LeetCode [668] Kth Smallest Number in Multiplication Table

668. Kth Smallest Number in Multiplication Table

Hard

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 l = 1, r = m*n;
        while(l<r){
            int mid = l + (r-l)/2;
            if(count(mid, m, n) < k){
                l = mid+1;
            }else{//cnt>=k
                r = mid;
            }
        }
        return l;
    }

    //return numbers <= X
    int count(int X, int m, int n){
        int ret = 0;
        for(int i=1; i<=m; ++i){
            ret += Math.min(X/i, n);
        }
        return ret;
    }
}