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Patrick2788's avatar
Patrick2788
Silver Contributor
Jul 14, 2022
Solved

A LAMBDA Word Search Puzzle

I've created a 15x10 Word Search.  I've included a word list (dynamic range) containing words which might be found in the word search.  The goal is to then extract those words when they appear in the...
excel
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  • SergeiBaklan's avatar
    SergeiBaklan
    Jul 16, 2022

    Patrick2788 

    Here is one more variant

    //------ variant without TEXTJOIN()

reverseColumns=
LAMBDA( data,
    LET(
        n, COLUMNS( data ),
        CHOOSECOLS( data, SEQUENCE(n,,n,-1) )
    ));

reversedText=
LAMBDA( str,
    LET(
        head, LEFT(str),
        tail, RIGHT(str, LEN(str) - 1),
        IF(str = "", "", reversedText(tail) & head)
    ));

isPolindrom=
LAMBDA( text, text = reversedText( text ) );

checkSingleWord=
LAMBDA( str, vector,
    LET(
        getWord, REDUCE("", vector,
            LAMBDA( a,v,
                IF( LEFT(str, LEN(a&v)) = a&v, a&v,
                IF( LEFT(str) = a, v,
                    IF( a = str, a, "" )
                ) ) ) ),
        IF( getWord = str, str, "")
    ));

checkListOfWords=
LAMBDA( wordsVector, vector,
    LET(
        getWords,
            REDUCE("", wordsVector,
                LAMBDA(a,v, VSTACK(a, checkSingleWord( v, vector) ) )
            ),
        IFERROR( FILTER( getWords, getWords <> ""), "" )
    ));

wordsInMatrix=
LAMBDA( data, wordsVector,
    LET(
        k, SEQUENCE( ROWS(data) ),
        scanData, REDUCE(1, k,
            LAMBDA(a,v,
                CHOOSECOLS(
                    IF( v < SEQUENCE(,v,v,-1),
                        a,
                        VSTACK(a, checkListOfWords( Words, CHOOSEROWS(data,v) ) ) ),
                1 )
            )),
        removeFirst, DROP( scanData, 1 ),
        FILTER( removeFirst, removeFirst <> "")
));

wordsInPuzzle=
LAMBDA( data, wordsVector,
    LET(
    allWords, SORT( VSTACK(
        wordsInMatrix( data, wordsVector ),
        wordsInMatrix( reverseColumns( data ), wordsVector ),
        wordsInMatrix( TRANSPOSE( data ), wordsVector ),
        wordsInMatrix( reverseColumns( TRANSPOSE( data ) ), wordsVector )
    )),
    ifPolindroms, MAP(allWords, LAMBDA(v, isPolindrom(v) ) ),
    polindroms, UNIQUE( FILTER(allWords, ifPolindroms)),
    notPolindroms, FILTER(allWords, ifPolindroms -1),
    stack, IF( ISERR(polindroms), notPolindroms, VSTACK( polindroms, notPolindroms ) ),
    SORT( stack )
));
mtarler's avatar
mtarler
Silver Contributor
Jul 24, 2022

Patrick2788 I haven't evaluated the actual functions developed here (but duly impressed). but I noticed this proposed method:

Ideally, the SCAN results would be like this:

 

and wanted to mention that in word search you can often have overlapping words.  So you could have WAVE and VENUS overlapping so after finding WAVE you shouldn't reset the search array to the next letter D but should start with AVE (maybe the next word is AVENUE).

Patrick2788's avatar
Patrick2788
Silver Contributor
Jul 24, 2022
For this exercise, I didn't do overlapping words or diagonals (Things might really get out of hand if those were included!). I think SCAN can locate the words, but it seems easier to go by the row (Less letters to discard and no need to account for the row changing) or convert the matrix to a vector to pull the words.
  • mtarler's avatar
    mtarler
    Silver Contributor
    Jul 25, 2022
    yes I saw the no diagonals but didn't see any exclusion for overlap. Besides, I don't think overlap adds a lot of complexity, just prevents some tricks that make it more efficient.
    • Patrick2788's avatar
      Patrick2788
      Silver Contributor
      Jul 23, 2023

      mtarler 

      SergeiBaklan 

      PeterBartholomew1 

       

      I thought it would be interesting to re-visit this task with a fresh set of eyes.  I scrapped my solution from 2022 and made things more interesting.

       

      Functionality added:

      • Diagonals are now supported
      • Multiple dictionary support

      There's a bit of calculation crunch when using the dictionary with 9,500+ words.  I was going to add an Oxford dictionary that contained 100,000 words but the CSV needed extensive cleanup (Probably for the best as larger word lists contain a lot of made-up words).

       

      =LET(
    height, ROWS(Puzzle),
    width, COLUMNS(Puzzle),
    AccumulateText, LAMBDA(a, letter, a & letter),
    Letter2Array, LAMBDA(arr, SCAN("", arr, AccumulateText)),
    WordsReversed, MAP(dictionary, LAMBDA(e, Reverse(e))),
    results, REDUCE(
        "",
        Puzzle,
        LAMBDA(a, letter,
            LET(
                r, ROW(letter),
                c, COLUMN(letter),
                across, INDEX(Puzzle, r, SEQUENCE(, width - c + 1, c, 1)),
                down, INDEX(Puzzle, SEQUENCE(height - r + 1, , r), c),
                diagonal_c, SEQUENCE(width - c + 1, , c),
                diagonal_r, SEQUENCE(width - c + 1, , r),
                diagonal, INDEX(Puzzle, diagonal_r, diagonal_c),
                neg_diagonal_c, SEQUENCE(c, , c, -1),
                neg_diagonal_r, SEQUENCE(width - c, , r),
                neg_diagonal, INDEX(Puzzle, neg_diagonal_r, neg_diagonal_c),
                arrAcross, TOCOL(Letter2Array(across)),
                arrDown, Letter2Array(down),
                arrDiagonal, Letter2Array(diagonal),
                arrDiagonalNeg, TOCOL(Letter2Array(neg_diagonal)),
                WordStack, IF(
                    c = width,
                    VSTACK(arrDown, arrDiagonalNeg),
                    IF(
                        r = height,
                        VSTACK(arrAcross, arrDiagonal, arrDiagonalNeg),
                        IF(
                            c = 1,
                            VSTACK(arrAcross, arrDown, arrDiagonal),
                            VSTACK(arrAcross, arrDown, arrDiagonal, arrDiagonalNeg)
                        )
                    )
                ),
                WordBank, VSTACK(dictionary, WordsReversed),
                FoundWords, VSTACK(dictionary, dictionary),
                GetWords, TOCOL(XLOOKUP(WordStack, WordBank, FoundWords, ""), 2),
                VSTACK(a, GetWords)
            )
        )
    ),
    SORT(FILTER(results, results <> "", "no words found"))
)

       

       

       

      • mtarler's avatar
        mtarler
        Silver Contributor
        Jul 31, 2023

        Patrick2788  so I finally got back to this and did my version.  Love to hear about the performance testing you do on them ....

         

         

         

        =LET(
    h, ROWS(puzzleRange),
    w, COLUMNS(puzzleRange),
    space, " ",
    spaceLine, EXPAND(space, 1, w, space),
    PuzzleReverseH, CHOOSECOLS(puzzleRange, SEQUENCE(, w, w, -1)),
    PuzzleStack1, VSTACK(puzzleRange, spaceLine, PuzzleReverseH),
    PuzzleReverseV, CHOOSEROWS(PuzzleStack1, SEQUENCE(, 2 * h + 1, 2 * h + 1, -1)),
    PuzzleStack2, HSTACK(TRANSPOSE(puzzleRange), TRANSPOSE(TAKE(PuzzleReverseV, -h - 1, ))),
    PuzzleDiags, LAMBDA(stack,
        LET(
            nr, ROWS(stack),
            nc, COLUMNS(stack),
            REDUCE(
                EXPAND(INDEX(stack, , 1), nr + nc - 1, 1, space),
                SEQUENCE(nc - 1),
                LAMBDA(p, q,
                    HSTACK(
                        p,
                        EXPAND(
                            VSTACK(EXPAND(space, q, 1, space), INDEX(stack, , q + 1)),
                            nr + nc - 1,
                            1,
                            space
                        )
                    )
                )
            )
        )
    ),
    PuzzleStacksHalf1, VSTACK(
        PuzzleStack1,
        spaceLine,
        PuzzleDiags(VSTACK(PuzzleStack1, spaceLine, PuzzleReverseV))
    ),
    PuzzleStacksHalf2, PuzzleStack2,
    findWord, LAMBDA(puzzlestack,
        REDUCE(
            "",
            SEQUENCE(ROWS(puzzlestack)),
            LAMBDA(p, r,
                VSTACK(
                    p,
                    FILTER(
                        dictionary,
                        ISNUMBER(SEARCH(dictionary, CONCAT(INDEX(puzzlestack, r, )))),
                        ""
                    )
                )
            )
        )
    ),
    findWords, VSTACK(findWord(PuzzleStacksHalf1), findWord(PuzzleStacksHalf2)),
    out, SORT(FILTER(findWords, findWords <> "")),
    out
)

         

         

        ok so I did a quick test and mine seems to fair pretty well.  (*** note I have made a few edits as I found my diagonals were not as I thought and needed to adjust my sets to get all 4 diagonals correctly.  Note, I also found that your solution is also missing some)

        btw my concept was to take the puzzle and create a stack of:

        orig puzzle, 

        puzzle reversed by rows, columns, and both

        the above 2 shifted by 1 row for each column (i.e. creating the diagonals)

        and then find any words found in any row

        and repeat for the transpose of the orig and rev by rows to get vertical up/down words.

        so I originally output the UNIQUE list but noted you showed all.  As noted above I orig had some issues with missing 1 or 2 diagonals so my list had some you didn't you had some i didn't.  I fixed it and now have every word in your list but when I removed UNIQUE i notice you have more copies in a couple cases.  I don't know why that is the case but submit this as is for now)

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