Edit Distance

Given two words word1 and word2, find the minimum number of steps required to convert word1 to word2. (each operation is counted as 1 step.)

You have the following 3 operations permitted on a word:

Insert a character

Delete a character

Replace a character

Example

Given word1 = "mart" and word2 = "karma", return 3.

Solution

state: f[i][j]a的前i个字符最少要用几次编辑可以变成b的前j个字符function: f[i][j] = MIN(f[i-1][j]+1, f[i][j-1]+1, f[i-1][j-1]) // a[i] == b[j]

= MIN(f[i-1][j]+1, f[i][j-1]+1, f[i-1][j-1]+1) // a[i] != b[j] initialize: f[i][0] = i, f[0][j] = j

answer: f[a.length()][b.length()]

class Solution: 
    # @param word1 & word2: Two string.
    # @return: The minimum number of steps.
    def minDistance(self, word1, word2):
        # write your code here
        m = len(word1)
        n = len(word2)

        f = [[0 for x in range(n + 1)] for y in range(m + 1)]

        f[0][0] = 0 

        for i in range(1, m + 1):
            f[i][0] = i
        for i in range(1, n + 1):
            f[0][i] = i

        for i in range(1, m + 1):
            for j in range(1, n + 1):
                if word1[i - 1] == word2[j - 1]:
                    f[i][j] = f[i - 1][j - 1]
                else:
                    f[i][j] = min(f[i - 1][j], f[i][j - 1], f[i - 1][j - 1]) + 1
        return f[m][n]