[week 17][Leetcode][Binary Search] Arranging Coins

最新推荐文章于 2018-11-09 16:33:32 发布

原创最新推荐文章于 2018-11-09 16:33:32 发布 · 258 阅读

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本文介绍了一个使用二分查找算法解决特定问题的方法。该问题是：给定一定数量的硬币，需要将这些硬币堆成楼梯形状，每一层比上一层多一个硬币，目标是计算最多可以完整形成多少层。通过使用二分查找，可以在O(log n)的时间复杂度内找到答案。

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Question:

You have a total of n coins that you want to form in a staircase shape, where everyk-th row must have exactlyk 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.

Analysis:

利用二分法，我们可以计算前i行的和与n的大小关系，由此找到溢出n的边界，也就是我们需要找到的最多能排的行数。

Code:

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