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]

668. Kth Smallest Number in Multiplication Table
``````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);
}
``````