What is the time complexity of LeetCode 2400. Number of Ways to Reach a Position After Exactly k Steps?

The Python solution on this page runs in O(k^2).

What is the space complexity of LeetCode 2400. Number of Ways to Reach a Position After Exactly k Steps?

The Python solution on this page uses O(k^2) auxiliary space.

Number of Ways to Reach a Position After Exactly k Steps — LeetCode 2400 Python Solution

MediumMathDynamic ProgrammingCombinatorics

Problem: #2400
Pattern: Dynamic Programming
Reading time: 2 min
Source: leetcode.com

The problem

You are given two positive integers startPos and endPos. Initially, you are standing at position startPos on an infinite number line.

Example

Input: startPos = 1, endPos = 2, k = 3
Output: 3
Explanation: We can reach position 2 from 1 in exactly 3 steps in three ways:

Python solution

Python

class Solution:
    def numberOfWays(self, startPos: int, endPos: int, k: int) -> int:
        @cache
        def dfs(i: int, j: int) -> int:
            if i > j or j < 0:
                return 0
            if j == 0:
                return 1 if i == 0 else 0
            return (dfs(i + 1, j - 1) + dfs(abs(i - 1), j - 1)) % mod

        mod = 10**9 + 7
        return dfs(abs(startPos - endPos), k)

Complexity

Measure	Complexity
Time	O(k^2)
Space	O(k^2) auxiliary

Pattern: Dynamic Programming

Define a state, write the transition, and stop recomputing the same subproblem. LeetCode 2400. Number of Ways to Reach a Position After Exactly k Steps 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 2400. Number of Ways to Reach a Position After Exactly k Steps?: LeetCode 2400. Number of Ways to Reach a Position After Exactly k Steps is rated Medium on LeetCode.
What is the time complexity of LeetCode 2400. Number of Ways to Reach a Position After Exactly k Steps?: The Python solution on this page runs in O(k^2).
What is the space complexity of LeetCode 2400. Number of Ways to Reach a Position After Exactly k Steps?: The Python solution on this page uses O(k^2) auxiliary space.
What topics does LeetCode 2400. Number of Ways to Reach a Position After Exactly k Steps cover?: LeetCode 2400. Number of Ways to Reach a Position After Exactly k Steps is tagged Math, Dynamic Programming and Combinatorics on LeetCode.