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Edit Distance

Tags : string, dynamic-programming, leetcode, cpp, hard

Problem Statement - link #

Given two strings word1 and word2, return the minimum number of operations required to convert word1 to word2.

You have the following three operations permitted on a word:

Examples #

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')

Constraints #

Solutions #

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