Edit Distance

Given two strings word1 and word2, return the minimum number of operations required to convert word1 to word2.

You have the following three operations permitted on a word:

Insert a character Delete a character Replace a character

Example 1:

Input: word1 = “horse”, word2 = “ros” Output: 3 Explanation: horse -> rorse (replace ‘h’ with ‘r’) rorse -> rose (remove ‘r’) rose -> ros (remove ‘e’) Example 2:

Input: word1 = “intention”, word2 = “execution” Output: 5 Explanation: intention -> inention (remove ‘t’) inention -> enention (replace ‘i’ with ‘e’) enention -> exention (replace ‘n’ with ‘x’) exention -> exection (replace ‘n’ with ‘c’) exection -> execution (insert ‘u’)

class Solution:
  def minDistance(self, word1: str, word2: str) -> int:
    m = len(word1)
    n = len(word2)
    # dp[i][j] := min # Of operations to convert word1[0..i) to word2[0..j)
    dp = [[0] * (n + 1) for _ in range(m + 1)]

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

    for j in range(1, n + 1):
      dp[0][j] = j

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

    return dp[m][n]

Solution().minDistance('abcd','ab')

2