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
andn
will be in the range [1, 30000]. - 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);
}
dbg!(res);
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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