Source code for lego_recursion

"""A recursive solution to the lego problem from Homework #4. This 
solution performs mix and match, but does not check for two different
ways to satisfy the 4x2 lego substitution.

"""

def read_legos(fname):
    """Util function to read legos from a file. Assumes each line 
    contains a lego type, comma, number of that lego type.

    """

    legos = []
    for line in open(fname):
        m = line.strip().split(",")
        lego = m[0].strip()
        cnt = int(m[1])
        legos.extend( [lego]*cnt )
    return legos


def subs(lego):
    """Returns a substitution for a lego as a list of legos, by finding 
    the largest possible pieces that taken together make up the input lego.

    """
    
    if lego == '1x1':
        return []  ## No substitution exists.
    elif lego == '2x1':
        return ['1x1']*2
    elif lego == '2x2':
        return ['2x1']*2
    elif lego == '4x2':
        return ['4x1']*2
    elif lego == '4x1':
        return ['2x1']*2

def replacement(lego, legolist):
    """Find replacement legos recursively. For the replacement,
    all the substitutions should be satisfiable. The function 
    returns:   

        list of substituted legos, list of remaining legos

    if a substitition is found. Otherwise, it returns None.

    """

    if lego in legolist:
        remaining = legolist[:]
        remaining.remove(lego)
        return  [ lego ], remaining  ##Searched lego is found, return success
    else:
        subslegos = subs(lego)
        if len(subslegos) == 0:
            return None  ## No more substitutions, return failure
        ##Substitutions exist, search for each one separately
        ##Modify the lego list alog the way.

        lego1 = subslegos[0]
        lego2 = subslegos[1]
        result1 = replacement(lego1, legolist)
        ## If no substitution for the first piece, report failure
        if result1 == None: 
            return None
        result2 = replacement(lego2, result1[1])
        ## If no substitution for the first piece, report failure
        if result2 == None:
            return None
        ##If we came here, both pieces have substitutions, report their
        ##combination
        return result1[0] + result2[0], result2[1]
        

if __name__ == "__main__":
    mylegos = read_legos("mylegos.txt")
    reqlegos = read_legos("legosrequired.txt")

    foundlegos = []
    missinglegos = []
    
    for lego in reqlegos:
        result = replacement(lego, mylegos)
        if result == None: # No substitutions were found.
            missinglegos.append(lego)
        else: ##A substitution was found.
            match = result[0]
            remaining_legos = result[1]
            foundlegos.append( [lego, match] )
            mylegos = remaining_legos
        
 
    print "My remaining legos", mylegos
    print "Required legos", reqlegos
    print "Still missing legos", missinglegos
    
    print
    print "Found legos:" 
    for item in foundlegos:
        print item