**Physical Address**

304 North Cardinal St.

Dorchester Center, MA 02124

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:

- 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')

**Constraints:**

`0 <= word1.length, word2.length <= 500`

`word1`

and`word2`

consist of lowercase English letters.

```
class Solution:
def minDistance(self, word1, word2):
"""Dynamic programming solution"""
m = len(word1)
n = len(word2)
table = [[0] * (n + 1) for _ in range(m + 1)]
for i in range(m + 1):
table[i][0] = i
for j in range(n + 1):
table[0][j] = j
for i in range(1, m + 1):
for j in range(1, n + 1):
if word1[i - 1] == word2[j - 1]:
table[i][j] = table[i - 1][j - 1]
else:
table[i][j] = 1 + min(table[i - 1][j], table[i][j - 1], table[i - 1][j - 1])
return table[-1][-1]
```

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

```
public class Solution {
public int minDistance(String word1, String word2) {
int m = word1.length();
int n = word2.length();
int[][] cost = new int[m + 1][n + 1];
for(int i = 0; i <= m; i++)
cost[i][0] = i;
for(int i = 1; i <= n; i++)
cost[0][i] = i;
for(int i = 0; i < m; i++) {
for(int j = 0; j < n; j++) {
if(word1.charAt(i) == word2.charAt(j))
cost[i + 1][j + 1] = cost[i][j];
else {
int a = cost[i][j];
int b = cost[i][j + 1];
int c = cost[i + 1][j];
cost[i + 1][j + 1] = a < b ? (a < c ? a : c) : (b < c ? b : c);
cost[i + 1][j + 1]++;
}
}
}
return cost[m][n];
}
}
```

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