# Cheat at 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.)

## Techniques¶

• 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 xsc}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
..

## 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.