leetcode解题: Arranging Coins (441)

发表于 | 分类于

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.

解法1： O(logN)

一道很典型的binary search的题目，实际上这题是求最大的K， 满足1+2+… + k <= n.
记录1+2+…+k = k*(k+1)/2
那么我们就可以用二分法来求出最大的k。
要注意的是当计算乘积的时候可能会溢出，所以需要用long来存放start和end。
C++

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
class Solution {
public:
    int arrangeCoins(int n) {
        if (n <= 0) {
            return 0;
        }
        long start = 1, end = n;
        while (start + 1 < end) {
            long mid = start + (end - start) / 2;
            if (mid * (mid + 1) / 2 < n) {
                start = mid;
            } else {
                end = mid;
            }
        }
        if (end * (end + 1) / 2 <= n) {
            return (int)end;
        }
        return (int)start;
    }
};

Java

1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
class Solution {
    public int arrangeCoins(int n) {
        if (n <= 0) return 0;
        long start = 1, end = n;
        while (start + 1 < end) {
            long mid = start + (end - start) / 2;
            if ( mid * (mid + 1) / 2 < n) {
                start = mid;
            } else {
                end = mid;
            }
        }
        if (end * (end + 1) / 2 <= n) {
            return (int)end;
        }
        return (int)start;
    }
}