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# Shortest Common Supersequence

Given two strings `str1` and `str2`, return the shortest string that has both `str1` and `str2` as subsequences.  If multiple answers exist, you may return any of them.

*(A string S is a subsequence of string T if deleting some number of characters from T (possibly 0, and the characters are chosen anywhere from T) results in the string S.)*

**Example 1:**

```
Input: str1 = "abac", str2 = "cab"
Output: "cabac"
Explanation: 
str1 = "abac" is a subsequence of "cabac" because we can delete the first "c".
str2 = "cab" is a subsequence of "cabac" because we can delete the last "ac".
The answer provided is the shortest such string that satisfies these properties.
```

**Note:**

1. `1 <= str1.length, str2.length <= 1000`
2. `str1` and `str2` consist of lowercase English letters.

```java
class Solution {
    public String shortestCommonSupersequence(String str1, String str2) {
        int m = str1.length();
        int n = str2.length();

        int[][] dp = new int[m + 1][n + 1];

        for (int i = 0; i <= m; i++) {
            for (int j = 0; j <= n; j++) {
                if (i == 0)
                    dp[i][j] = j;
                else if (j == 0)
                    dp[i][j] = i;
                else if (str1.charAt(i - 1) == str2.charAt(j - 1))
                    dp[i][j] = 1 + dp[i - 1][j - 1];
                else
                    dp[i][j] = 1 + Math.min(dp[i - 1][j], dp[i][j - 1]);
            }
        }

        int l = dp[m][n]; // Length of the ShortestSuperSequence
        char[] arr = new char[l];
        int i = m, j = n;
        while (i > 0 && j > 0) {
            /*
             * If current character in str1 and str2 are same, then current character is
             * part of shortest supersequence
             */
            if (str1.charAt(i - 1) == str2.charAt(j - 1)) {
                arr[--l] = str1.charAt(i - 1);
                i--;
                j--;
            } else if (dp[i - 1][j] < dp[i][j - 1]) {
                arr[--l] = str1.charAt(i - 1);
                i--;
            } else {
                arr[--l] = str2.charAt(j - 1);
                j--;
            }
        }
        while (i > 0) {
            arr[--l] = str1.charAt(i - 1);
            i--;
        }
        while (j > 0) {
            arr[--l] = str2.charAt(j - 1);
            j--;
        }
        return new String(arr);
    }
}
```


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