1866-number-of-ways-to-rearrange-sticks-with-k-sticks-visible.adoc

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

{leetcode}/problems/number-of-ways-to-rearrange-sticks-with-k-sticks-visible/[LeetCode - 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 10^9 ^+ 7) ways to rearrange the sticks such that exactly 11 sticks are visible.

Constraints:

• 1 ⇐ n ⇐ 1000

• 1 ⇐ k ⇐ n

思路分析

一刷

link:{sourcedir}/_1866_NumberOfWaysToRearrangeSticksWithKSticksVisible.java[role=include]

参考资料