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:

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;
}
};