edit-distance

Edit Distance

LeetCode #: 72

Difficulty: Hard

Topic: String, Dynamic Programming.

Problem

Given two words word1 and word2, find the minimum number of operations required to convert word1 to word2.

You have the following 3 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')

Solution Explanation

The idea here is to use a (m+1)*(n+1) matrix where rows represent characters in word1 and columns represent characters in word2. Each cell represent the number of operations required to change word1[0..i] to word2[0..j].

In the end, the result would be dp[i][j].

Reference: C++ O(n)-space DP by jianchao-li.

Complexity Analysis

Assume m is the length of word1 and n is the length of word2.

Time complexity: O(m*n)

Space complexity: O(m*n)