BackTrace for EditDistace

#!/usr/bin/env python

#encoding=gbk

import sys

"""

1. Set n to be the length of s.

   Set m to be the length of t.

   If n = 0, return m and exit.

   If m = 0, return n and exit.

 

2. Construct a matrix containing 0..m rows and 0..n columns.

   Initialize the first row to 0..n.

   Initialize the first column to 0..m.

 

3. Examine each character of s (i from 1 to n).

 

4. Examine each character of t (j from 1 to m).

 

5. If s[i] equals t[j], the cost is 0.

   If s[i] doesn't equal t[j], the cost is 1.

 

6. Set cell d[i,j] of the matrix equal to the minimum of:

   a. The cell immediately above plus 1: d[i-1,j] + 1.

   b. The cell immediately to the left plus 1: d[i,j-1] + 1.

   c. The cell diagonally above and to the left plus the cost: d[i-1,j-1] + cost.

 

After the iteration steps (3, 4, 5, 6) are complete, the distance is found in cell d[n,m].

"""

def show(matirx):

    for ir in range(0,len(matirx)):

        cl = matirx[ir]

        for il in range(0,len(cl)):

            print "%d "%matirx[ir][il],

        print ""

    print ""

 

def minimum(a, b, c):

    mi = a

    if (b < mi): mi = b

    if (c < mi): mi = c

    return mi

 

def BLD(t, p):

    ut = unicode(t, "gbk")

    up = unicode(p, "gbk")

    m = len(ut)

    n = len(up)

 

    if m == 0:return " ".join("*" * len(up)), " ".join(up.encode("gbk")), " ".join("I"*len(up))

    if n == 0:return " ".join(ut.encode("gbk")), " ".join("*" * len(ut)), " ".join("D"*len(ut))

 

    d = [[0] * (m + 1)for i in range(0, n + 1)]

    b = [[0] * (m + 1)for i in range(0, n + 1)]

    #show(d)

    #show(b)

 

    for i in range(1, len(d[0])):d[0][i] = i

    for i in range(1, len(d)):d[i][0] = i

 

    #show(d)

 

    for i in range(1, len(d)):#row num, p's length

        for j in range(1, len(d[0])):#column num, t's length

            """ins cost:d[i - 1][j] + 1; del cost:d[i][j - 1] + 1; sub cost:d[i - 1][j - 1] + 0 if up[i - 1] == ut[j - 1] else 1"""

            d[i][j] = minimum(d[i - 1][j] + 1, d[i][j - 1] + 1, d[i - 1][j - 1]+ (0 if up[i - 1] == ut[j - 1] else 1))

            """backtrace matrix:[1:tag ins | 2:tag del | 3:tag sub]"""

            if d[i][j] == d[i - 1][j] + 1: b[i][j] = 1

            elif d[i][j] == d[i][j - 1] + 1: b[i][j] = 2

            elif d[i][j] == d[i - 1][j - 1] + 0 if up[i - 1] == ut[j - 1] else 1: b[i][j] = 3

     

    show(d)

    show(b)

    #print "t: %s\np: %s\ncost: %d"%(ut,up,d[n][m])

 

    """put the best path point into a list"""

    bestPath = []

    i = len(d) - 1 #row num

    j = len(d[0]) - 1 #column num

 

    while i != 0 or j != 0:

        bestPath.append([i, j, b[i][j]])

        """

        if tag is sub : i - 1, j - 1; b[i - 1][j - 1]

        if tag is del : j - 1       ; b[i][j - 1]

        if tag is ins : i - 1       ; b[i - 1][j]

 

        """

        if b[i][j] == 1: i -= 1

        elif b[i][j] == 2: j -= 1

        elif b[i][j] == 3: i -= 1; j -= 1

        else:

            if i > 0: i -= 1

            if j > 0: j -=1

    print bestPath

     

    """ read best path and print info

        part  I: handle best path's first point

        part II: handle best path's left points

    """

    it = "*" if bestPath[-1][1] == 0 else ut[bestPath[-1][1] - 1].encode("gbk")

    ip = "*" if bestPath[-1][0] == 0 else up[bestPath[-1][0] - 1].encode("gbk")

    sf = ""

    if bestPath[-1][2] == 1: sf = "I"

    elif bestPath[-1][2] == 2: sf = "D"

    elif bestPath[-1][2] == 3: sf = " " if ut[0] == up[0] else "S"

    else: sf = "I" if bestPath[-1][1] == 0 else "D"

     

    for i in range(len(bestPath) - 1, 0, -1):

        current = bestPath[i - 1]

        forward = bestPath[i]

        ip += up[current[0] - 1].encode("gbk") if current[0] != forward[0] and current[0] > 0 else "*"

        it += ut[current[1] - 1].encode("gbk") if current[1] != forward[1] and current[1] > 0 else "*"

        if current[2] == 1: sf += "I"

        elif current[2] == 2: sf += "D"

        elif current[2] == 3: sf += "S" if up[current[0] - 1] != ut[current[1] - 1] else " "

        else: sf += "I" if current[1] == 0 else "D"

     

    return " ".join(it), " ".join(ip), " ".join(sf)

 

t = "abcdfx"

p = "fdsxdf"

st,sp,sf = BLD(t, p)

print "\n%s\n%s\n%s"%(st, sp, sf)

"""

time cost:  O(m * n)

space cost: O(m * n)

backtrace cost: O(m + n)

"""