[LeetCode]441. Arranging Coins

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:
¤
¤ ¤
¤ ¤ ¤
¤ ¤
Because the 4th row is incomplete, we return 3.

解题思路:根据等差数列求和公式可知sum = ((1 + mid) * mid)/2，利用二分查找在0~n中查找mid，时间复杂度为O(log(n))

public int arrangeCoins(int n) {        long nLong = (long)n;        long s = 0;        long e = n;        long mid = 0;        while(s<=e){            mid = s+(e-s)/2;            if(mid*(mid+1)<=2*nLong){                s = mid+1;            }else{                e = mid-1;            }        }        return (int)s-1;}