Author  : Turfa Auliarachman Date    : October 12, 2016 This is a pure Python implementation of Dynamic Programming solution to the edit distance problem. The problem is : Given two strings A and B. Find the minimum number of operations to string B such that A  B. The permitted operations are removal,  insertion, and substitution. Use : solver               EditDistance editDistanceResult   solver.solvefirstString, secondString  EditDistance.mindisttopdownintention, execution 5  EditDistance.mindisttopdownintention,  9  EditDistance.mindisttopdown,  0  EditDistance.mindistbottomupintention, execution 5  EditDistance.mindistbottomupintention,  9  EditDistance.mindistbottomup,  0
class EditDistance:
    """
    Use :
    solver              = EditDistance()
    editDistanceResult  = solver.solve(firstString, secondString)
    """

    def __init__(self):
        self.word1 = ""
        self.word2 = ""
        self.dp = []

    def __min_dist_top_down_dp(self, m: int, n: int) -> int:
        if m == -1:
            return n + 1
        elif n == -1:
            return m + 1
        elif self.dp[m][n] > -1:
            return self.dp[m][n]
        else:
            if self.word1[m] == self.word2[n]:
                self.dp[m][n] = self.__min_dist_top_down_dp(m - 1, n - 1)
            else:
                insert = self.__min_dist_top_down_dp(m, n - 1)
                delete = self.__min_dist_top_down_dp(m - 1, n)
                replace = self.__min_dist_top_down_dp(m - 1, n - 1)
                self.dp[m][n] = 1 + min(insert, delete, replace)

            return self.dp[m][n]

    def min_dist_top_down(self, word1: str, word2: str) -> int:
        """
        >>> EditDistance().min_dist_top_down("intention", "execution")
        5
        >>> EditDistance().min_dist_top_down("intention", "")
        9
        >>> EditDistance().min_dist_top_down("", "")
        0
        """
        self.word1 = word1
        self.word2 = word2
        self.dp = [[-1 for _ in range(len(word2))] for _ in range(len(word1))]

        return self.__min_dist_top_down_dp(len(word1) - 1, len(word2) - 1)

    def min_dist_bottom_up(self, word1: str, word2: str) -> int:
        """
        >>> EditDistance().min_dist_bottom_up("intention", "execution")
        5
        >>> EditDistance().min_dist_bottom_up("intention", "")
        9
        >>> EditDistance().min_dist_bottom_up("", "")
        0
        """
        self.word1 = word1
        self.word2 = word2
        m = len(word1)
        n = len(word2)
        self.dp = [[0 for _ in range(n + 1)] for _ in range(m + 1)]

        for i in range(m + 1):
            for j in range(n + 1):
                if i == 0:  # first string is empty
                    self.dp[i][j] = j
                elif j == 0:  # second string is empty
                    self.dp[i][j] = i
                elif word1[i - 1] == word2[j - 1]:  # last characters are equal
                    self.dp[i][j] = self.dp[i - 1][j - 1]
                else:
                    insert = self.dp[i][j - 1]
                    delete = self.dp[i - 1][j]
                    replace = self.dp[i - 1][j - 1]
                    self.dp[i][j] = 1 + min(insert, delete, replace)
        return self.dp[m][n]


if __name__ == "__main__":
    solver = EditDistance()

    print("****************** Testing Edit Distance DP Algorithm ******************")
    print()

    S1 = input("Enter the first string: ").strip()
    S2 = input("Enter the second string: ").strip()

    print()
    print(f"The minimum edit distance is: {solver.min_dist_top_down(S1, S2)}")
    print(f"The minimum edit distance is: {solver.min_dist_bottom_up(S1, S2)}")
    print()
    print("*************** End of Testing Edit Distance DP Algorithm ***************")
