668. Kth Smallest Number in Multiplication Table

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]

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