MediumLeetCode #72Dynamic Programming

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: Insert, Delete, Replace a character.

Constraints

0 <= word1.length, word2.length <= 500

Examples

Input: word1 = "horse", word2 = "ros"

Output: 3

Solution

Approach

2D DP where dp[i][j] = min ops to convert word1[0:i] to word2[0:j]. If chars match, dp[i][j] = dp[i-1][j-1]. Else take min of insert, delete, replace + 1.

def minDistance(word1, word2):
    m, n = len(word1), len(word2)
    dp = [[0] * (n + 1) for _ in range(m + 1)]
    for i in range(m + 1):
        dp[i][0] = i
    for j in range(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] = 1 + min(dp[i-1][j], dp[i][j-1], dp[i-1][j-1])
    return dp[m][n]

Complexity

Time:O(mn)

Space:O(mn)

Hints

1.Classic 2D DP problem
2.Think about subproblems on prefixes
3.Three choices when chars differ: insert, delete, replace

Asked at

Google