## Algorithm

Problem Name: 1239. Maximum Length of a Concatenated String with Unique Characters

You are given an array of strings `arr`. A string `s` is formed by the concatenation of a subsequence of `arr` that has unique characters.

Return the maximum possible length of `s`.

A subsequence is an array that can be derived from another array by deleting some or no elements without changing the order of the remaining elements.

Example 1:

```Input: arr = ["un","iq","ue"]
Output: 4
Explanation: All the valid concatenations are:
- ""
- "un"
- "iq"
- "ue"
- "uniq" ("un" + "iq")
- "ique" ("iq" + "ue")
Maximum length is 4.
```

Example 2:

```Input: arr = ["cha","r","act","ers"]
Output: 6
Explanation: Possible longest valid concatenations are "chaers" ("cha" + "ers") and "acters" ("act" + "ers").
```

Example 3:

```Input: arr = ["abcdefghijklmnopqrstuvwxyz"]
Output: 26
Explanation: The only string in arr has all 26 characters.
```

Constraints:

• `1 <= arr.length <= 16`
• `1 <= arr[i].length <= 26`
• `arr[i]` contains only lowercase English letters.

## Code Examples

### #1 Code Example with Javascript Programming

```Code - Javascript Programming```

``````
const maxLength = function(arr) {
let maxLen = 0;
arr = arr.filter(isUnique);
const mem = {};
maxLen = dfs(arr, "", 0, maxLen, mem);

return maxLen;
};

function dfs(arr, path, i, maxLen, mem) {
if (mem[path]) return mem[path];
let pathIsUnique = isUnique(path);
if (pathIsUnique) {
maxLen = Math.max(path.length, maxLen);
}
if (i === arr.length || !pathIsUnique) {
mem[path] = maxLen;
return maxLen;
}
for (let j = i; j < arr.length; j++) {
maxLen = dfs(arr, path + arr[j], j + 1, maxLen, mem);
}

mem[path] = maxLen;
return maxLen;
}

function isUnique(str) {
const map = {}
for (let i = 0; i < str.length; i++) {
if (map[str[i]]) return false;
map[str[i]] = 1;
}

return true;
}
``````
Copy The Code &

Input

cmd
arr = ["un","iq","ue"]

Output

cmd
4

### #2 Code Example with Python Programming

```Code - Python Programming```

``````
class Solution:
def maxLength(self, arr: List[str]) -> int:
bfs = [""]
for b in filter(lambda x: len(x) == len(set(x)), arr):
bfs += [a + b for a in bfs if not set(a) & set(b)]
return max(map(len, bfs))
``````
Copy The Code &

Input

cmd
arr = ["un","iq","ue"]

Output

cmd
4