This DP Problem Looks EASY Until the Follow-Up
A dynamic programming coding interview where the classic climbing stairs problem takes an unexpected turn. What starts as a straightforward Fibonacci-style DP question quickly evolves into a generalized step-climbing challenge that tests real problem-solving ability under pressure.
In this coding interview, we work through the staircase problem: given n steps and the ability to climb 1 or 2 steps at a time, find the number of distinct ways to reach the top. The initial solution uses a bottom-up dynamic programming approach with O(n) time complexity. But the real challenge begins with the follow-up: what if instead of just 1 or 2 steps, you can climb any number of steps from a given set of options like 1, 3, and 5? This generalization changes the base case setup, space complexity, and requires careful handling of edge cases where step options exceed the current position.
0:00 Problem statement and initial examples
1:15 Recognizing the dynamic programming pattern
2:45 Building the bottom-up recurrence relation
4:30 Time and space complexity analysis
5:45 Follow-up: generalizing to k step sizes
8:00 Redesigning the algorithm for arbitrary step options
10:30 Implementing the generalized solution
13:00 Debugging index boundary errors
15:30 Walkthrough with test case (n=7, steps=[1,3,5])
18:00 Edge case discussion and final verification
Problem reference:
LeetCode 70 - Climbing Stairs: https://leetcode.com/problems/climbin...