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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]

Solution:


class Solution {
    public int findKthNumber(int m, int n, int k) {
        int left=1,right=m*n;
        while(left<right)
        {
            int mid=left+(right-left)/2;
            if(smallest(mid,m,n,k))
                right=mid;
            else left=mid+1;
            
        }
        return left;
    }
    
    private boolean smallest(int num,int m,int n,int k)
    {
        int count=0;
        for(int i=1;i<=m;i++)
        {
            count+=Math.min(num/i,n);
        }
        return count>=k;
    }
}

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