Word Spinner Puzzle

Question

This is a word puzzle.

Your program should accept two words on the standard input.
Word one is the start word. Word two is the end word.

From the start word you have to reach the end word changing/add/remove one letter at a time. After each modification it must form a new valid word. Added letters are added to the beginning or end. You can remove letters from any location (but word must not fall bellow three letters in length). Note: You can not rearrange the letters to form a word.

The output of the program is the sequence of words to get from the start word to the end word.

Example:

Input:
    Post Shot

Output:
    Post
    cost
    coat
    goat
    got
    hot
    shot

Winner:

• The program must run in a reasonable time (less than a 10 seconds).
• The program that can generate the shortest output sequence to the prize words.
  • Zink -> Silicon
• If more than one program gets the shortest sequence then the shortest program in chars (ignoring white space).
• If we still have more than one program submission date/time shall be used.

Notes:

• Capitalization is not relevant.
• The code to build a dictionary does not count towards code cost.
  • Prize Words and sequence will be generated from:
    http://dl.packetstormsecurity.net/Crackers/wordlists/dictionaries/websters-dictionary.gz

Answer 1

traceroute - 10 chars

traceroute 

detail

post#traceroute shot

Type escape sequence to abort.
Tracing the route to shot (1.1.4.2)

  1 pot (1.1.1.2) 40 msec 68 msec 24 msec
  2 hot (1.1.3.2) 16 msec 32 msec 24 msec
  3 shot (1.1.4.2) 52 msec *  92 msec

Routers are preconfigured with OSPF enabled and arranged this way.

And yes, I need 233614 routers to fully support all the words. :-)

Answer 2

PHP - 886 689 644 612

Dictionary loading:

<?php foreach(file('websters-dictionary') as $line) {
    $word = strtolower(trim($line));
    if (strlen($word) < 3) continue;
    $c[$word] = 1;
}

Actual code (just concat both) :

list($d,$e)=explode(' ',strtolower(trim(`cat`)));$f=range(@a,@z);function w($a,&$g){global$c;if(isset($c[$a]))$g[]=$a;}$h[$d]=$b=@levenshtein;$i=new SplPriorityQueue;$i->insert($d,0);$j[$d]=0;$k[$d]=$b($d,$e);while($h){if(isset($c[$l=$i->extract()])){unset($h[$l],$c[$l]);if($l==$e){for(;$m=@$n[$o[]=$l];$l=$m);die(implode("\n",array_reverse($o)));}for($p=strlen($l),$g=array();$p--;){w(substr_replace($q=$l,"",$p,1),$g);foreach($f as$r){$q[$p]=$r;w($q,$g);w($r.$l,$g);w($l.$r,$g);}}foreach($g as$m){$s=$j[$l]+1;if(!isset($h[$m])||$s<$j[$m]){$n[$m]=$l;$i->insert($m,-(($k[$m]=$b($m,$e))+$j[$m]=$s));}$h[$m]=1;}}}

usage:

php puzzle.php <<< 'Zink Silicon'
# or
echo 'Zink Silicon'|php puzzle.php

Result:

zink
pink
pank
pani
panic
pinic
sinic
sinico
silico
silicon
(0.23s)

This should run in less than 0.5 second for 'Zink Silicon', and less than 1 second for most cases (sometimes longer when no solution exists, but it sill returns).

This uses the A* algorithm with levenshtein distance to estimate a lower bounds of the distances.

Some intersting tests:

• vas arm -> vas bas bar barm arm (with a word longer than both start and end)
• oxy pom -> oxy poxy poy pom
• regatta gyrally -> (none, but the script correctly terminates)
• aal presolution -> +8 chars
• lenticulated aal -> -9 chars
• acarology lowness -> 46 hops
• caniniform lowness -> 51 hops
• cauliform lowness -> 52 hops
• overfoul lowness -> 54 hops
• dance facia -> some words in the path have 4 more chars than both start/end

Answer 3

Python

Since I couldn't golf dijkstra codes to compress to few hundreds bytes, here is ungolfed version of mine.

import sys, heapq, time

# dijkstra algorithm from 
# http://code.activestate.com/recipes/119466-dijkstras-algorithm-for-shortest-paths/
def dijkstra(G, start, end):
   def flatten(L):
      while len(L) > 0:
         yield L[0]
         L = L[1]

   q = [(0, start, ())]
   visited = set()
   while True:
      (cost, v1, path) = heapq.heappop(q)
      if v1 not in visited:
         visited.add(v1)
         if v1 == end:
            return list(flatten(path))[::-1] + [v1]
         path = (v1, path)
         for (v2, cost2) in G[v1].iteritems():
            if v2 not in visited:
               heapq.heappush(q, (cost + cost2, v2, path))

nodes = tuple(sys.argv[1:])

print "Generating connections,",
current_time = time.time()

words = set(x for x in open("websters-dictionary", "rb").read().lower().split() if 3 <= len(x) <= max(5, *[len(l)+1 for l in nodes]))

print len(words), "nodes found"

def error():
    sys.exit("Unreachable Route between '%s' and '%s'" % nodes)

if not all(node in words for node in nodes):
    error()

# following codes are modified version of
# http://norvig.com/spell-correct.html
alphabet = 'abcdefghijklmnopqrstuvwxyz'

def edits(word):
   splits = [(word[:i], word[i:]) for i in range(len(word) + 1)]
   deletes = [a + b[1:] for a, b in splits if b]
   replaces = [a + c + b[1:] for a, b in splits for c in alphabet if b]
   prepends = [c+word for c in alphabet]
   appends = [word+c for c in alphabet]
   return words & set(deletes + replaces + prepends + appends)

# Generate connections between nodes to pass to dijkstra algorithm
G = dict((x, dict((y, 1) for y in edits(x))) for x in words)

print "All connections generated, %0.2fs taken" % (time.time() - current_time)
current_time = time.time()

try:
    route = dijkstra(G, *nodes)
    print '\n'.join(route)
    print "%d hops, %0.2fs taken to search shortest path between '%s' & '%s'" % (len(route), time.time() - current_time, nodes[0], nodes[1])
except IndexError:
    error()

Tests

$ python codegolf-693.py post shot
Generating connections, 15930 nodes found
All connections generated, 2.09s taken
post
host
hot
shot
4 hops, 0.04s taken to search shortest path between 'post' & 'shot'

$ python codegolf-693.py zink silicon
Generating connections, 86565 nodes found
All connections generated, 13.91s taken
zink
pink
pank
pani
panic
pinic
sinic
sinico
silico
silicon
10 hops, 0.75s taken to search shortest path between 'zink' & 'silicon'

Added user300's Tests

$ python codegolf-693.py vas arm
Generating connections, 15930 nodes found
All connections generated, 2.06s taken
vas
bas
bam
aam
arm
5 hops, 0.07s taken to search shortest path between 'vas' & 'arm'

$ python codegolf-693.py oxy pom
Generating connections, 15930 nodes found
All connections generated, 2.05s taken
oxy
poxy
pox
pom
4 hops, 0.01s taken to search shortest path between 'oxy' & 'pom'

$ python codegolf-693.py regatta gyrally
Generating connections, 86565 nodes found
All connections generated, 13.95s taken
Unreachable Route between 'regatta' and 'gyrally'

Some more

$ python codegolf-693.py gap shrend
Generating connections, 56783 nodes found
All connections generated, 8.16s taken
gap
rap
crap
craw
crew
screw
shrew
shrewd
shrend
9 hops, 0.67s taken to search shortest path between 'gap' & 'shrend'

$ python codegolf-693.py guester overturn
Generating connections, 118828 nodes found
All connections generated, 19.63s taken
guester
guesten
gesten
geste
gest
gast
east
ease
erse
verse
verset
overset
oversee
overseed
oversend
oversand
overhand
overhard
overcard
overcare
overtare
overture
overturn
23 hops, 0.82s taken to search shortest path between 'guester' & 'overturn'

Answer 4

Python, 288 characters

(not counting the dictionary reading line)

X=set(open('websters-dictionary').read().upper().split())

(S,E)=raw_input().upper().split()
G={S:0}
def A(w,x):
 if x not in G and x in X:G[x]=w
while E not in G:
 for w in G.copy():
  for i in range(len(w)):
   for c in"ABCDEFGHIJKLMNOPQRSTUVWXYZ":A(w,w[:i]+c+w[i+1:]);A(w,w[:i]+w[i+1:]);A(w,c+w);A(w,w+c)
s=''
while E:s=E+'\n'+s;E=G[E]
print s

for the challenge zink to silicon:

ZINK
PINK
PANK
PANI
PANIC
PINIC
SINIC
SINICO
SILICO
SILICON

There are some strange words in that dictionary...