Lowest Common Ancestor Binary Tree

[@cheofusi3562]

Recursion is indeed a divine art

[@blatogh1277]

It is easy to go through, and everything is so nice, besides if the binary tree contains Integer.MAX_VALUE layer, for example, the call stack may be passing away.

[@kylanali9575]

you probably dont give a damn but does any of you know of a way to log back into an Instagram account?? I was stupid lost the login password. I would love any tips you can give me

[@coltonjad4825]

@Kylan Ali instablaster =)

[@ok123ut]

the way this was explained in 11 min. I don't think i can find more valuable solutions for this in such a short time anywhere else. Amazing!

[@depression_plusplus6120]

After 5 years he's still helping

[@aravindreddy1792]

Yep

[@prelimsiscoming]

tera naam mast hai

[@depression_plusplus6120]

@@prelimsiscoming thanks..

[@xuwang3253]

I love this guy's multiple walking-through examples on white board!

[@kevinbaijnath6974]

Wow, great explanation about the algorithm! I appreciated the fact that you gave multiple examples that tested different things!

[@guru007pavan]

Too good explanation. short and sweet. I can say this particular solution is way better explained than Back ToBack SWE. Thanks and appreciate your effort...

[@hrishikeshkonderu1638]

Yes u r correct

[@sharansingh4956]

After i get tired of the logics and code explained by everyone, i do watch your video to understand it in layman and practical way.

[@shreekantwaphare6063]

The space complexity of both the algorithms is O(height), because the recursive algorithm will have function calls on the stack.

[@mtjokro]

Thank you! Finally a video that helped me understand the recursive details of the various cases of binary tree

[@The_Promised_Neverland...]

Can't agree more

[@cosmicgirl910]

Thank you for covering multiple cases. Other videos didn’t explain as thoroughly as you and didn’t go through many test cases

[@dianel.344]

Thank you, sir! I was confused about this recursive code, but now I understand how it works perfectly!

[@dnl_blkv]

Another great explanation with a beautiful solution!

[@abdallaelmedani8933]

This is a very useful, well explained, and simple algorithm. Thank you, Tushar.

[@jlecampana]

Best Video on LCA available on KZbin, Thanks Tushar!

[@leonlew1386]

This was a great visual walkthrough. Clear and concise.

[@learnsharegrow7294]

Nicely explained. This is a popular problem statement in Amazon interviews.

[@AlancRodriguez]

Six years later and im still learning from you

[@robinsoni4778]

The other solution also takes the implicit stack during recursion, so yes it does require the extra space.

[@cachegrk]

You are videos are just awesome! Great job! Can't imagine prep without your videos!

[@generalroboskel]

Excellent video/explanation. Your videos make algorithms so much easier.

[@jinny5025]

Your explanation always hits the spot. Thanks :)

[@decisionguider4911]

Great job Tushar! Absolutely awesome walkthrough..

[@lpatrasco]

Clear and straight to the point.

[@b9944236]

Last example is really important to explain both nodes in the same path.

[@foreverursabhi]

Optimization note, if the left subtree search yielded the LCA, there's no need to search the right subtree. This can only be avoided by keeping track of how many of the target nodes have been found; it's not sufficient to check if the left subtree search returned a node that is not one of the target nodes, because one of the target nodes may as well be the LCA. For example, 6, and 2.

[@dileepbc5901]

ASSUMTION: We may assume that either both n1 and n2 are present in the tree or none of them are present.

[@dileepbc5901]

NOTE : optimisation not works for special case

[@sase1017]

Excellence! Real knowledge, thank you.

[@joycer5293]

thank you so much this is the most helpful video ive found for this question

[@sleepypanda7172]

great explanation! this dry run really helped me a lot

[@shubhamkale735]

Thank you sir for this dry run feeling lucky to find this video ... Keep making such dry run video sir Thank you

[@nimishbajaj3815]

Great work, as you recommended I started solving problems on GeeksForGeeks, your videos + that website together make up a great learning experience thanks again, keep up the good work !

[@biboswanroy6699]

In the recursive solution isn't anyway space is consumed due to stacks

[@MIRAZIB]

yes, obviously .. space complexity is O( h ) .. worst case will occur when the tree is skewed and the ancestor lies beneath of it.

[@harshitpruthi5744]

I think the method you explained above is based on the assumption that both n1 and n2 are present Can you please explain what if one of the two or both nodes aren't present in Binary tree Thanks in Advance

[@SuperHARIS14]

its given in the question that both n1 and n2 will always be there in the tree.

[@antuancaraballo9691]

Love your explanations Tushar! You are awesome!

[@14rucha]

Awesome video! Your explanation is too good. I can understand recursion very easily through your video.

[@mayankmittal6552]

man, your hair style and explanation a true entertainer!!

[@uRamPlus]

Hahahaha !!! He’s cool tho

[@nadiiaparsons6088]

It's much clear now. Thanks a lot for your explanation.

[@vuleenguyen]

Thanks a lot. You gave me the idea to solve this problem

[@sase1017]

Thanks for the great explanation

[@sumedhaj9017]

Very nice explanation with the examples!

[@sureshgarine]

hi Thushar, so nice of you...explained very well

[@levtunik997]

great explanation, you have high-quality videos..thanks.

[@AP-eh6gr]

in the last 8,7 example, is there an assumption that both given nodes whose ancestor we are looking for, have to be present in the tree? bcoz we returned 8, and never went down to 7 to see if it was actually there or not

[@hemanthp2367]

I think we should make assumptions clear that is both nodes should exist and nodes are not equal, tree with one node etc? static Node lca(Node rootNode, int a, int b, AtomicBoolean found) { if (rootNode == null) { return null; } if (found.get()) { return null; } Node left = lca(rootNode.left, a, b, found); Node right = lca(rootNode.right, a, b, found); if (left != null && right != null) { found.set(true); return rootNode; } final boolean rootMatched = rootNode.i == a || rootNode.i == b; if (rootMatched) { if (left != null || right != null || a == b) { found.set(rootMatched); } return rootNode; } if (left != null) { return left; } else if (right != null) { return right; } else { return null; } } This should work for all the cases. I used AtomicBoolean but can be replaced by MutableBoolean. You have a match only when found returns true.

[@mrdude1084]

I saw the solution to this problem over gfg but couldn't get the part of searching even after we were using maps for given 2 values... thnx for your question.. helped me alot

[@nishantharava9181]

Even if we traverse until node 7, it would eventually return the same value 8 to the root of the tree. This case holds true every time when one of the nodes is a ancestor.

[@abhinavmishra7617]

this algo is based ln the assumption that that both nodes will be present in the tree...nice observation btw

[@abhinavmishra7617]

4 years ago....damn

[@HieuLe-mh4bc]

Great explanation! Thank you for the video.

[@anandsakthivel9425]

Thank you so much for your contribution..I think it is one of the best lectures i have ever seen for like this focusing on interview problems alone..Again thank you so much...please keep on share more and more challenging problems

[@kfliden]

Great explanation as usual!

[@shreyaa_21]

Recursion Explained nicely, thanks

[@stonecoldcold2941]

Awsome Explanation Bro!!

[@444not]

Thank you for the explanation. Very helpful.

[@trinityartworld9732]

what if, if n1=8 and n2=17. n2 doesn't exist as per this code it will return 8 but this is not correct. Can you please cover this scenario as well?

[@rohitkumar-yz5qy]

you have given best explanation..thanks a lot

[@shubham709]

Great job, the explanation is very clear and lucid. Thanks a lot :).

[@shubhamtalks9718]

Amazing explanation!!!

[@gourab469]

Excellent explanation! Hats off!

[@nikkis8102]

Thank you so much, Tushar!!

[@RoshanKumar-nx6rk]

Your second algorithm has also O(n) space complexity!!! You can't neglect the function stack calls.

[@reassume4826]

above & beyond awesomeness!

[@hmoiz52]

Very nicely explained! Thanks.

[@chrisy.703]

best lca video in youtube so far!

[@GowthamBharadwaj]

Very lucid explanation

[@learnsharegrow7950]

Very well explained. Small correction required in your code, instead of doing nodes equals comparison using '==', you need to do node data comparison as shown below. if(root.data == n1.data || root.data == n2.data){ return root; }

[@RightMeow28]

That doesn't need to be corrected. The value is irrelevant. Node n1 and n2 hold the address of the nodes that need to be found. All you need to do is compare the address.

[@Sameer88530]

Checking only one node should not be enough . What if the 8 is present on the left and right of the 11 then 11 will be lowest common ancestor . @Tushar checked 11 and then directly returned 11 which is wrong.

[@shreyasingh-sn4bs]

I have become a fan! Great work Sir :)

[@rhondawang2639]

Thank you so much!

[@aloksharma3480]

In this algorith the 2nd last line "if(left==NULL && right==NULL) return NULL;" is not required as last line will return NULL if both are NULL.

[@samratdr]

Thank you for the video. One feedback I have is that the mic is too hard for the ears

[@evantheking]

finally good explanation. I understand it now

[@whyarewehere9555]

Thank you sir

[@bumbarumbado]

beautiful explanation!

[@nitinagrawal6637]

I checked various sites, even during interviews of big companies & everywhere the same kind of solution is given & I have following issues with this problem & I wonder that why people don't raise this concern, either they don't understand English or they are just interested in clearing the interviews to get the money - a) How can you assume that both nodes are present in the tree without saying it anywhere. b) Because above assumption is missing then you might be returning wrong answer even if there is not common ancestor, rather we should say that one or both the given nodes not found. c) When you use some other language's word in your problems then respect the meaning of that word also or don't use that word at all. How can I be my own ancestor in any condition, so how can 8 be its own ancestor. So if you have different definition then use different word also, say like find the common meeting point etc. But using the word 'Ancestor' here is not right. Improvement - If we follow the correct definition of Ancestor then we can apply the same solution to find the common ancestor for multiple nodes. Assumption : All nodes in the tree are unique.

[@mehrdadk.6816]

complexity can be O(logn) since it is a binary tree

[@xxbighotshotxx]

Thank you for the explanation! I was able to write the code for it myself as a result!

[@bipul2138]

Genius approach...well explained

[@atulavhad1661]

@ 6:31 the idea to return 11 from the node itself is wrong because the other node 8 could have been a child of 11. So even if we find 11 we need to explore the tree below and ensure the absence of the other node 8.

[@prathashukla6596]

@tushar can you cover this edge case in your algo.

[@AKHILESHKUMAR-nk2rk]

it is assumed that the two nodes are present in the tree

[@ShaliniNegi24]

Very nice Explanation.

[@carloslaguna7036]

Correct me if I'm wrong: In your last example. The algorithm does not take into account the possibility that 7 is not part of the tree.

[@haoli2976]

Genius. Thank you very much.

[@adampatrick7687]

Really really helpful.

[@ayushpalak]

great video Tushar. Thanks for taking out your time to explain all these stuffs. They really help a lot. Btw, do you speak Hindi ? :P

[@mohammedghabyen721]

Great explanation, Thanks a lot

[@GaneshSatputeAtPlus]

Here we assume that both nodes are present. If one of them is not present, we return a wrong output.

[@madiyar8079]

amazing!! Thanks Tushar! PLease continue!

[@chetansarnad1232]

Thanks for the video, really helpful

[@BhatiJhabarSingh]

Excellent Explaination

[@jubiliudu]

Your solutions are amazing!! Keep doing it :)

[@MLAICS]

The recursive approach uses far more space than finding the paths to the nodes. In terms of space efficiency the approach taken in the first two minutes is actually more efficient!

[@0xeb-]

Perfect. Thank you.

[@HoanNguyen-fc8vb]

Very nice. Thank you very much.

[@volodymyrkot6277]

Not sure if the described solution is optimal. It still takes O(N) space because of the recursion, and that is stack space, which is much more precious.

[@RottenWoodInPower]

Very clear. Thanks

[@jaspertienny8976]

The amazing Tushar. Thanks!

[@rajusaratkar2599]

Very nice and Clear Explanation ..Thanks for the Video.

[@shivampandey8837]

No bro

[@shimul6680]

Thank you very much.....! Super solution!!!

[@harshkanani6605]

Very nice explanation thank you sir

[@jacobstech1777]

i really love this guy

[@umberto3271]

this is excellent, thank you

[@SiddharthKulkarniN]

Great videos dude. Thanks!

[@Balaji-cv5bz]

Hey Tushar, wonderful explanation. can you please post a video of an inorder successor of a binary search tree. Thanks!

[@adithiaa4385]

Great explanation! Thank you.!

[@manishbhatt3614]

@Tushar: Good work and good explanations.

[@liangchen4439]

A follow up of this question is to find the LCA of a list of nodes (more then 2) in this tree. Any ideas?