668. Kth Smallest Number in Multiplication Table

Description

Nearly every one have used theMultiplication Table. But could you find out thek-thsmallest number quickly from the multiplication table?

Given the heightmand the lengthnof am * nMultiplication Table, and a positive integerk, you need to return thek-thsmallest 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. Themandnwill be in the range [1, 30000].
2. Thekwill be in the range [1, m * n]

Discussion

Method 1

iterating from 1 to m*n - 1, for each number, calculate the number of times occurring in the m*n table. return number, when count is >= k.

Method 2

Binary Search

From 1 to m*n - 1, calculating number of values smaller than the mid. return mid, when count == k;