Description

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

Example 1:

Input: 
"horse"
"ros"
Output: 3
Explanation: 
horse -> rorse (replace 'h' with 'r')
rorse -> rose (remove 'r')
rose -> ros (remove 'e')

Example 2:

Input: 
"intention"
"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')

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