Edit Distance

Desicription

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

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