import sys

def print_table(s1,s2,table,trace=None):
    """print the DP table, t, for strings s1 and s2.  
    If the optional 'trace' is present, print * indicators for the alignment.
    Fancy formatting ensures this will also work when s1 and s2 are lists of strings"""
    print "       ",
    for i in range(len(s1)):
        print "%3.3s" % s1[i],
    print
    for i in range(len(table)):
        if i > 0: print "%3.3s" % s2[i-1], 
        else: print '   ',
        for j in range(len(table[i])):
            if trace and trace[i][j] == "*":
                print "*" + "%2d" % table[i][j],
            else:
                print "%3d" % table[i][j],
        print

def argmin (*a):
    """Return two arguments: first the smallest value, second its offset"""
    min = sys.maxint; arg = -1; i = 0
    for x in a:
        if (x < min):
            min = x; arg = i
        i += 1
    return (min,arg)
            

def stredit (s1,s2, showtable=True):
    "Calculate Levenstein edit distance for strings s1 and s2."
    len1 = len(s1) # vertically
    len2 = len(s2) # horizontally
    # Allocate the table
    table = [None]*(len2+1)
    for i in range(len2+1): table[i] = [0]*(len1+1)
    # Initialize the table
    for i in range(1, len2+1): table[i][0] = i
    for i in range(1, len1+1): table[0][i] = i
    # Do dynamic programming
    for i in range(1,len2+1):
        for j in range(1,len1+1):
            if s1[j-1] == s2[i-1]:
                d = 0
            else:
                d = 1
            table[i][j] = min(table[i-1][j-1] + d,
                              table[i-1][j]+1,
                              table[i][j-1]+1)
    if showtable:
        print_table(s1, s2, table)
    return table[len2][len1]

def stredit2 (s1,s2, showtable=True):
    "String edit distance, keeping trace of best alignment"
    len1 = len(s1) # vertically
    len2 = len(s2) # horizontally
    # Allocate tables
    table = [None]*(len2+1)
    for i in range(len2+1): table[i] = [0]*(len1+1)
    trace = [None]*(len2+1)
    for i in range(len2+1): trace[i] = [None]*(len1+1)
    # initialize table
    for i in range(1, len2+1): table[i][0] = i
    for i in range(1, len1+1): table[0][i] = i
    # in the trace table, 0=subst, 1=insert, 2=delete
    for i in range(1,len2+1): trace[i][0] = 1
    for j in range(1,len1+1): trace[0][j] = 2
    # Do dynamic programming
    for i in range(1,len2+1):
        for j in range(1,len1+1):
            if s1[j-1] == s2[i-1]:
                d = 0
            else:
                d = 1
            # if true, the integer value of the first clause in the "or" is 1
            table[i][j],trace[i][j] = argmin(table[i-1][j-1] + d,
                                             table[i-1][j]+1,
                                             table[i][j-1]+1)
    if showtable:
	# If you are implementing Smith-Waterman, then instead of initializing
	# i=len2 and j=len1, you must initialize i and j to the indices 
	# of the table entry that has the miminum value (it will be negative)
        i = len2
        j = len1
        while i != 0 or j != 0:
            if trace[i][j] == 0:
                nexti = i-1
                nextj = j-1
            elif trace[i][j] == 1:
                nexti = i-1
                nextj = j
            elif trace[i][j] == 2:
                nexti = i
                nextj = j-1
	    else:
		nexti = 0
		nextj = 0
            trace[i][j] = "*"
            i = nexti
            j = nextj
	    print "ij", i, j
        print_table(s1, s2, table, trace)
    return table[len2][len1]


#stredit2('mccallum', 'mcalllomo')
#stredit(['this', 'is', 'a', 'test'], ['this', 'will', 'be', 'another', 'test'])
#stredit2("s'allonger", "lounge")
#stredit2("lounge", "s'allonger")
#stredit2('cow over the moon', 'moon in the sky')
#stredit2('another fine day', 'anyone can dive')
#stredit2('another fine day in the park', 'anyone can see him pick the ball')

# import dicts
# argvlen = len(sys.argv)
# target = sys.argv[argvlen-2].lower()
# filename = sys.argv[argvlen-1]
# d = dicts.DefaultDict(0)
# for word in open(filename).read().split():
#     if word not in d:
#       word = word.lower()
#       d[word] = stredit(word, target, False)
# print d.sorted(rev=False)[:20]