[leetcode]441. Arranging Coins

[leetcode]441. Arranging Coins

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Analysis

everyday is the first day of your rest life—— [间歇性迷茫+2~]

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.
简单来说就是1+2+3+…+k<=n && 1+2+3+…+(k+1)>=n，求满足条件的k.

Implement

方法一（二分搜索 O(lgN)）：

class Solution {
public:
    int arrangeCoins(int n) {
        if(n <= 1)
            return n;
        long lo = 1;
        long hi = n;
        long mid;
        while(lo<hi){
            mid = lo+(hi-lo)/2;
            if((1+mid)*mid/2 <= n)
                lo = mid + 1;
            else
                hi = mid;
        }
        return lo-1;
    }
};

方法二（暴力 O(N)）：

class Solution {
public:
    int arrangeCoins(int n) {
        if(n <= 1)
            return n;
        int res = 0;
        int tmp = 1;
        while(n >= tmp){
            res++;
            n -= tmp;
            tmp++;
        }
        return res;
    }
};