kartik8800's blog

By kartik8800, history, 4 weeks ago, In English,

Hello Codeforces!!

In this blog, I want to present to you a beginner-friendly video lecture series on dynamic programming on trees/an editorial for the CSES tree algorithms section.

CSES is a brilliant problemset for people wanting to get started at competitive programming and get good at it.

My aim till now has been to make the explanations intuitive, crisp and clear. I feel even a beginner will be able to benefit from these video lectures.

So let's get started.
Link to the problems

Subordinates

Explanation : https://youtu.be/fGznXJ-LTbI
AC code : https://github.com/kartik8800/CSES/blob/master/Subordinates

Tree Matching

Somehow I feel some other nice approaches are also possible, please do share.
Explanation : https://youtu.be/RuNAYVTn9qM
AC code : https://github.com/kartik8800/CSES/blob/master/Tree%20Matching

Tree Diameter

Explanation : https://youtu.be/qNObsKl0GGY
AC code : https://github.com/kartik8800/CSES/blob/master/Tree%20Diameter

Tree Distances I

This problem uses the rerooting technique, we evaluate the answer for every node assuming it to be the root of the tree. If we do this naively this will be O(N^2) time but if we do this using something known as the reroorting technique and propogate partial answers of parent node with respect to the child nodes we can optimize our solution to O(N) overall time complexity.
I feel Tree Distances II is easier compared to Tree Distances I and would recommend to try it first.

Explanation : https://youtu.be/N7e4CTfimkU
AC code : https://github.com/kartik8800/CSES/blob/master/Tree%20Distances%201

Tree Distances II

This problem also uses the rerooting technique.
Explanation : https://youtu.be/nGhE4Ekmzbc
AC code : https://github.com/kartik8800/CSES/blob/master/Tree%20Distances%202

Distance in Tree

This problem also uses the rerooting technique.
Problem link: https://codeforces.com/contest/161/problem/D
Explanation : https://youtu.be/SOhZqL6HPjQ

Company Queries I

This problem uses a technique(the technique itself uses DP) known as Binary lifting. I will be adding a detailed lecture on binary lifting with code.

Explanation : https://youtu.be/FAfSArGC8KY

Company Queries II

This problems requires us to know a technique to calculate LCA of two nodes in a tree in O(logN) time. Evaluation of LCA in O(logN) can be done using binary lifting. I will add a more detailed video soon.

LCA using binary Search: https://youtu.be/qPxS_rY0OJw
LCA slightly different from standard algorithm: https://youtu.be/s9zZOVsF_eo

Distance Queries

Problem Statement : what is the distance between nodes a and b?
Short explanation : Let LCA(a,b) be node x, what is distance between a and x?
Preprocess the levels of all the nodes in the tree.

lvl[i] : level of node i in the tree.
Ans to query distance(a,b) = (lvl[a] — lvl[x]) + (lvl[b] — lvl[x]) where x is the LCA(a,x).

Again finding LCA of two nodes can be done in O(logN) time and levels of all nodes can be found in O(N) time preprocessing.
Explanation: https://youtu.be/i9ctLWyVSsA

Will try to add the remaining problems also as soon as possible for me.

I am also planning to add video lecture series on more topics which might be helpful to beginners as well intermediates. I will be open to feedback and suggestions.

I hope people find this helpful :)

UPD: added detailed explanation for binary lifting and video solution to Company Queries I.
UPD: added detailed explanation for LCA techniques.
UPD: added solution to distance queries(CSES) and Distance in Tree(CF, VKCup,Problem D).

 
 
 
 
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4 weeks ago, # |
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Very usefull!! Thanks!

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4 weeks ago, # |
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Nice I was looking for some tutorials and I found this!!

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4 weeks ago, # |
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Auto comment: topic has been updated by kartik8800 (previous revision, new revision, compare).

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4 weeks ago, # |
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Your Range Queries CSES Editorials, now these. You are surely doing a great help to all of us. Thanks a lot :)

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    4 weeks ago, # ^ |
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    Thankyou for the positive words :)
    I'm also making a series on dynamic programming on my channel, do check that out too.

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      4 weeks ago, # ^ |
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      surely your content will help many just keep uploading content .Channel will surely grow with time once it has a quality content.

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4 weeks ago, # |
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Tree Distances I can be solved without rerooting. The idea is to calculate the two longest paths that go only downward from each node, and then to start another dp to consider also the paths that go upward, being careful not to choose the same node twice on the same path. Submission

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    4 weeks ago, # ^ |
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    Thankyou for sharing. It would be great if you could elaborate a little more on:
    start another dp to consider also the paths that go upward
    I have trouble understanding what exactly will this dp state represent?

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4 weeks ago, # |
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Checkout thumbnail for my new video on Binary lifting.

PS: will upload by tonight.

UPD : check it out here: https://youtu.be/FAfSArGC8KY

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4 weeks ago, # |
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for Tree Distances II, a good article , https://leetcode.com/articles/sum-of-distances-in-tree/

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    4 weeks ago, # ^ |
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    looks somewhat like the reroorting technique only, not sure though didn't read it thoroughly.
    My video solution is similar to this I guess.

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4 weeks ago, # |
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All hail _LeMur_ the God of DP on trees.

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Auto comment: topic has been updated by kartik8800 (previous revision, new revision, compare).

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4 weeks ago, # |
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Is tree distance 1 can be solved like this — find the maximum of (distance between node and diameter end point1,distance between node and diameter end point2).

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    4 weeks ago, # ^ |
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    Yes it looks alright to me.
    nice Algorithm. I think the proof will be similar to tree diameter BFS approach proof.

    Did you try and Implement your idea?

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      4 weeks ago, # ^ |
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      Yes, it's working but I prefer rerooting technique as rerooting is used in many questions.

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        4 weeks ago, # ^ |
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        Hi5, same here.
        I try to avoid Algorithms which I cannot prove mathematically.
        still i did like your approach:)

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4 weeks ago, # |
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Interested people may also checkout detailed video explanations for the DP section of CSES.

Introduction to Dynamic Programming

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4 weeks ago, # |
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Carry on brother!!

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4 weeks ago, # |
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I think "tree distances I" can be solved in an easier way by using the diameter of the tree. I guess the maximum distance for each node is max of distance between the node and the two ends of diameter. This passed for me.

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3 weeks ago, # |
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Auto comment: topic has been updated by kartik8800 (previous revision, new revision, compare).

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3 weeks ago, # |
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Auto comment: topic has been updated by kartik8800 (previous revision, new revision, compare).