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]

awice’s solution

def findKthNumber(self, m, n, k):
    def enough(x):
        return sum(min(x / i, n) for i in xrange(1, m+1)) >= k

    lo, hi = 1, m*n
    while lo < hi:
        mi = (lo + hi) / 2
        if not enough(mi):
            lo = mi + 1
        else:
            hi = mi
    return lo

 

Leave a Reply

Your email address will not be published. Required fields are marked *