Get this book -> Problems on Array: For Interviews and Competitive Programming. However, notice a few things about the performance of the algorithm: As shown, theres a significant increase in the number of times our function is called. True/False. Remark: We trade space for time. < v n (all integers). Mass Tech Layoff in 2023: How to stay safe? The two most previous values are added to a result, which is appended to the main array sequence. 0000005285 00000 n
Lately, I've practiced several dp problems, but when I stuck in a task, I don't find great info to improve my dp skills. Introduction. Of course, recording these subproblem solutions is memoization, but theres more to it. 0000011143 00000 n
Return(a,b) endobj So take the first question, solve it and then move to the next one. The more you get experienced, the more you'll learn the importance of sorting things for practicing. Show problem tags # Title Acceptance Difficulty Frequency; 5: Longest Palindromic Substring. Problem Statement Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight doesnt exceed a given limit and the total value is as large as possible. trailer
Assume that the numbers given below represent counts of letters in the hundreds from a file (similar to the CLRS example). Short answer: a) (3pts) Huffman coding is a Dynamic Programming problem. However, we can see the value of 3 doesnt exist, so the algorithm will repeat the same process for the next value (in our case, 10) until it finds a successful matching pair. First, use a recursive approach to implement the given recurrence relation. Now that youve gone through some of the most popular dynamic programming problems, its time to try implementing the solutions by yourself. A well-known example of recursion can be seen with the Fibonacci sequencea numerical sequence made by adding the two preceding numbers (0, 1, 1, 2, 3, 5, 8, 13, 21, etc): When examined, our code is error-free and works as expected. xref
You have solved 0 / 419 problems. Why You Shouldn't Trust ChatGPT With Confidential Information, How to Combine Two Columns in Microsoft Excel (Quick and Easy Method), Microsoft Is Axing Three Excel Features Because Nobody Uses Them, 3 Ways to Fix the Arrow Keys Not Working in Excel, The maximum obtainable value by including item i is the sum of item, Perform this step until you find the maximum value for the, Since there is no denomination for 0, initialise the base case where. 0000005530 00000 n
0 Attempts 14 Tests 0% Codemonk Be better at programming one step at time. /R 22050 ), Simple mistake that some people make when analysing time complexity, Ukrainian Olympiad in Informatics 2023 Mirror, [Seeking Help] Problem: 999C. Optimal control requires the weakest assumptions and can, therefore, be used to deal with the most general problems. Notice how the refactored code no longer requires a recursive technique. WebProgramming Tutorials and Practice Problems Interview Prep Ace your upcoming interview. (Quora): https://www.quora.com/How-can-I-be-perfect-in-dynamic-programming-How-should-I-practice/answer/Bohdan-Pryshchenko?ch=10&share=9a742611&srid=DDSy, SOS Dynamic Programming [Tutorial] (Codeforces Blog): http://codeforces.com/blog/entry/45223. While you dont necessarily need to memorize the solution to every problem, its good to have an idea of how to go about implementing one. I think this article could lead someone to think that memoization is synonym for dynamic programming. The idea: Compute thesolutionsto thesubsub-problems endobj xTMO0W G4@B
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I8F>& Dynamic programming problems can catch you off-guard in an interview or exam. WebFundamentals of Reinforcement Learning. Dynamic Programming is mainly an optimization over plain recursion. And practice more, take your time. 25 0 obj 0000014029 00000 n
Recursively define value of optimal solution. Those three methods are (i) cal-culus of variations,4 (ii) optimal control, and (iii) dynamic programming. ): https://www.youtube.com/watch?v=rlTkd4yOQpE, Dynamic Programming (Go Code): https://www.youtube.com/playlist?list=PLawezQIZQjju9cZPjjD1vQK8IuNxcRD8u, Dynamic Programming from Novice to Advanced (Topcoder): https://www.topcoder.com/community/competitive-programming/tutorials/dynamic-programming-from-novice-to-advanced/, Tutorial on Dynamic Programming (Codechef): https://www.codechef.com/wiki/tutorial-dynamic-programming, Getting started with Dynamic Programming (Quora Discussion): https://www.quora.com/How-can-one-start-solving-Dynamic-Programming-problems/, Dynamic Programming (Hackerearth): https://www.hackerearth.com/practice/algorithms/dynamic-programming/introduction-to-dynamic-programming-1/tutorial/, A Brief Introduction to Dynamic Programming (Obada AlAbbadi): https://drive.google.com/file/d/1K68sWVc5e4MnyACr2i5sLKWIhShn638S/view?usp=sharing, Everything About Dynamic Programming (Codeforces Blog): https://codeforces.com/blog/entry/43256. /Length 406 13 0 obj The longest increasing subsequence is a subsequence within an array of numbers with an increasing order. WebDynamic Programming. Web2 Dimensional. 0000012871 00000 n
Minimizing the downsides of dynamic programming languages, The Overflow #162: The great testing flake off, From Smalltalk to smart contracts, reflecting on 50 years of programming (Ep. By using our site, you (String Similarity) /@K(nvWF|3,*Z4Ur&hM\eaaD|R;P^.u_VS (Weighted Interval Scheduling) Similar to our previous example, the algorithms performance decreases exponentially based on the input size. WebGreed. :PL Ba7eMvIlsk::QMBl\ =.%?l'u;`JaAUg7rt_3?p hg9&=nC*0tvWbG ]A/z-\[eae*?#"P]|yo8p2bY\Q-7O*]Po]zixM9mM{c91._-0v%? WebDynamic Programming Summary Recipe. Let me know what you think. 0000026333 00000 n
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When learning various programming techniques, one topic that comes to mind is recursion. 0000066663 00000 n
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Lets review both techniques. >> Weve learned that dynamic programming isnt a specific design pattern as it is a way of thinking. ): https://www.youtube.com/watch?v=U4O3SwDamA4, Episode 20 Bitmask Dynamic Programming (Algorithms Live! False H2. 20 0 obj Optimal control requires the weakest Web1 Huffman code tree - Solution H1. for j,b in enumerate(sequence): Dynamic programming isn't about design patterns; it's a way of thinking that breaks down a problem into individual components. This occurs because the operation does not store previously calculated values. For example, in the file there will be exactly 20 * 100 occurrences of the letter a , 11*100 Save my name, email, and website in this browser for the next time I comment. Short answer: a) (3pts) Huffman coding is a Dynamic Programming problem. x However, the fact is that many of these brain-teaser questions are designed to test for a basic understanding of computer science fundamentals. Break up a problem into two sub-problems, solve each sub-problem If(i != j and b==diff): See here for the origin of the term: https://en.wikipedia.org/wiki/Dynamic_programming#History. There `value(i,j)=min( value(i-1,j),value(i,j-1) )` so you make a wavefront for values as you progress through `i,j` space. If you are beginner, start from the first question. In comparison, a greedy algorithm treats the solution as some sequence of steps and picks the locally optimal choice at each step. 0000007809 00000 n
As someone who doesnt usually click on article-links from the Overflow, I have to say I was disappointed with this one. It helps newcomer like me a lot. The main idea of dynamic programming is to consider a significant problem and break it into smaller, individualized components. WebWe demonstrate this effectiveness and simplicity by showing how the dynamic programming technique can be applied to several different types of problems, including matrix-chain prod- ucts, telescope scheduling, game strategies, the above-mentioned longest common subsequence problem, and the 0-1 knapsack problem. WebSolve practice problems for Introduction to Dynamic Programming 1 to test your programming skills. Thanks, added. thank youu. Essays, opinions, and advice on the act of computer programming from Stack Overflow. As we know, a variables purpose is to reserve a specific place in memory for a value to be recalled later. endobj We break down a big problem into smaller problems. << This is the List of 100+ Dynamic Programming (DP) Problems along with different types of DP problems such as Mathematical DP, Combination DP, String DP, Tree DP, Standard DP and Advanced DP optimizations. 0000003885 00000 n
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2. WebProblems related to Dynamic Programming: You have to solve these problems to develop DP skills Simple DP Problems: Lightoj Problems New Year and the 0000013182 00000 n
Simply put, dynamic programming is an optimization method for recursive algorithms, most of which are used to solve computing or mathematical problems. Each dynamic programming practice problem has its solution with the examples, detailed explanations of the solution approaches. Suppose youre given an array of numbers that represent the values of each coin. This further streamlines the solution, as the set is designed to retrieve values in an optimized way regardless of size. solutions for larger subproblems, and eventually solving the original problem. 0000009241 00000 n
WebLINEAR PROGRAMMING: EXERCISES - V. Kostoglou 10 The first product is completed in three phases, while the second one is required to pass a fourth phase, which can be performed either by machine M 2 or machine M 3. Sd?2QlUbbQM,z>nkwL
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Maybe I mentioned this in the beginning. Step 4 can be omitted if only the value of an opti-mal solution is required. This essay will examine what dynamic programming is and why you would use it. Compute value of optimal solution. It'll help me too. The correction for the brute force solution could be (python): 27 0 obj 151 0 obj
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The official account of OpenGenus IQ backed by GitHub, DigitalOcean and Discourse. Yash is an aspiring computer science student who loves to build things and write about all things tech. It doesnt even begin to touch upon what I consider the basics of DP, which is the solving of problems by solving other (smaller) sub-problems. Muhammad Afifi): https://www.youtube.com/watch?v=TNgPT91sn90, Dynamic Programming (Prof. Mostafa Saad): https://www.youtube.com/playlist?list=PLPt2dINI2MIattDutu7IOAMlUuLeN8k2p, Dynamic Programming Practice (Solver To Be): https://www.youtube.com/playlist?list=PLPSFnlxEu99Gc6mSTVoYzPG77tnUW8znJ, Dynamic Programming Practice (IDeserve): https://www.youtube.com/playlist?list=PLamzFoFxwoNjtJZoNNAlYQ_Ixmm2s-CGX, Dynamic Programming (Gaurav Sen): https://www.youtube.com/playlist?list=PLMCXHnjXnTnto1pZVvH7rbZ9W5neZ7Yhc, Dynamic Programming, Recursion, & Backtracking (Back To Back SWE): https://www.youtube.com/playlist?list=PLiQ766zSC5jM2OKVr8sooOuGgZkvnOCTI, Dynamic Programming (Tushar Roy): https://www.youtube.com/playlist?list=PLrmLmBdmIlpsHaNTPP_jHHDx_os9ItYXr, Dynamic Programming (Abdul Bari): https://www.youtube.com/playlist?list=PLJULIlvhz0rE83NKhnq7acXYIeA0o1dXb, Dynamic Programming (GeeksforGeeks): https://www.youtube.com/playlist?list=PLqM7alHXFySGbXhWx7sBJEwY2DnhDjmxm, Dynamic Programming: From Zero To Hero (Rachit Jain): https://www.youtube.com/playlist?list=PLfBJlB6T2eOtMXgK3FLUTawHjzpIEySHF, Dynamic Programming (MIT Open Course): https://www.youtube.com/playlist?list=PLZDUDpMlJOnzqEo45zDQjuZqv2PGRNHI1, Dynamic Programming AtCoder educational dp contest (Errichto): https://www.youtube.com/watch?v=FAQxdm0bTaw, Dynamic Programming Tutorials (VPlanet): https://www.youtube.com/channel/UCdNNY8Y8meG3z9Wy6MTzcLg/videos, Episode 19 Knapsack (Algorithms Live! 0000013425 00000 n
These are not just random links. This technique chunks the work into tiny pieces so that the same work is being performed over and over again. 0000010809 00000 n
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WebEach dynamic programming practice problem has its solution with the examples, detailed explanations of the solution approaches. Storing the whole lot in an array is a waste of memory and isnt showing a novice programmer how this problem should be solved. Ill be illustrating this concept with specific code examples in Swift, but the concepts I introduce can be applied to your language of choice. A"v@*a :'(/R"iH~2N5(YL#\Q[. 35 0 obj ?|DD?qsv'Mj0v4bmNzG{Lw Qy-rI'CC++hs,s9fDI#sCEDS@I*Qjd]r'z:=\Pf,\tH0=*k'a,ycu^u{?$q:R`5xFq6qH3$Q%M>")3h}zF>$&F|gy9_nT-W~kVz}Y5Yo8cm;/
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>> 26 0 obj The best way to be good at dynamic programming problems is to go through as many of them as you can. Recursive solutions work by having a model that refers to itself. We have covered Idea of Approximate algorithms for NP problems. 0000005853 00000 n
Bookmark this page and practice each problem. This is not the complete guide and DP is much more than just memoization. If only there was a site you could put up code for review before you publish it on your blog. 1315 2"N2z.jo$Oc{ 985 Theres no doubt that dynamic programming problems can be very intimidating in a coding interview. 9 0 obj New Collective for Azure, the logic of the universe, and !document.write(). Auto comment: topic has been updated by Ahnaf.Shahriar.Asif (previous revision, new revision, compare). Computer science: theory, graphics, AI, compilers, systems, If this is the quality of articles I can expect from that newsletter, I may not be clicking in too often. 776 Typical DP Contest: https://atcoder.jp/contests/tdpc. As well see, many questions in software development are solved using various forms of dynamic programming. These questions are sorted by the difficulty level. 28 0 obj << The idea is to simply store the results of subproblems so that we do not have to re-compute them when needed later. 28.0%: Hard: 22: Generate Parentheses. xVPSW$!bb M
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SoFv&wse.X zZwE.='RxkG]?/; ]n&WJM#5{/qx To call this guide complete even for beginners, would be a bit of a stretch. Now that you have a good idea of what dynamic programming is, its time to check out a few common problems and their solutions. In DP tutorials, isn't 1. and 2. the same? 0000014410 00000 n
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7. There is another DP contest in atcoder but looks only Japanese statements. Start with a recursive approach where you calculate the value of the longest increasing subsequence of every possible subarray from index zero to index i, where i is lesser than or equal to the size of the array. %PDF-1.5 0000003686 00000 n
True/False. endobj I'll add them. WebDynamic Programming Problems Dynamic Programming Steps to solve a DP problem 1De ne subproblems 2Write down the recurrence that relates subproblems 3Recognize A-143, 9th Floor, Sovereign Corporate Tower, We use cookies to ensure you have the best browsing experience on our website. Thank you and if you have other tutorials or problems do mention them. Of course this time the cost is worse since you need to build the dictionary O(n) and then search the list with length 2 O(n-1). https://www.includehelp.com some rights reserved. You have to solve these problems to develop DP skills, Different types of Dynamic programming problems in one blog. The Fibonacci Series is a sequence of integers where the next integer in the series is the sum of the previous two. xK0>&{D*.CvHmM}%4@zZ?3=adNy7`(Z4)gnh _C9;WZ7kkFO[ZdlZj2x3FT1:V-}MU9d$^4i G{,X&ye6
Fe1/2&Os! Also given is an integer W which represents the knapsack capacity. Ponzi schemes and transversality conditions. 0000009660 00000 n
https://www.youtube.com/watch?v=FAQxdm0bTaw&t=312s Here Errichto explains some DP problems. Here's how to add some guardrails to your code. %PDF-1.4
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Problems. <> Standard problems on Dynamic Programming: If you like GeeksforGeeks and would like to contribute, you can also write an article and mail your article to [emailprotected] See your article appearing on the GeeksforGeeks main page and help other Geeks. While examples include basic algorithms, dynamic programming provides a foundation in almost all programs. Unfortunately, I have to agree with Miles Smarcks comment with the lack of quality and clickbait title of this post. >> 0000009110 00000 n
A key principle that dynamic programming is based on is that the optimal solution to a problem depends on the solutions to its sub-problems. The trick is recognizing when optimal solutions can be devised using a simple variable or require a sophisticated data structure or algorithm. You are assuming that there is no repetition of numbers in your sequence and the query number is the sum of those. Add this: https://www.youtube.com/watch?v=YBSt1jYwVfU and this: https://www.youtube.com/watch?v=1mtvm2ubHCY&t=72s if you haven't already. % To turn this method into a dynamic one, create an array to store the value for every subsequence. 204 0 obj
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bJU,f>ZP2UjLjnZ0\/Wj~9Ofc|\~; XFk|+%Q@I-?hJK_)&bB6c;Y6SoGCcd@$EI7[5Q.$}`% )zx{7*J:UGS\!n%!'3|`iF{&>$> bo7 stream 10 0 obj Naturally, having the know-how of common problems is bound to pay dividends when you go for your next interview. It provides a systematic procedure for determining the optimal com Build up a solution incrementally, myopically optimizing some local criterion. Given a set of items, each with a weight and a value, determine the number of each item to include in a collection so that the total weight doesnt exceed a given limit and the total value is as large as possible. The main idea of dynamic programming is to consider a significant problem and break it into smaller, individualized components. Theorem. Can we avoid using quadratic space? ut [O' x='=]im= F
y(V :+Z(. While using a standard array is feasible, a set collection object (also referred to as a hash table or hash map) could provide an optimized solution. 0000072769 00000 n
WebQ. endobj So, I am listing down them below and dividing them into different Youre given two integer arrays values[0..n-1] and weights[0.. There are many problems in online coding contests which involve finding a minimum-cost path in a grid, finding the number of ways to reach a particular position from a given starting point in a 2-D grid and so on. 17 0 obj This will ensure that for every n. For any subsequent calculations, its value can simply be retrieved from the array in constant time. stream Discuss. ;'o#)~ cF#l5dvi8CL
lfuQ@'~>8Ea6tk]m=MR*C'H@)0~0vRTNTT%Ynq$/6cxMwH Ihlendstream Bitmasking and Dynamic Programming | Set 1 (Count ways to assign unique cap to every person), Bell Numbers (Number of ways to Partition a Set), Introduction and Dynamic Programming solution to compute nCr%p, Count all subsequences having product less than K, Maximum sum in a 2 x n grid such that no two elements are adjacent, Count ways to reach the nth stair using step 1, 2 or 3, Travelling Salesman Problem using Dynamic Programming, Find all distinct subset (or subsequence) sums of an array, Count number of ways to jump to reach end, Count number of ways to partition a set into k subsets, Maximum subarray sum in O(n) using prefix sum, Maximum number of trailing zeros in the product of the subsets of size k, Minimum number of deletions to make a string palindrome, Find if string is K-Palindrome or not | Set 1, Find the longest path in a matrix with given constraints, Find minimum sum such that one of every three consecutive elements is taken, Dynamic Programming | Wildcard Pattern Matching | Linear Time and Constant Space, Longest Common Subsequence with at most k changes allowed, Largest rectangular sub-matrix whose sum is 0, Maximum profit by buying and selling a share at most k times, Introduction to Dynamic Programming on Trees, Traversal of tree with k jumps allowed between nodes of same height, Learn more about Dynamic Programming in DSA Self Paced Course, Introduction to Dynamic Programming Data Structures and Algorithm Tutorials, Bitmasking and Dynamic Programming | Set 1, Bitmasking and Dynamic Programming | Set-2 (TSP), Longest subsequence such that difference between adjacents is one, Maximum size square sub-matrix with all 1s, Longest Common Substring (Space optimized DP solution), Count all possible paths from top left to bottom right of a mXn matrix, Unbounded Knapsack (Repetition of items allowed), Travelling Salesman Problem | Set 1 (Naive and Dynamic Programming), Longest Common Increasing Subsequence (LCS + LIS), Count Derangements (Permutation such that no element appears in its original position), Ways to arrange Balls such that adjacent balls are of different types, Printing brackets in Matrix Chain Multiplication Problem, Minimum cost to sort strings using reversal operations of different costs, Count of AP (Arithmetic Progression) Subsequences in an array, Maximum height of Tree when any Node can be considered as Root, Longest repeating and non-overlapping substring, Learn Data Structure and Algorithms | DSA Tutorial, Top 20 Dynamic Programming Interview Questions, Practice Problems on Dynamic Programming. 0000005775 00000 n
Patent story: Google is not owner of PageRank patent? <> Dynamic languages allow for a lot of flexibility in typing sometimes too much. << /S /GoTo /D (Outline4) >> Often a key subject in technical interviews, the idea will also come up in design review meetings or regular interactions with fellow developers. stream WebSolve practice problems for Introduction to Dynamic Programming 1 to test your programming skills. The numbers within the subsequence have to be unique and in ascending order. <> Short answer: a) (3pts) Huffman coding is a Dynamic Programming problem. << /S /GoTo /D (Outline3) >> 12 0 obj WebHighlights. Even when you may know that a problem needs to be solved using a dynamic programming method, its a challenge to be able to come up with a working solution in a limited time frame. t;OgPWR:2@muO( l8Rpz*tXbc+'xBSEpR(p2o)EP+ endstream
Unlike specific coding syntax or design patterns, dynamic programming isnt a particular algorithm but a way of thinking. Lets begin! Web1) Given solution table partially filled out, finish filling it out. Bookmark this page and practice each problem. If you understand Bengali, it may help. Dynamic programming practice problems: Here, you will find the various dynamic programming practice problems with solutions that are commonly asked in the various interview rounds of the companies. Divide-and-conquer. So practice more and gather experiences. endobj I will list my favorite problems that you can solve with dynamic programming:https://acm.timus.ru/problem.aspx?space=1&num=1844 (Warlord of the Army of Mages Easy)https://acm.timus.ru/problem.aspx?space=1&num=1508 (Japanese Puzzle Easy-Medium)https://acm.timus.ru/problem.aspx?space=1&num=1552 (Brainfuck Medium)https://acm.timus.ru/problem.aspx?space=1&num=1177 (Like Comparisons Medium)https://acm.timus.ru/problem.aspx?space=1&num=1532 (Lost in Translation Hard) -> DP optimization problem https://acm.timus.ru/problem.aspx?space=1&num=2107 (Oppa Funcan Style Hard) -> BitwiseMany will disagree with the difficulties, but that was my experience. stream tutorial, OpenGenus IQ: Computing Expertise & Legacy, Position of India at ICPC World Finals (1999 to 2021). Feel free to share your opinion. diff =sum-a Without going into the details of big-O notation, we can assume this type of solution would have an average runtime of O(n ^ 2)time or greater, mainly because our algorithm works by comparing each value with every other value. Count all subsequences in an array with product less than K, Number of arithmetic progression subsequences, Find if a Subset with sum divisible by m exist, Find Number of Subset with sum divisible by M, Largest rectangular sub matrix having sum divisible by k, Break a number in 3 parts (n/2, n/3, n/4) recursively to get maximum sum, Partition a set into two subsets such that sum of each subset is same, Minimum number of increment or decrement (by 1) operations to make array in increasing order, Number of substrings divisible by 8 but not 3, Longest repeating and non overlapping substring in a string, Maximum Sum Increasing Subsequence of size K, Maximum product of an increasing subsequence, Minimum number of elements which are not part of Increasing or decreasing subsequence in array, Minimum number of increment or decrement (by 1) operations to make array in decreasing order, number of subsets of an array having a given XOR value, number of subsets with given Bitwise OR value, Number of non unique Partitions of an Integer, Number of unique partitions of an integer, Number of ways to reach a given number using increments of 1 and 2, Number of ways to reach a number using increments of 1 and 2 (consecutive 2s are not allowed), Number of ways to reach a number using increments of 1 and 2 (consecutive 1s are not allowed), Number of ordered pairs such that (A[i] & A[j])=0, number of sub matrices having sum divisible by K, number of subsets with sum divisible by given number M, Ways to increase LCS length of two strings by one, Find if a string is interleaved of two other strings, Number of ways to insert a character to increase the LCS by one, Number of ways to divide string in sub-strings such to make them in lexicographically increasing sequence, minimum number of deletions to make a string palindrome, Minimum number of characters to be deleted to make string a palindrome. Edit Distance (ED), Longest Common Subsequence (LCS), Longest Increasing Subsequence (LIS) P1-MIX. Operations research. >> Store the results of all function calls in an array. This includes the use of simple variables and complex data structures. << /S /GoTo /D (Outline1) >> The idea is to simply store the results of subproblems, so that we do not have to re-compute them when needed later. True/False. While you might not run into these problems on a daily basis, you'll surely encounter them in a technical interview. Its defined by the following recursive relation: F(0) = 0, F(n) = F(n-1) + F(n-2), where F(n) is the nth term. 0 Solved 314 Problems 0% Data Structure Master important data structures. stream Any query or difficulty? The idea: Compute thesolutionsto thesubsub-problems once and store the solutions in a table, so that they can be reused (repeatedly) later. When it comes to implementation, << /S /GoTo /D [26 0 R /Fit ] >> So open up your favourite IDE, and get started! 0000011732 00000 n
Information theory. Here were solving the 0/1 knapsack problem, which means that we can choose to either add an item or exclude it. lxZu5HH`oVarzb|LOUzi_p(H>74snp .J`HtEM*4(isj=4}(\(pL{[ nH?Sf1Bf"KgA~d^(IA_> Learn how your comment data is processed. Today I've listed some DP tutorials and problems. False H2. Alphabetic Removals, Invitation to SmallForces Monthly Contest #1, Invitation to NUS CS3233 Final Team Contest 2023 Mirror, Mirror of Independence Day Programming Contest 2023 by MIST Computer Club, Invitation to Bug Game [marathon problem, mirror of buglab.ru], Java fastest output method for interactive problems, Dynamic Programming,from novice to advanced, A little bit of classics: dynamic programming over subsets and paths in graphs, Algorithms Series | Session 3 | Dynamic Programming (Arabic), New Year and the Permutation Concatenation, https://www.youtube.com/watch?v=34Drti_iMsg, https://www.youtube.com/watch?v=TNgPT91sn90, https://www.youtube.com/playlist?list=PLPt2dINI2MIattDutu7IOAMlUuLeN8k2p, https://www.youtube.com/playlist?list=PLPSFnlxEu99Gc6mSTVoYzPG77tnUW8znJ, https://www.youtube.com/playlist?list=PLamzFoFxwoNjtJZoNNAlYQ_Ixmm2s-CGX, https://www.youtube.com/playlist?list=PLMCXHnjXnTnto1pZVvH7rbZ9W5neZ7Yhc, https://www.youtube.com/playlist?list=PLiQ766zSC5jM2OKVr8sooOuGgZkvnOCTI, https://www.youtube.com/playlist?list=PLrmLmBdmIlpsHaNTPP_jHHDx_os9ItYXr, https://www.youtube.com/playlist?list=PLJULIlvhz0rE83NKhnq7acXYIeA0o1dXb, https://www.youtube.com/playlist?list=PLqM7alHXFySGbXhWx7sBJEwY2DnhDjmxm, https://www.youtube.com/playlist?list=PLfBJlB6T2eOtMXgK3FLUTawHjzpIEySHF, https://www.youtube.com/playlist?list=PLZDUDpMlJOnzqEo45zDQjuZqv2PGRNHI1, https://www.youtube.com/watch?v=FAQxdm0bTaw, https://www.youtube.com/channel/UCdNNY8Y8meG3z9Wy6MTzcLg/videos, https://www.youtube.com/watch?v=U4O3SwDamA4, https://www.youtube.com/watch?v=rlTkd4yOQpE, https://www.youtube.com/playlist?list=PLawezQIZQjju9cZPjjD1vQK8IuNxcRD8u, https://www.topcoder.com/community/competitive-programming/tutorials/dynamic-programming-from-novice-to-advanced/, https://www.codechef.com/wiki/tutorial-dynamic-programming, https://www.quora.com/How-can-one-start-solving-Dynamic-Programming-problems/, https://www.hackerearth.com/practice/algorithms/dynamic-programming/introduction-to-dynamic-programming-1/tutorial/, https://drive.google.com/file/d/1K68sWVc5e4MnyACr2i5sLKWIhShn638S/view?usp=sharing, https://www.quora.com/How-can-I-be-perfect-in-dynamic-programming-How-should-I-practice/answer/Bohdan-Pryshchenko?ch=10&share=9a742611&srid=DDSy, https://www.youtube.com/watch?v=FAQxdm0bTaw&t=312s, https://www.youtube.com/watch?v=YBSt1jYwVfU, https://www.youtube.com/watch?v=1mtvm2ubHCY&t=72s, https://acm.timus.ru/problem.aspx?space=1&num=1844, https://acm.timus.ru/problem.aspx?space=1&num=1508, https://acm.timus.ru/problem.aspx?space=1&num=1552, https://acm.timus.ru/problem.aspx?space=1&num=1177, https://acm.timus.ru/problem.aspx?space=1&num=1532, https://acm.timus.ru/problem.aspx?space=1&num=2107. 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