# Delete Operation for Two Strings

Updated: Mar 25, 2021

Given two words *word1* and *word2*, find the minimum number of steps required to make *word1* and *word2* the same, where in each step you can delete one character in either string.

**Example 1:**

**Input****:** "sea", "eat"
**Output****:** 2
**Explanation****:** You need one step to make "sea" to "ea" and another step to make "eat" to "ea".

**Note:**

The length of given words won't exceed 500.

Characters in given words can only be lower-case letters.

**Solution:**

**Approach 1: Using Longest Common subsequence**

```
class Solution {
public int minDistance(String word1, String word2) {
int[][] dp = new int[word1.length() + 1][word2.length() + 1];
for (int i = 0; i <= word1.length(); i++) {
for (int j = 0; j <= word2.length(); j++) {
if (i == 0 || j == 0)
continue;
if (word1.charAt(i - 1) == word2.charAt(j - 1))
dp[i][j] = 1 + dp[i - 1][j - 1];
else
dp[i][j] = Math.max(dp[i - 1][j], dp[i][j - 1]);
}
}
return word1.length() + word2.length() - 2 * dp[word1.length()][word2.length()];
}
}
```

**Approach 2: Without LCS (dynammic programming)**

```
public class Solution {
public int minDistance(String s1, String s2) {
int[][] dp = new int[s1.length() + 1][s2.length() + 1];
for (int i = 0; i <= s1.length(); i++) {
for (int j = 0; j <= s2.length(); j++) {
if (i == 0 || j == 0)
dp[i][j] = i + j;
else if (s1.charAt(i - 1) == s2.charAt(j - 1))
dp[i][j] = dp[i - 1][j - 1];
else
dp[i][j] = 1 + Math.min(dp[i - 1][j], dp[i][j - 1]);
}
}
return dp[s1.length()][s2.length()];
}
}
```