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1239. Maximum Length of a Concatenated String with Unique Characters

Description

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.

Solutions

Solution 1: Bit Manipulation + State Compression

State compression is used, with a 32-bit number recording the occurrence of letters, and masks storing the strings enumerated before.

The time complexity is $O(2^n + L)$, and the space complexity is $O(2^n)$. Where $n$ and $L$ are the length of the string array and the sum of the lengths of the strings in the array, respectively.

• Java
• C++
• Python
• Go
• TypeScript

• class Solution {
      public int maxLength(List<String> arr) {
          int ans = 0;
          List<Integer> masks = new ArrayList<>();
          masks.add(0);
          for (var s : arr) {
              int mask = 0;
              for (int i = 0; i < s.length(); ++i) {
                  int j = s.charAt(i) - 'a';
                  if (((mask >> j) & 1) == 1) {
                      mask = 0;
                      break;
                  }
                  mask |= 1 << j;
              }
              if (mask == 0) {
                  continue;
              }
              int n = masks.size();
              for (int i = 0; i < n; ++i) {
                  int m = masks.get(i);
                  if ((m & mask) == 0) {
                      masks.add(m | mask);
                      ans = Math.max(ans, Integer.bitCount(m | mask));
                  }
              }
          }
          return ans;
      }
  }
  

• class Solution {
  public:
      int maxLength(vector<string>& arr) {
          int ans = 0;
          vector<int> masks = {0};
          for (auto& s : arr) {
              int mask = 0;
              for (auto& c : s) {
                  int i = c - 'a';
                  if (mask >> i & 1) {
                      mask = 0;
                      break;
                  }
                  mask |= 1 << i;
              }
              if (mask == 0) {
                  continue;
              }
              int n = masks.size();
              for (int i = 0; i < n; ++i) {
                  int m = masks[i];
                  if ((m & mask) == 0) {
                      masks.push_back(m | mask);
                      ans = max(ans, __builtin_popcount(m | mask));
                  }
              }
          }
          return ans;
      }
  };
  

• class Solution:
      def maxLength(self, arr: List[str]) -> int:
          ans = 0
          masks = [0]
          for s in arr:
              mask = 0
              for c in s:
                  i = ord(c) - ord('a')
                  if mask >> i & 1:
                      mask = 0
                      break
                  mask |= 1 << i
              if mask == 0:
                  continue
              for m in masks:
                  if m & mask == 0:
                      masks.append(m | mask)
                      ans = max(ans, (m | mask).bit_count())
          return ans
  
  

• func maxLength(arr []string) (ans int) {
  	masks := []int{0}
  	for _, s := range arr {
  		mask := 0
  		for _, c := range s {
  			i := int(c - 'a')
  			if mask>>i&1 == 1 {
  				mask = 0
  				break
  			}
  			mask |= 1 << i
  		}
  		if mask == 0 {
  			continue
  		}
  		n := len(masks)
  		for _, m := range masks[:n] {
  			if m&mask == 0 {
  				masks = append(masks, m|mask)
  				ans = max(ans, bits.OnesCount(uint(m|mask)))
  			}
  		}
  	}
  	return
  }
  

• function maxLength(arr: string[]): number {
      const s: number[] = [0];
      let ans = 0;
      for (const t of arr) {
          let x = 0;
          for (const c of t) {
              const b = c.charCodeAt(0) - 97;
              if ((x >> b) & 1) {
                  x = 0;
                  break;
              }
              x |= 1 << b;
          }
  
          if (x > 0) {
              for (let i = s.length - 1; ~i; --i) {
                  const y = s[i];
                  if ((x & y) === 0) {
                      s.push(x | y);
                      ans = Math.max(ans, bitCount(x | y));
                  }
              }
          }
      }
  
      return ans;
  }
  
  function bitCount(i: number): number {
      i = i - ((i >>> 1) & 0x55555555);
      i = (i & 0x33333333) + ((i >>> 2) & 0x33333333);
      i = (i + (i >>> 4)) & 0x0f0f0f0f;
      i = i + (i >>> 8);
      i = i + (i >>> 16);
      return i & 0x3f;
  }
  
  

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