How to Solve Number of Ways to Rearrange Sticks With K Sticks Visible Problem
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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...
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Problem Statement
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.
Number of Ways to Rearrange Sticks With K Sticks Visible
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Examples
n = 3, k = 2
3
[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.
n = 5, k = 5
1
[1,2,3,4,5] is the only arrangement such that all 5 sticks are visible. The visible sticks are underlined.
n = 20, k = 11
647427950
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
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