{"id":753,"date":"2022-01-28T21:09:09","date_gmt":"2022-01-28T21:09:09","guid":{"rendered":"https:\/\/perfectionatic.org\/?p=753"},"modified":"2022-01-30T11:02:14","modified_gmt":"2022-01-30T11:02:14","slug":"exploring-wordle-with-julia-part-i","status":"publish","type":"post","link":"https:\/\/perfectionatic.org\/?p=753","title":{"rendered":"Exploring Wordle with Julia: Part I"},"content":{"rendered":"\n

Wordle<\/a> is a fun and easy game that has shot to fame recently. It is completely minimalistic, no-fills and highly addictive<\/a>. We will explore here how to write as simple solver for Wordle with Julia and then adding layers of complexity and sophistication as we go along. <\/p>\n\n\n\n

In Wordle we are successively guessing five-letter words. After each guess the game tells us which of our letters occur in the secret<\/em> word and whether they are in the correct position. As explained in their website. <\/p>\n\n\n\n

\"\"<\/a><\/figure>\n\n\n\n

So after each guess we narrow the set of possible words to choose from till we arrive at the secret word, and we only have six tries. <\/p>\n\n\n\n

Our Dictionary <\/h2>\n\n\n\n

Wordle only deals with a valid five-letter English words. So we need to start grabbing such words. A good place to start is the Standford GraphBase<\/a> data set. <\/p>\n\n\n\n

\nhttps:\/\/gist.github.com\/mbeltagy\/51e4672379a71e5d73c789e6106bc296#file-word_dict-jl\n<\/div><\/figure>\n\n\n\n

Constraints<\/h2>\n\n\n\n

The next step is the try narrow down the set of feasible words as we are getting clues. Towards that end, we construct a Dict<\/code> to map letters that are in the word at the correct spot<\/mark> to their location, another Dict<\/code> to maps letter in the word that are in the wrong spot<\/mark>, and finally a Set<\/code> of letters that are not in the word<\/mark>:<\/p>\n\n\n\n

\nhttps:\/\/gist.github.com\/mbeltagy\/51e4672379a71e5d73c789e6106bc296#file-constraint_definition-jl\n<\/div><\/figure>\n\n\n\n

Now we can encode the the response we get the game as String<\/code> of numbers, where 0<\/mark> means that the character is not in the word, 1<\/mark> means the that character is the word but not in the right spot, and 2<\/mark> means that the character is in the word at the correct spot. For example <\/p>\n\n\n\n

\n
\n
Secret Word<\/strong>:    perky\nCandidate<\/strong> Word<\/strong>: e<\/mark>bon<\/mark>y<\/mark>\nResponse<\/strong>:       10002<\/pre>\n<\/div>\n<\/div>\n\n\n\n
We can update our set of constraint for any response by the following function:<\/p>\n\n\n\n
\nhttps:\/\/gist.github.com\/mbeltagy\/51e4672379a71e5d73c789e6106bc296#file-update_constraints_by_response-jl\n<\/div><\/figure>\n\n\n\n
Shrinking the feasible set of words <\/h2>\n\n\n\n
The constraints will reduce the feasible set of possible words. This can be done by applying filters that make use of constraints as in the following function:  <\/p>\n\n\n\n
\nhttps:\/\/gist.github.com\/mbeltagy\/51e4672379a71e5d73c789e6106bc296#file-word_set_reduction-jl\n<\/div><\/figure>\n\n\n\n
Putting it all together<\/h2>\n\n\n\n
So all what we have to do now is to apply the following step <\/p>\n\n\n\n
  1. Guess a candidate first word <\/li>
  2. Get response from the Game<\/li>
  3. Use that response to update the set of constraints<\/li>
  4. Use the constraints to reduce the set of possible words <\/li>
  5. Guess the new candidate word <\/li>
  6. Repeat step 2 until a word is found or the game is over<\/li><\/ol>\n\n\n\n
    In the steps 1 and 5 above, the simplest approach is just to pick a word at random. Below is Julia repl session showing how we go about applying the above. The secret word here is “super” <\/p>\n\n\n\n
    \nhttps:\/\/gist.github.com\/mbeltagy\/51e4672379a71e5d73c789e6106bc296#file-blog_julia_wordle_repl_session1-jl\n<\/div><\/figure>\n\n\n\n
    We see that we arrived at the correct word after guessing<\/p>\n\n\n\n