README.md

1866. Number of Ways to Rearrange Sticks With K Sticks Visible

There are n uniquely-sized sticks whose lengths are integers from 1 to n. You want to arrange the sticks such that exactly k sticks are visible from the left. A stick is visible from the left if there are no longer sticks to the left of it.

• For example, if the sticks are arranged [1,3,2,5,4], then the sticks with lengths 1, 3, and 5 are visible from the left.

Given n and k, return the number of such arrangements. Since the answer may be large, return it modulo 109 + 7.

Example 1:

Input: n = 3, k = 2
Output: 3
Explanation: [1,3,2], [2,3,1], and [2,1,3] are the only arrangements such that exactly 2 sticks are visible.
The visible sticks are underlined.

Example 2:

Input: n = 5, k = 5
Output: 1
Explanation: [1,2,3,4,5] is the only arrangement such that all 5 sticks are visible.
The visible sticks are underlined.

Example 3:

Input: n = 20, k = 11
Output: 647427950
Explanation: There are 647427950 (mod 109 + 7) ways to rearrange the sticks such that exactly 11 sticks are visible.

Constraints:

• 1 <= n <= 1000
• 1 <= k <= n

Solutions (Rust)

1. Solution

impl Solution {
    pub fn rearrange_sticks(n: i32, k: i32) -> i32 {
        let mut dp0 = vec![0; n as usize + 1];

        for i in 1..=k as usize {
            let mut dp1 = vec![0; n as usize + 1];
            dp1[i] = 1;

            for j in i + 1..=n as usize {
                dp1[j] = (dp1[j - 1] as i64 * (j as i64 - 1) % 1_000_000_007) as i32
                    + dp0[j - 1] % 1_000_000_007;
            }

            dp0 = dp1;
        }

        dp0[n as usize] % 1_000_000_007
    }
}