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EARTH, WATER, WIND AND FIRE (Posted on 2007-10-26) Difficulty: 3 of 5

This is another variation of the classic problem of changing one word into another. Instead of changing one word into another one letter at a time for each step, this variation alternates each step by anagramming one word into another.

For example: CAT to DOG can occur as such:
CAT
ACT (anagram)
ANT (letter change)
TAN (anagram)
TON (letter change)
NOT (anagram)
NOD (letter change)
DON (anagram)
DOG (letter change)

Either the letter change or the anagram may occur first, but must then alternate.

I offer four challenges. In the fewest steps,
1) transform EARTH to WATER,
2) convert WIND to FIRE,
3) cross from RIVER to SHORE, and
4) transmute LEAD to GOLD.

See The Solution Submitted by Dej Mar    
Rating: 3.3333 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution computer solution (spoilers) | Comment 1 of 7
earth
hater
water

comes to mind immediately.

I asked my computer about

wind

and got

kind
dink
dine
nide
ride
dire
fire

taking 7 steps, a nide being a nest or brood, esp. of pheasants.

If you don't like hater, there are longer ones for earth ... water such as:


heart
peart
taper
tamer
mater
water

For river, to avoid rarer words we can accept 7 steps:

rifer
frier
fries
fires
hires
shire
shore

or accept the rarer words for 5 steps:

rives 
vires       
hires       
shire       
shore   

For lead a good sequence of 6 is:

lade
lode
dole
dolt
told
gold

or this 7-step:

leas
sale
sole
oles
olds
sold
gold


The program:

DECLARE FUNCTION isAnag% (s1$, s2$)
DECLARE FUNCTION diffCt% (a$, b$)
DEFINT A-Z
DECLARE SUB ladder (w$, lev)
DIM SHARED lad$(10), maxWd, goal$, maxSteps, typ(10)

 

INPUT "start word:", w1$
l = LEN(w1$)
INPUT "end word:", goal$
IF LEN(goal$) <> l THEN PRINT "Words must be same length.": END
INPUT "max steps (8 wds inclusive -> 7 steps):", maxSteps
OPEN "words" + LTRIM$(STR$(l)) + ".txt" FOR BINARY AS #1
maxWd = LOF(1) / l
lad$(0) = w1$
OPEN w1$ + ".lad" FOR OUTPUT AS #10
ladder w1$, 0
CLOSE

FUNCTION diffCt (a$, b$)
    ct = 0
    FOR i = 1 TO LEN(a$)
      IF MID$(a$, i, 1) <> MID$(b$, i, 1) THEN
        ct = ct + 1
      END IF
    NEXT
    diffCt = ct
END FUNCTION

FUNCTION isAnag (s1$, s2$)
  IF s1$ = s2$ THEN isAnag = 0: EXIT FUNCTION
  h$ = s2$
  FOR i = 1 TO LEN(s1$)
    c$ = MID$(s1$, i, 1)
    ix = INSTR(h$, c$)
    IF ix THEN
      h$ = LEFT$(h$, ix - 1) + MID$(h$, ix + 1)
    ELSE
      isAnag = 0: EXIT FUNCTION
    END IF
  NEXT
  isAnag = 1
END FUNCTION

SUB ladder (w$, lev)
  l = LEN(w$)
  w2$ = SPACE$(l)
  p& = 1
  FOR wNum = 1 TO maxWd
    GET #1, p&, w2$
    p& = p& + l
    IF lev = 0 OR typ(lev) = 1 THEN
      ct = diffCt(w$, w2$)
      IF ct = 1 THEN
        sb = lev - 1 ' : IF sb < 0 THEN sb = 0
        okToUse = 1
        IF sb >= 0 THEN
          FOR i = 0 TO sb
            IF w2$ = lad$(i) THEN okToUse = 0: EXIT FOR
          NEXT
        END IF
        IF okToUse THEN
          lv = lev + 1 '  ***** lev changes HERE *****
          lad$(lv) = w2$
          typ(lv) = 0
          IF w2$ = goal$ THEN    ' OR lv = 6 THEN
            FOR i = 1 TO lv
              IF w2$ = goal$ THEN PRINT "   ";
              PRINT lad$(i)
              PRINT #10, lad$(i)
            NEXT
            PRINT "-------"; lv
            PRINT #10, "-------"; lv
          ELSEIF lv > maxSteps THEN
          ELSE
            ladder w2$, lv
          END IF
        END IF
      END IF
    END IF
    IF lev = 0 OR typ(lev) = 0 THEN
      ct = isAnag(w$, w2$)
      IF ct THEN
        sb = lev - 1 ' : IF sb < 0 THEN sb = 0
        okToUse = 1
        IF sb >= 0 THEN
          FOR i = 0 TO sb
            IF w2$ = lad$(i) THEN okToUse = 0: EXIT FOR
          NEXT
        END IF
        IF okToUse THEN
          lv = lev + 1 '  ***** lev changes HERE *****
          lad$(lv) = w2$
          typ(lv) = 1
          IF w2$ = goal$ THEN    ' OR lv = 6 THEN
            FOR i = 1 TO lv
              IF w2$ = goal$ THEN PRINT "   ";
              PRINT lad$(i)
              PRINT #10, lad$(i)
            NEXT
            PRINT "-------"; lv
            PRINT #10, "-------"; lv
          ELSEIF lv > maxSteps THEN
          ELSE
            ladder w2$, lv
          END IF
        END IF
      END IF
    END IF
  NEXT
END SUB

 

 


  Posted by Charlie on 2007-10-26 14:13:38
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