量。
然后我们要找到的行数的总 coins 数量 一定是 小于等于 n 的。所以可以从 x * (x + 1) / 2 <= n 求出 x。
Java Solution:
Runtime beats 66.14%
完成日期：02/08/2018
关键词：math
关键点：利用公式 x * (x + 1) / 2 和 quadratic equation
1 class Solution 2 { 3 public int arrangeCoins(int n) 4 { 5 return (int)((-1 + Math.sqrt(1 + 8.0 * n)) / 2); 6 } 7 }
参考资料：https://leetcode.com/problems/arranging-coins/discuss/92298/Java-O(1)-Solution-Math-Problem
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