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:

a) Insert a character b) Delete a character c) Replace a character

Solution

class Solution(object):
    def minDistance(self, word1, word2):
        """
        :type word1: str
        :type word2: str
        :rtype: int
        """
        m, n = len(word1), len(word2)
        dp = [[0 for i in range(n+1)] for j in range(m+1)]
        for i in range(n+1):
            dp[0][i] = i
        for j in range(m+1):
            dp[j][0] = 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]

public class Solution {
    public int minDistance(String word1, String word2) {
        int m = word1.length();
        int n = word2.length();

        int [][] dp = new int[m+1][n+1];

        for(int i = 0;i<=n;i++)
            dp[0][i] = i;
        for(int i = 0;i<=m;i++)
            dp[i][0] = i;

        for(int i = 1;i<=m;i++)
            for(int j = 1;j<=n;j++) {
                if(word1.charAt(i - 1) == word2.charAt(j - 1))
                    dp[i][j] = dp[i-1][j-1];
                else {
                    dp[i][j] = 1 + Math.min(Math.min(dp[i-1][j-1], dp[i-1][j]), dp[i][j-1]);
                }
            }

        return dp[m][n];
    }
}