# 441. Arranging Coins 排列硬币

@TOC

## # 题目描述

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.

## # 解题方法

### # 模拟计算

class Solution(object):
def arrangeCoins(self, n):
"""
:type n: int
:rtype: int
"""
level = 0
count = 0
while count + level + 1 <= n:
level += 1
count += level
return level

### # 二分查找

class Solution(object):
def arrangeCoins(self, n):
"""
:type n: int
:rtype: int
"""
left, right = 0, n + 1 #[left, right)
while left < right:
mid = left + (right - left) / 2
if mid * (mid + 1) / 2 <= n:
left = mid + 1
else:
right = mid
return left - 1

### # 数学公式

public class Solution {
public int arrangeCoins(int n) {
return (int)((-1 + Math.sqrt(1 + 8 * (long) n)) / 2);
}
}

## # 日期

2017 年 5 月 6 日 2018 年 11 月 24 日 —— 周六快乐