668. Kth Smallest Number in Multiplication Table

转载于 2018-01-17 08:19:04 发布 · 161 阅读

本文介绍了一种高效的算法来找到指定大小的乘法表中第K小的数字。通过二分搜索的方法，可以在较短的时间内找到目标数值。举例说明了当输入不同的乘法表尺寸与K值时，该算法如何工作。

Nearly every one have used the Multiplication Table. But could you find out the k-th smallest number quickly from the multiplication table?

Given the height m and the length n of a m * n Multiplication Table, and a positive integer k, you need to return the k-th smallest number in this table.

Example 1:

Input: m = 3, n = 3, k = 5
Output: 
Explanation: 
The Multiplication Table:
1	2	3
2	4	6
3	6	9

The 5-th smallest number is 3 (1, 2, 2, 3, 3).

Example 2:

Input: m = 2, n = 3, k = 6
Output: 
Explanation: 
The Multiplication Table:
1	2	3
2	4	6

The 6-th smallest number is 6 (1, 2, 2, 3, 4, 6).

Note:

The m and n will be in the range [1, 30000].
The k will be in the range [1, m * n]

class Solution {
public:
    int findKthNumber(int m, int n, int k) {
        int left = 1;
        int right = m*n;
        while(left<right)
        {
            int mid = left + (right-left)/2;
            int cnt = 0;
            for(int i=1; i<=m; i++)
            {
                cnt += mid/i<=n ? mid/i : n;
            }
            if(cnt<k)
            {
                left = mid+1;
                
            }else
            {
                right = mid;
            }
        }
        return left;
    }
};