Edit_Distance_Formula.py

# A Dynamic Programming based Python program for edit
# distance problem
def editDistDP(str1, str2, m, n):
    # Create a table to store results of subproblems
    dp = [[0 for x in range(n + 1)] for x in range(m + 1)]

    # Fill d[][] in bottom up manner
    for i in range(m + 1):
        for j in range(n + 1):

            # If first string is empty, only option is to
            # insert all characters of second string
            if i == 0:
                dp[i][j] = j  # Min. operations = j

            # If second string is empty, only option is to
            # remove all characters of second string
            elif j == 0:
                dp[i][j] = i  # Min. operations = i

            # If last characters are same, ignore last char
            # and recur for remaining string
            elif str1[i - 1] == str2[j - 1]:
                dp[i][j] = dp[i - 1][j - 1]

                # If last character are different, consider all
            # possibilities and find minimum
            else:
                dp[i][j] = 1 + min(dp[i][j - 1],  # Insert
                                   dp[i - 1][j],  # Remove
                                   dp[i - 1][j - 1])  # Replace

    return dp[m][n]


def editDistance(str1, str2, m, n):
    # If first string is empty, the only option is to
    # insert all characters of second string into first
    if m == 0:
        return n

        # If second string is empty, the only option is to
    # remove all characters of first string
    if n == 0:
        return m

        # If last characters of two strings are same, nothing
    # much to do. Ignore last characters and get count for
    # remaining strings.
    if str1[m - 1] == str2[n - 1]:
        return editDistance(str1, str2, m - 1, n - 1)

        # If last characters are not same, consider all three
    # operations on last character of first string, recursively
    # compute minimum cost for all three operations and take
    # minimum of three values.
    return 1 + min(editDistance(str1, str2, m, n - 1),  # Insert
                   editDistance(str1, str2, m - 1, n),  # Remove
                   editDistance(str1, str2, m - 1, n - 1)  # Replace
                   )