In a staircase problem, you try to calculate the different ways to reach the n'th stair where you are allowed to take up to m steps at a time. Say you are given a staircase problem with 5 stairs to climb, and you can take 1 or 2 steps at a time. How would you solve this problem? This and its variants are the focus in this video. It is a great problem to demonstrate the properties of dynamic programming and how to solve problems with it. Due to this, staircase problem and its variants like unique paths problem are commonly used as programming interview questions.
In the video, you will find the solutions to the following questions, as well as their time and space complexities:
* Medium Difficulty: Staircase Problem - Different Ways to Reach the N'th Stair: Given n stairs, you can climb 1 or 2 stairs at a time. Count the number of different ways that you can reach the top.
* Medium Difficulty: Generalized Fibonacci-like Sequences: Same question but you can climb up to m steps at a time.
* Medium Difficulty: Generalized Fibonacci-like Sequences With Variable Steps: Same question but you can only climb 2, 3, 6 steps at a time.
0:00 Intro
0:36 Overview
1:24 Question #1
15:58 Tips
16:13 Question #2
20:32 Tips
21:48 Question #3
28:59 Tips
In summary:
* Staircase problem is just a special case of "unique variations" questions like that of unique paths problem. I might make quick videos for those too, but you can apply the same methods that you will learn here to solve them also.
* You can identify variation finding questions if you are asked to find unique ways of doing XXX.
* Solutions to these problems are a subset of Dynamic Programming (the technique of solving a problem by dividing it into subproblems). We can solve them using recursion or iteration.
* Since solutions to these questions resemble Fibonacci Sequences, they are referred to as Fibonacci Puzzles, and they commonly appear in programming interviews and LeetCode. Especially the staircase problem!
Solution code to examples are available on:
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My "Sliding Window Technique + 4 Questions" video, which will help you solve Fibonacci problems more efficiently:
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My "Big O Time/Space Complexity Types Explained" video, which can help you refresh your memory on Big O notation:
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QuanticDev Shop where you can find "Alternative Big O Notation" stickers, mugs, and more:
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Recursion visualization tool used in the video:
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If you can read the article version of this video at:
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My "Algorithms" Playlist for all other algorithm questions & answers:
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