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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posted @ 2018-02-09 11:35  Jimmy_Cheng  阅读(236)  评论(0编辑  收藏  举报