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.

 

public class Solution {
    /**
     * @param word1 & word2: Two string.
     * @return: The minimum number of steps.
     */
    public int minDistance(String word1, String word2) {
        // write your code here
        if(word1==null && word2==null) return 0;
        if(word1==null || word1.length()==0) return word2.length();
        if(word2==null || word2.length()==0) return word1.length();
        
        int m=word1.length();
        int n=word2.length();
        
        int[][] dp=new int[m+1][n+1];
        
        for(int i=0;i<=m;i++)
        {
            dp[i][0]=i;
        }
        
        for(int i=0;i<=n;i++)
        {
            dp[0][i]=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]=Math.min(dp[i-1][j-1]+1,Math.min(dp[i-1][j]+1,dp[i][j-1]+1));
                }
            }
        }
        
        return dp[m][n];
    }
}