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 boolean enough(int x, int m, int n, int k) {
int count = 0;
for (int i = 1; i <= m; i++) {
count += Math.min(x / i, n);
}
return count >= k;
}

public int findKthNumber(int m, int n, int k) {
int lo = 1, hi = m * n;
while (lo < hi) {
int mi = lo + (hi - lo) / 2;
if (!enough(mi, m, n, k))
lo = mi + 1;
else hi = mi;
}
return lo;
}
}