How to Code Combinations Using Recursion

In this video, we provide a deep dive into what combinations are and how to determine all combinations using recursion.

Table of Contents:
0:18 Learning Objectives
0:38 Combinatorics Overview
1:18 What is a Combination?
3:28 Diagramming Combinations Using a Tree
6:57 Javascript Implementation Using Recursion
20:04 Time & Space Complexity
21:39 Recap

Need a review on recursion? Check out our other videos:

[pjmiravalle]

Alvin I've been studying data structures and algorithms for the past 6 months on various platforms (Leetcode, Algoexpert, Youtube, Stackoverflow, etc etc), and you are by far the best instructor I've come across. Nobody else even comes close, and you have a real gift in being able to simplify these problems while making it extremely clear through visualization. Thank you so much for this content you are providing!

[abhijitpaul]

oh god. I don't know why I have never found this channel before in top search result. Its a treasure trove. Thanks a lot, sir.

[SirNoire]

I was searching high and low for this channel again. Your video on memoization more specifically your techniques for implementing it really solidified it for me. I thought I had bookmarked, subscribed, and liked the video so I was filled with dread when I looked through my playlists, and likes and couldn't find it. But then I stumbled upon this video and was like "Ah it's him!"

[nguyenhohai]

long live my Master. love your way of teaching. you should live forever to teach generations

[VincentEdwardCastro]

Racking my brain preping of an interview and could not for the life of me remember how to do combinations. This explained it so well, thank you! Thinking of the tree starting with the empty combination set and not the arr of numbers you want to combine is what clicked for me. Thank you so much!!

[vmalonbc]

Alvin explains problems perfectly and I am purchasing his Structy course tomorrow because he understands and explains problems way better than the rest.

However, this explanation had me a little confused because the visualization didn’t match the code implementation like he normally does.

The recursion was just a stack of 4 function calls with a loop on the inside of an array increasing by 2 for each nth call back up the stack. This gives the function a O(2^n) complexity.

The code that would match the visualization would require two recursive calls. You can think of each branch of the visualization like a recursion call.

[amerrashed]

This guy is really gifted genius in both .. programming skills & teaching abilities..he made the most difficult part of programming quite simple. Thanks a alot 🙏🏼

[Pooja-xulp]

You are an excellent teacher. This is one of the best illustration I saw after mycodeschool's Harsha's. Thanks a lot for sharing it for FREE as well, this means a lot to all who wouldn't be able to afford otherwise.
In next video, please help dry run the program too. visualising and backtracking in recursive is complex to dry run :(

[pisco]

Just got here after the Dynamic Programming one at FCC.
These are all great, good job!

[johnmcaulay]

Ugh I had to watch this 4 times and draw several diagrams to finally get it. Thanks so much great video.

[emmanuelbyiringiro]

Gold is not always buried underground. If found here on top of the floor. Thanks, Alvin to democratize quality education for everyone. Watching from somewhere in Africa.

[robertkozik]

For anybody who's working in a synchronous language, no, you did not go insane. The recursive call to 'combinations' will always result in an empty array and the for loop below it will only ever get executed once... after the recursive call to 'combinations' completes.

[alidinabylkasymuulu]

Hey Alvin!!! Thanks for your videos. You are the best, I mean it. All your videos are so beginner friendly and understandable. I have learnt a lot from those videos. Keep that up buddy!!!

[karennino]

Hey Alvin thanks for your well crafted videos, to be honest I was implementing it by myself at the beginning and I was doing quite well then I came across with the option of having the nested foreach and I got really hesitant and stop trusting myself. So I came here and this gave me hope ! thanks

[lizblackledge]

Wow! This is so clear and helpful! Thanks a million!

[mariusandries]

Thanks. Finding all combinations of a set is also called Power Set.

[dawid_dahl]

This was so amazing and useful to learn. Thank you very much!

[mahmud-ahsan]

Excellent presentation. Easy to understand. Thank You.

[ambareen]

I don’t understand how const combsWithoutFirst = combinations(rest); produces the output [ [ ], [ ‘c’ ], [ ‘b’ ], [ ‘c’, ‘b’ ] ]

[mbg]

Thank you, should have learnt this before my interview with Amazon
Now I know :)