Compute ways to climb n steps
Problem: Ways to Climb N Steps
Implement a function that calculates the number of distinct ways to reach the top of a staircase with n steps. You are allowed to climb either 1 or 2 steps at a time.
Constraints
- Input: An integer
n(assume1 <= n <= 45). - Output: The number of distinct ways.
Discussion Point
Discuss how you would improve a naive recursive solution using dynamic programming, specifically covering both top-down memoization and bottom-up iteration.
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Core dilemma
Identifying and efficiently solving overlapping subproblems to transform an exponential time complexity into a linear one, balancing between recursive elegance and iterative performance.
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Compute ways to climb n steps
Problem: Ways to Climb N Steps
Implement a function that calculates the number of distinct ways to reach the top of a staircase with n steps. You are allowed to climb either 1 or 2 steps at a time.
Constraints
- Input: An integer
n(assume1 <= n <= 45). - Output: The number of distinct ways.
Discussion Point
Discuss how you would improve a naive recursive solution using dynamic programming, specifically covering both top-down memoization and bottom-up iteration.