Edit Distance - Dynamic Programming - Leetcode 72 - Python

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Problem Link: neetcode.io/problems/edit-dis...
0:00 - Read the problem
1:28 - Explaining Intuition
10:40 - Drawing Explanation
15:28 - Coding Explanation
leetcode 72
This question was identified as an interview question from here: github.com/xizhengszhang/Leet...
#edit #distance #python
Disclosure: Some of the links above may be affiliate links, from which I may earn a small commission.

[@NeetCode]

💡 DP PLAYLIST: kzbin.info/www/bejne/bWTVZH6Nnqqpr80

[@kwetuligee8087]

Oh my, this is so sweet! Great explanation, I haven’t seen a clear and concise explanation for edit distance like this.

[@abhishekmukherjee7348]

Hey NeetCode, I really enjoy your explanations! Most channels and videos on coding do explain the algorithm before code, but they are not nearly as good, as you are with such a nuanced approach towards describing the intuition and the thought process behind the applicable algorithm. Please keep it up, this has potential to change lives!

[@hooriehmarefat5972]

Your explanations are absolutely awesome! Thanks for creating such helpful content!

[@Akshay.Ramanathan]

This is the sweetest explanation of DP in general and how the bottom up approach suggests itself. Thanks a lot for this.

[@ngalatalla4032]

You are amazing man and a great teacher. I had never understood the logic of the insertion and delete part of this question but you explained it very logically and beautifully. This is the best channel on KZbin on how to approach and solve coding problems and coming out with an optimized solution. Continue the great work.

[@ChanChan-pg4wu]

DP problems have a lot of similarity, bottom up or top down. The difficult part is more on how to derive the relation equation to connect sub-problem to main problem. More like an IQ test. Thank you Neet for another excellent explanation video. Your code is also super clean, PEP stylish!

[@mnchester]

Amazing explanation of what the insert, delete, and replace operations mean in terms of the indexes of the words!

[@yuqian822]

I have to say that again... I LOVE NEETCODE!!!!! You are the FIRST one to look for whenever I am confused about an algo question.

[@sasageyo9571]

Great explanation ! Finally after scratching my head for 2 days, i understand and have an intuition for the algorithm !

[@technophile_]

Hands down THE BEST EXPLANATION of the solution to this question in the ENTIRE PLANET! Couldn't have explained it any better! Thank you sooo much NeetCode!

[@chenbin0802]

This helps me a lot, your explaination is very good. I don't think I can finish edit distance and BK-tree problem before I saw your video.

[@augustdanellhakansson7400]

Extremely well explained! Picture perfect tutorial!

[@yossarian2909]

oh man you made it so easy to understand this.. I spent hours watching various videos and blogs but never understood it.. i think i understand it now..

[@MP-ny3ep]

After listening to your solution , this problem feels more like a medium level problem. That's how good your explanation is. Thank you !

[@priyanshudeep1008]

I don't even code in python, I learn a lot from your thinking process. big fan!!

[@onemoretube]

I'm studying Comp Sci online due to covid and the recorded lecture on Dynamic Programming was a bit difficult to follow. A class mate recommended your video. I checked it out and was glad I did. Liked and subcribed. Thank you so much!

[@shivamsingh3727]

That way it was explained is really impressive. Thanks a bunch!

[@AshwaniSharma-of2nq]

Easy to understand explanation, clear, concise and to the point.

[@julesrules1]

You never fails at giving me an awe moment. Thank you!

[@Sam-vi8iw]

Very clearly explained with code. Like it!

[@yinglll7411]

Again, thank you so much for this explanation, please keep it up!

[@jeremyliang7159]

Pure art! Best explanation!

[@amogchandrashekar8159]

Awesome explaination as always 🙏

[@jadenlin3724]

Hey NeetCode, your code is the best. Your code always helps me understand how you solved the problem.

[@xinniu3145]

Thanks for the explanation! So one of the key points is you don't need to change word1 and word2 in the function, just need to move i and j!

[@L0ukh4ck5]

you really deserve being at G

[@ytg6663]

G ?

[@suraj8092]

​@@ytg6663google

[@assgoblin3981]

​@@ytg6663gock

[@user-kt2kk2bq6f]

Google

[@dollyvishwakarma2]

Super clear explanation! Kudos!

[@thestarinthesky_]

Amazing! Great explanations have ever seen!

[@shiweiwong5292]

the best explanation on the internet! thanks!

[@am_rxd]

nicely done i am learning through these videos cause I was not able to understand what to dointially no idea what can I do or not just doing hit and rum stuff thanks for this its help me understand what to start with and what kind of concept I would have to keep in tracjk while having something of this caliber it was quite a easy code but without this explanation of your I would never able to understand the the logic how to do .

[@NingenVRC]

kudos to you man, you explained it majestically, I hope you are pursuing some teaching career cause you really are amazing

[@yang5843]

Elegant explanation, thank you

[@theteacher010]

Wouldn't have guessed this was LCS until you mentioned it!

[@prayag_vaibhav]

Great video, helped a lot.

[@nitin9042]

I love your explanation. Love u neetcode hope

[@ax5344]

You are the best! I usually browsing news in the morning, but your tutorial uploads changed that! Love the frequency recently! Is N queens on your target list? ;-)

[@NeetCode]

Thanks! Yes, I plan on doing N-Queens soon.

[@sallaklamhayyen9876]

a big thank for you , you are doing a great job ❤❤❤

[@river.]

i am just so happy when i find your video

[@DatascienceConcepts]

Excellent Content!

[@abc00gh]

Best explanation for 2d dp ever!

[@karavind7814]

Best explanation for edit distance

[@feilianhuang4604]

THAT IS BRILLIANT

[@emmatime2016]

You are just great!!!!

[@samaygandhi7182]

Best explanation ever!

[@ArcGaming07YT]

very helpful, thanks man

[@JustTrace17]

Thank you so much!

[@clintondannolfo714]

It makes sense after seeing the solution but before that it's not so obvious that editing, replacing and inserting is just an off by one lookup in the DP table.. thanks for the vid

[@jxw7196]

Brill. GOod job!

[@simbol5638]

Thanks so much for your videos

[@konradhunter1407]

😯 I never would have come up with this.

[@anujchoudhary5645]

Best explanation as always

[@wat5931]

Insert and remove are functionally the same. If you always make word 1 longer than word 2 (by swapping if necessary), you can always use just insert or just remove

[@xiaoweidu4667]

great tutorial!

[@deepika5880]

Very helpful 👍

[@firezdog]

it's interesting that you go forward instead of backward. i always thought of going backward (from the empty strings up) -- maybe just the way the class i took was taught (i.e. you can do it by suffixes or prefixes)

[@brawnybytes]

Great explanation

[@hudsonvan4322]

真的讚

[@paradox2738]

dp = [[i+j for i in range(len(word2),-1,-1)] for j in range(len(word1),-1,-1)] this combines the first 3 loops into one

[@begula_chan]

Brooooo, thanks!

[@edwardteach2]

U a DP God

[@dk20can86]

You can reduce the space complexity to O(len(word2)) or O(len(word1)) (depending on the shape of your rows) by having 2 rows in memory instead of a full grid, as you only ever need to depend on the next row.

[@deadlyecho]

Nice, you would have to just replace the old row values with the next row values one by one each time you decrement the column while traversing

[@arjunv1624]

subscribed

[@mama1990ish]

Please add the cherry pickup problem. Your DP solutions are simple and understandable especially the bottom up approaches.

[@messi_codes]

GOD LEVEL EXPLANATION 😵

[@DonaldFranciszekTusk]

Wonderful explanation, but the 0 -> n approach makes for better code readability than n -> 0.

[@MrPhantomYT7]

Awesome

[@arijaa.9315]

Thanks! what do ou use the explain and draw on the screen?

[@hoyinli7462]

ure really legendary

[@ferb7o2]

Ok this is crazy

[@arnabpersonal6729]

Great explanation. Is there a possibility to optimize for space

[@miladjamali5123]

thank you so much.could you help me how to use EDR on two point sets?

[@shawn_yg1394]

Can not believe that it has been downgraded to a medium question. I have completely no idea the first time saw it lol.

[@dumdumbringgumgum2940]

to everyone who feels DP is tough. Keep at it. One day it will suddenly click and it will be worth it. 💪

[@chowtuk]

holy shit, things look so simple after this video

[@lucamantova3070]

How do they expect me to know this? Lololol

[@lucamantova3070]

They don’t. They expect me to have it memorized from a book lolol

[@ersinerdem7285]

I learnt that this is a well known question which is taught at the start of NLP lessons. From its number "72", can see that it is an old question and known for quite some time. But yeah, even if we know the solution, explaning the thought process in an interview is tricky.

[@kuangyimeng8850]

wow, brilliant explanation. Would you like to share how to come up with this idea?

[@joshkjoby8400]

this is crazy

[@arijaa.9315]

I have noticed that the result does not change if we reverse the column and rows does that mean that converting word2 to word1 have the same distance as converting word1 to word2?

[@dataadvantage1890]

try this --- for j in range(len(word1) + 1, -1, -1)

[@amansinghal2431]

Daaammmmnnn

[@christinemello694]

How on earth will I come up with that table logic in an interview? God bless me

[@vickyarora7380]

LEgenday explanation

[@user-gq1ij]

Nice explanation, BTW you are Canadian lad

[@AdenGolden]

for the else statement:cache[i + j] = 1 + min(cache[i][j + 1], cache[i+ 1][j], cache[i + 1][j +1]) why do we use 1+, where the 1 comes from? Thanks!

[@zaid6527]

We can do this in O(word2.size()) space complexity, but just using 2 arrays instead of using a 2d, we can use prev and cur array to construct the answer from bottom to up, here's the code in cpp, class Solution { public: int minDistance(string word1, string word2) { int counter = 0; int sizes = word2.size(); vector prev(sizes+1); vector cur(sizes+1); for(int i=0; i=0; i--){ counter++; cur[sizes] = counter; for(int j=sizes-1; j>=0; j--){ if(word1[i] == word2[j]){ cur[j] = prev[j+1]; } else{ int curs = min(cur[j+1], prev[j+1]); cur[j] = min(curs, prev[j]); cur[j] += 1; } } prev = cur; } return prev[0]; } };

[@ShailPM]

does the goat respond

[@sumanth6299]

This is called Excellence

[@Siddhii_]

I think instead of using a whole new 2d cache we can use two arrays, that way my acceptance is 84% and 95% respectively.

[@romo119]

What's the purpose for initializing every elem to inf? Aren't we filling every element right to left, bottom up anyways? We just need to make sure the edges of the matrix are filled and solve the problem in the correct order, so the value at dp[i][j] can originally be 0

[@chaitanyanimma2939]

Hey,can you make a video on burst balloons (LC 312) anytime soon?

[@NeetCode]

Sure, I'll try to do that soon.

[@charlielin188]

Why cache[i+1, j+1] is always less or equal than (cache[i+1, j] + 1) and (cache[i, j+1] + 1) ?

[@tanngo1564]

I have same question 🤔

[@ZQutui]

Nice explanations. Btw, it can be solved using dfs + memoization with the same time + space complexity

[@kumarvivek02]

hmm at 11:20, when you highlight cell 1,1, you're actually solving for substring "ab" for word1 & "ac" for word2. But you mention "bc" and "cd". Since this is solving for smaller problems first.

[@kumarvivek02]

Also, shouldn't initialisation happen for row = 0 & col = 0, you seem to doing it inverted. for row + 1 & col + 1. Seems counter intuitive

[@yanjimmy8794]

Hi I have a question. I'm confused about why when word1[i] == word2[j] we need to use the diagonal value? How to find this pattern which is crucial to this problem. I'm new to dynamic programming. Hope someone can help. thanks in advance

[@messi_codes]

[@aditya3984]

This question is difficult 😅

[@sagarchawla4926]

After watching you explanation, me be like - isn't there any hard dp problem on leetcode 🤣

[@dave6012]

Have you ever done a “total unique combinations that add up to n” algorithm? I had that problem come up and I couldn’t write an algorithm efficient enough to pass all cases in the allotted time. It’s pretty wild, 200 ends up producing 487 million unique combinations. I know there must be a dynamic programming solution, but I couldn’t crack it.

[@tommclean9208]

You need a way to stop searching for more candidates when you know a path will exceed the sum. I assume the values are all positive, which means if you add an item, the sum will only increase. This means, if you sort the array, you can start with the smallest values first and subtract from the target value, if the target goes negative then you no longer need to keep on searching for candidates. Here is some python code of the solution: class Solution: def combinationSum(self, candidates: List[int], target: int) -> List[List[int]]: res = [] candidates.sort() def dfs(target, index, path): if target < 0: return if target == 0: res.append(path) return for i in range(index, len(candidates)): dfs(target-candidates[i], i, path+[candidates[i]]) dfs(target, 0, []) return res

[@dave6012]

@@tommclean9208 thanks for taking the time to think about the problem and write your solution. I agree when you say I need a way to stop calculating when the candidates reach the sum. I created several working solutions that were unfortunately not fast enough. The only thing with your solution is it’s solving a slightly different problem. In the problem I was solving, we are not given a list of candidates, only a number that all combos must add up to. In addition, we only need to return the number of combinations. So essentially, 200 goes in, 487 million is returned. It’s terribly intensive, resource wise, and I sincerely doubt there a tidy solution for this, but open to finding out! I benchmarked my best solution, it was 5 minutes to calculate 200 🙃

[@hepbitkin9854]

I think you should draw rest of the problem.