Day 31 Edit Distance.cpp

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:


class Solution {
public:
    int minDistance(string word1, string word2) {
        
        int i,j,n,m;
        n = word1.size();
        m = word2.size();
        
        vector<vector<int>> dp(n+1,vector<int>(m+1,0));
        
        for(i=0;i<=n;i++)
        {
            for(j=0;j<=m;j++)
            {   
                if(i==0)
                    dp[i][j]=j;
                
                else if(j==0)
                    dp[i][j]=i;
                
                else 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[n][m];
    }
};