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]

Rust Solution

struct Solution;

impl Solution {
    fn find_kth_number(m: i32, n: i32, k: i32) -> i32 {
        let mut lo = 1;
        let mut hi = m * n;
        while lo < hi {
            let mi = lo + (hi - lo) / 2;
            if Self::count(mi, m, n) < k {
                lo = mi + 1;
            } else {
                hi = mi;
            }
        }
        lo
    }

    fn count(x: i32, m: i32, n: i32) -> i32 {
        let mut res = 0;
        for i in 1..=m {
            res += n.min(x / i);
        }
        res
    }
}

#[test]
fn test() {
    let m = 3;
    let n = 3;
    let k = 5;
    let res = 3;
    assert_eq!(Solution::find_kth_number(m, n, k), res);
}

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