Search A Maze For Any Path - Depth First Search Fundamentals (Similar To "The Maze" on Leetcode)
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Question: Given a 2D array of black and white entries representing a maze with designated entrance and exit points, find a path from the entrance to the exit, if one exists.
Graph search methodologies apply well to problems that have an aspect of a spatial relationship.
Approach 1 (Brute Force)
We could try to enumerate all possible paths in the maze from the start to the finish and then check all paths to see if any of them are valid (have all white squares, aka do not run over a wall).
This is both naive and extremely costly in terms of time.
Approach 2 (Graph BFS or DFS)
We will imagine each cell as a vertex and each adjacent relationship as the edges connecting nodes.
Do we use DFS or BFS?
If we use BFS we know that the path that we find will be the shortest path because of how it searches (wide, going out layer by layer).
If we use DFS we can have the call stack remember the path making things easier to implement.
If we hit the end cell, then we will know that every call below in the call stack has a node apart of the answer path.
Since the problem just wants any path then we will use DFS since it is more straight-forward.
Complexities
Time: O( | V | + | E | )
The standard time complexity for DFS
Space: O( | V | )
We will at maximum the length of the path on the call stack through our recursion
Note: The problem on Leetcode requires BFS to pass because DFS will not always find the shortest path, but I did DFS in this video just for teaching purposes.
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This question is number 19.1 in "Elements of Programming Interviews" by Adnan Aziz, Tsung-Hsien Lee, and Amit Prakash.
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Honestly, you sitting in front of a computer would be a waste of talent! Take advantage of your skill to explain complex stuff the easy way and make a business out of it.
You and Abdul Bari are the kings of explaining algorithms and problem solving. Thanks a LOT for everything you do!
Great video and great explanation, but could have been a lot shorter and concise if you didn't explain/repeat what we already understand for every single box. - Can't go right/up/ etc, have to backtrack. We get it already. No need to stop and go verbose on every single white square in the maze. Had to watch it on 2x speed. But still, thanks for the video.
The call stack is a state! So brilliant words!
Where is the code for the DFS approach
Where is the code?
Don't mind me... just a Masters CS student trying to remember how the heck DFS works.
He got locked in the library by 2 and a half minutes.
I really like that you explain things in such a simple way and teaches the most fundamental method. As a matter of fact, it is always most difficult to learn the most fundamental stuff.
Best explanation I've seen of DFS so far. I wish my professors explained things this way. I likely would have dropped out of my MSc if it wasn't for your channel!
Bruh, your lectures are WAY clearer and more concise than some of the “best” professors I’ve encountered.
Man, you are an excellent teacher. I stumbled onto one of your videos earlier and immediately started up another, right after. I'm about five videos in, now.
Big thanks to you! Currently I am a bit angry that my university is not capable of explaining such stuff in a nice way, but you did it in less time and in a much clearer way!
Best Explanation for DFS I've come across so far. Thanks a lot !!!
This dude is a brilliant tutor. Never have i ever understood an algorithm this clearly, Juss did.
Till now, your video is still saving lives. I finally completed my damn maze assignment after your explanation. Wherever you are bro, THANK YOU!!!
I saw the BFS & DFS (15 min) video followed by the maze problem. Wow! It clears out when and where to chose BFS over DFS. Thanks a LOT!
This is so clear to me, I’m amazed at how easy you make this to understand
This was fantastic. Thank you so much for such a clear, effective explanation of recursive DFS algorithms for maze traversal!