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1. Top results related to donald knuth mastermind algorithm

   • Donald Knuth Algorithm Mastermind

     Top Answer

     Answered Jun 17, 2020 · 2 votes

     Take the set of untried codes, and call it T.

     Iterate over T, considering each code as a guess, g.

     For each g, iterate over T again considering each code as a possible true hidden code, c.

     Calculate the black-white peg score produced by guessing g if the real code is c. Call it s.

     Keep a little table of possible scores, and as you iterate over the possible c, keep track of how many codes produce each score. That is, how many choices of c produce two-blacks-one-white, how many produce two-blacks-two-whites, and so on.

     When you've considered all possible codes (for that g) consider the score that came up the most often. You might call that the least informative possible result of guessing g. That is g's score; the lower it is, the better.

     As you iterate over g, keep track of the guess with the lowest score. That's the guess to make.

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   • Donald Knuth algorithm for Mastermind - can we do better?

     Top Answer

     Answered Feb 27, 2019 · 0 votes

     As far as I know, up till now there is no published work about this effect yet. I have made this observation some time ago, one can get better results by not always choosing the (canonically) first trial out of the "one-step-lookahead-set". I observed the different results by not starting with 1122 but with e.g. with 5544. One can also try to choose randomly and not use the canonically first. Yes, I agree with you, that is an interesting point - but a very, very special one.

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   • Knuth's algorithm for solving MasterMind with 5 guesses

     Top Answer

     Answered Dec 07, 2013 · 5 votes

     You need a constant collection of all possible outcomes, a collection of the remaining alternatives, and a method that can compute the outcome given a guess and a solution.

     First, model the relevant domain objects:

     public class Outcome{ public int White { get; set; } public int Black { get; set; }}public class Combination{ // however you like to model this}

     Then, create the method that checks the guess against the secret:

     public static Outcome Check(Combination guess, Combination solution){ // your implementation}

     Now the algorithm is as follows:

     Outcome[] outcomes = new[] { new Outcome { White = 0, Black = 0 }, new Outcome { White = 1, Black = 0 }, // ... all other possibilities };// assume we have some list of combinationsint min = Integer.MaxValue;Combination minCombination = null;foreach (var guess in combinations){ int max = 0; foreach (var outcome in outcomes) { var count = 0; foreach (var solution in combinations) { if (Check(guess, solution) == outcome) count++; } if (count > max) max = count; } if (max < min) { min = max; minCombination = guess; }}

     At the end of the loop, minCombination is your next guess.

     EDIT I messed up min and max in the first version, that is fixed now. The inner count gives the number of remaining options, provided the chosen combination and the assumed outcome. We want the maximum over the outcomes (the worst possible result for the chosen combination is the one that leaves most options remaining). After that we want the minimum over the combinations (the best possible combination is the one that leaves least options remaining in the worst case).

     If you like Linq, you could also write the algorithm as

     combinations.MaxBy(guess => outcomes.Min(outcome => combinations.Count(solution => Check(guess, solution) == outcome)));

     in which I used MaxBy from the MoreLinq project.

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   • Knuth–Morris–Pratt algorithm: border array

     Top Answer

     Answered May 11, 2023 · 1 votes

     OP 1."I don't really understand the border array meaning how to interpret it."

     In this case, border means prefix and suffix of string.Border value means longest prefix == suffix.Gassa example - brackets [] mean [prefix]==[suffix]

     why does border[3]=1? column: [0]12[3] string: [a]bc[a] why does border[4]=2? column: [01]2[34] string: [ab]c[ab] why does border[5]=1? column: [0]1234[5] string: [a]bcab[a]

     OP 2."For instance if the pattern does not equal at position (i+1) and (j-1) the variable i is set to border[i+1]. Why is that for example?"

     The comparison is checking if the last prefix/suffix character matchfor example: (p[i+1] != p[j-1])

     if they don't match, reduce comparison size of prefix/suffix from border[j-1]+1 to border[i+1]

     for example: i = border[i+1]

     OP 3."question that three consecutive entries in a border array cannot differ by one from its predecessor. E.g. border[10]=3, border[11]=2, border[12]=1"

     When size of string increases by 1, two things can happenSize of longest prefix/suffix can only increase by 1 or is less than thatIn other words, border[i+1]<=border[i]+1

     also, did you mean border array values canNOT differ more than one from its predecessor? because here is an example of predecessor CAN differ more than one column: 01234 string: babaa border: 00120

     as you can see border[3]=2 and border[4]=0 so they differ by 2 not 1

     sources: I learn that border value means longest prefix == suffix from gassa link stackoverflow

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   • Donald Trump Launches His New Social Media App 'Truth Social' on iOS

     Former US President Donald Trump has again made the headlines by launching his new social media venture “Truth Social” on Monday. Being banned from all the social media platforms Trump took this decision of starting his own application, which has been listed on the Apple Store in the United States. 

     This application has a resemblance to Twitter from where Trump was banned in the first place. He made Truth Social as same as Twitter because he preferred the same very much. The application has been developed by Trump’s new media company T Media Tech LLC. The app size is 12.4 MB and can be used free of cost. Although the app has not been launched for Android users, which they will get in some time.

     The main idea behind starting Truth Social is to give a platform to the active or constructive politicians who are banned or blocked from Twitter for giving their opinions or creating chaos among people. As we all know that in the year 2021 Donald Trump was blocked from Twitter as he was accused of posting violence-inciting messages. Thus, this incident gave him...

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2. stackoverflow.com › questions › 62430071Donald Knuth Algorithm Mastermind - Stack Overflow

   stackoverflow.com › questions › 62430071

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   Jun 17, 2020 · The algorithm works as follows: Create the set S of 1296 possible codes (1111, 1112 ... 6665, 6666). Start with initial guess 1122 (Knuth gives examples showing that other first guesses such as 1123, 1234 do not win in five tries on every code). Play the guess to get a response of colored and white pegs. If the response is four colored pegs ...

3. en.wikipedia.org › wiki › Mastermind_(board_game)Mastermind (board game) - Wikipedia

   en.wikipedia.org › wiki › Mastermind_(board_game)

   • Cached

   In 1977, Donald Knuth demonstrated that the codebreaker can solve the pattern in five moves or fewer, using an algorithm that progressively reduces the number of possible patterns. Described using the numbers 1–6 to represent the six colors of the code pegs, the algorithm works as follows:

4. betterprogramming.pub › solving-mastermindSolving Mastermind With Python - Better Programming

   betterprogramming.pub › solving-mastermind

   • Cached

   Mar 31, 2022 · I started doing some research and saw that Donald Knuth, a computer science legend, had actually written an algorithm to solve Mastermind. Perhaps it was born out of the same frustration that I was feeling with the game. I decided to implement Knuth’s paper: “ The Computer As Master Mind ”.

5. theses.liacs.nl › pdf › 2018-2019-GraafSdeCracking the Mastermind Code - Leiden University

   theses.liacs.nl › pdf › 2018-2019-GraafSde

   m is the length of the code we need to crack, and a/na tells us if it is allowed to use the same colour multiple times in the code. Back in 1977, Donald Knuth described an algorithm that can crack each of the 64 = 1296 possible codes of a Mastermind(6, 4, a) game, in five guesses or less [Knu77].

6. github.com › Mastermind-Five-Guess-AlgorithmNathanDuran/Mastermind-Five-Guess-Algorithm - GitHub

   github.com › Mastermind-Five-Guess-Algorithm

   • Cached

   Donal Knuth's five guess algorithm for solving the game Mastermind. In 1977, Donald Knuth demonstrated that the codebreaker can solve the pattern in five moves or fewer, using an algorithm that progressively reduced the number of possible patterns. The algorithm works as follows:

7. People also ask

   How did Donal Knuth solve mastermind?

   • Donal Knuth's five guess algorithm for solving the game Mastermind. In 1977, Donald Knuth demonstrated that the codebreaker can solve the pattern in five moves or fewer, using an algorithm that progressively reduced the number of possible patterns. Create the set S of 1296 possible codes (1111, 1112 ... 6665, 6666).

   NathanDuran/Mastermind-Five-Guess-Algorithm - GitHub

   github.com/NathanDuran/Mastermind-Five-Guess-Algorithm

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   How many Knuth codes do you need to crack a mastermind code?

   • We walk approximately 20 times more paths if we always check every code in guess codes when it does not contain any Knuth code. For EPBOK, only 2:87 10 3% of the total paths need six guesses to crack the Mastermind code, while 1.11% of the total paths need six guesses for EPB.

   Cracking the Mastermind Code - Leiden University

   theses.liacs.nl/pdf/2018-2019-GraafSde.pdf

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   How good is Knuth's guessing algorithm?

   • The guessing algorithm in action (GIF by author) Using this algorithm, it is guaranteed that the computer will guess the correct answer in sixmoves or less, meaning it never loses. Not quite as good as Knuth’s five guesses, but we have 1,829 more potential answers to contend with.

   Solving Mastermind With Python - Better Programming

   betterprogramming.pub/solving-mastermind-641411708d01

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   Does Knuth's selection procedure have a better algorithm?

   • @GilShafriri It's unlikely that when a better algorithm is found, someone will publish details about tweaks to a worse algorithm, so there may indeed be no published work on this particular tweak to Knuth's selection procedure.

   Donald Knuth algorithm for Mastermind - can we do better?

   stackoverflow.com/questions/53826287/donald-knuth-algorithm-for-mastermind-can-we-do-better

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8. archive.org › knuth-mastermind_textTHE COMPUTER AS MASTER - Archive.org

   archive.org › knuth-mastermind_text

   Computer Science Department. Stanford University. A deductive game called Master Mind, produced by Invicta Plastics, Ltd., enjoyed a wave of popularity during the 1975 Christmas season [2] . In this. game one player (the "codemaker") conceals a four-symbol code, and the other. player (the "codebreaker") tries to identify all four symbols by ...

9. www.seas.upenn.edu › ~ncollina › MastermindFastermind: Using a SAT-solver to play Mastermind more ...

   www.seas.upenn.edu › ~ncollina › Mastermind

   number of turns for player 2 to win. The earliest known Mastermind algorithm, presented by Donald Knuth in 1977, did just this. In Knuth’s strategy, each turn player 2 considers all possible moves and all possible consistent responses by player 1. They score these responses based upon how