What is the time complexity of LeetCode 1866. Number of Ways to Rearrange Sticks With K Sticks Visible?

The Python solution on this page runs in O(n \times k).

What is the space complexity of LeetCode 1866. Number of Ways to Rearrange Sticks With K Sticks Visible?

The Python solution on this page uses O(n \times k) auxiliary space.

Number of Ways to Rearrange Sticks With K Sticks Visible — LeetCode 1866 Python Solution

HardMathDynamic ProgrammingCombinatorics

Problem: #1866
Pattern: Dynamic Programming
Reading time: 2 min
Source: leetcode.com

The problem

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.

Example

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.

Python solution

Python

class Solution:
    def rearrangeSticks(self, n: int, k: int) -> int:
        mod = 10**9 + 7
        f = [[0] * (k + 1) for _ in range(n + 1)]
        f[0][0] = 1
        for i in range(1, n + 1):
            for j in range(1, k + 1):
                f[i][j] = (f[i - 1][j - 1] + f[i - 1][j] * (i - 1)) % mod
        return f[n][k]

Complexity

Measure	Complexity
Time	O(n \times k)
Space	O(n \times k) auxiliary

Pattern: Dynamic Programming

Define a state, write the transition, and stop recomputing the same subproblem. LeetCode 1866. Number of Ways to Rearrange Sticks With K Sticks Visible is filed here on both counts: the reference solution below belongs to the algorithm family this hub collects, and LeetCode tags it Dynamic Programming.

The dynamic programming guide has the Python template for the pattern and the 481 LeetCode problems that use it.

Frequently asked questions

How hard is LeetCode 1866. Number of Ways to Rearrange Sticks With K Sticks Visible?: LeetCode 1866. Number of Ways to Rearrange Sticks With K Sticks Visible is rated Hard on LeetCode.
What is the time complexity of LeetCode 1866. Number of Ways to Rearrange Sticks With K Sticks Visible?: The Python solution on this page runs in O(n \times k).
What is the space complexity of LeetCode 1866. Number of Ways to Rearrange Sticks With K Sticks Visible?: The Python solution on this page uses O(n \times k) auxiliary space.
What topics does LeetCode 1866. Number of Ways to Rearrange Sticks With K Sticks Visible cover?: LeetCode 1866. Number of Ways to Rearrange Sticks With K Sticks Visible is tagged Math, Dynamic Programming and Combinatorics on LeetCode.