Leetcode 668. Kth Smallest Number in Multiplication Table

Problem:

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:

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

Solution:

　　特殊二分法的典型，难点在于是否能看出用二分法解决这道题，原理很简单，就是在1到m*n之间寻找一个数pivot，计算小于它的数的数量，与k做比较不断缩小搜索范围。

Code:

 

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