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Cheat at Scrabble

Scrabble

Problem Given a string representing the letters in a Scrabble™ player’s rack, produce candidate words for the next turn, ranked by potential score. (The score ignores the effect of placement on the board, such as Double Letter Score, etc.)

Rules of Scrabble

Techniques

  • Download a word list from the Web
  • Make a q dictionary
  • Count frequencies of items in a list
  • Subtract one dictionary from another
  • Use function notation within a qSQL query

Solution

/ Scrabble tile values
TV:.Q.a!1 3 3 2 1 4 2 4 1 8 5 1 3 1 1 3 10 1 1 1 1 4 4 8 4 10  

/ Unix dictionary
UD:system "curl http://wiki.puzzlers.org/pub/wordlists/unixdict.txt"

/ frequency count
fc:{count each group x} 

/ dictionary table
DT:([] word:UD; fr:fc each UD; sc:{sum TV x}each UD) 

/ word builder
wb:{{x idesc x`sc}select word,sc from DT where fc[x]{all(x-y)>=0}/:fr}

Usage

q)wb "eobmagl"
word     sc
-----------
"gamble" 11
"gambol" 11
"amble"  9
"blame"  9
"mabel"  9
"bagel"  8
"balm"   8
..

Official Scrabble site word builder

Discussion

q)sum TV "scrabble"  / score a word
14

For each word, make a frequency count of its letters as a dictionary. 

q)fc "scrabble"
s| 1
c| 1
r| 1
a| 1
b| 2
l| 1
e| 1

Tabulate the words, their frequency counts, and the word scores.

q)DT
word     fr                sc
-----------------------------
,"a"     (,"a")!,1         1
"aaa"    (,"a")!,3         3
"aaas"   "as"!3 1          4
"aarhus" "arhus"!2 1 1 1 1 9
"aaron"  "aron"!2 1 1 1    5
"aau"    "au"!2 1          3
"aba"    "ab"!2 1          5
..

To test a word, subtract its frequency count from the frequency count of the tiles on your rack.

q)fc["eobmagl"]-fc "mangle"
e| 0
o| 1
b| 1
m| 0
a| 0
g| 0
l| 0
n| -1
q)all 0<=fc["eobmagl"]-fc "mangle"  / is "mangle" possible?
0b

If no item is negative, the word is a candidate.

The expression fc[x]{all(x-y)>=0}/:fr applies the test to flag words that can be formed from the letters in the tray x. It takes the frequency count of the tray letters fc[x] and uses Each Right to apply the test to the frequency counts in the fr column.

It remains only to sort the candidates descending by score.