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Formatted question description: https://leetcode.ca/all/1593.html

1593. Split a String Into the Max Number of Unique Substrings (Medium)

Given a string s, return the maximum number of unique substrings that the given string can be split into.

You can split string s into any list of non-empty substrings, where the concatenation of the substrings forms the original string. However, you must split the substrings such that all of them are unique.

A substring is a contiguous sequence of characters within a string.

 

Example 1:

Input: s = "ababccc"
Output: 5
Explanation: One way to split maximally is ['a', 'b', 'ab', 'c', 'cc']. Splitting like ['a', 'b', 'a', 'b', 'c', 'cc'] is not valid as you have 'a' and 'b' multiple times.

Example 2:

Input: s = "aba"
Output: 2
Explanation: One way to split maximally is ['a', 'ba'].

Example 3:

Input: s = "aa"
Output: 1
Explanation: It is impossible to split the string any further.

 

Constraints:

• 1 <= s.length <= 16

• s contains only lower case English letters.

Related Topics:
Backtracking

Solution 1. Backtrack

// OJ: https://leetcode.com/problems/split-a-string-into-the-max-number-of-unique-substrings/
// Time: O(2^N)
// Space: O(N)
class Solution {
    unordered_set<string> m;
    int ans = 0;
    void dfs(string &s, int i) {
        if (i == s.size()) {
            ans = max(ans, (int)m.size());
            return;
        }
        for (int j = i; j < s.size(); ++j) {
            string sub = s.substr(i, j - i + 1);
            if (m.count(sub)) continue;
            m.insert(sub);
            dfs(s, j + 1);
            m.erase(sub);
        }
    }
public:
    int maxUniqueSplit(string s) {
        dfs(s, 0);
        return ans;
    }
};

• Java
• C++
• Python
• Go

• class Solution {
      public int maxUniqueSplit(String s) {
          int length = s.length();
          if (length == 1)
              return 1;
          int maxSplit = 1;
          int total = 1 << (length - 1);
          for (int i = 1; i < total; i++) {
              boolean[] split = new boolean[length - 1];
              int mask = i;
              int splitCount = 1;
              for (int j = 0; j < length - 1 && mask > 0; j++) {
                  if (mask % 2 == 1) {
                      split[j] = true;
                      splitCount++;
                  }
                  mask /= 2;
              }
              if (splitCount > maxSplit && checkUnique(s, split, splitCount))
                  maxSplit = splitCount;
          }
          return maxSplit;
      }
  
      public boolean checkUnique(String s, boolean[] split, int splitCount) {
          Set<String> set = new HashSet<String>();
          int start = 0;
          int length = s.length();
          for (int i = 0; i < length - 1; i++) {
              if (split[i]) {
                  set.add(s.substring(start, i + 1));
                  start = i + 1;
              }
          }
          if (start < length)
              set.add(s.substring(start));
          return set.size() == splitCount;
      }
  }
  
  ############
  
  class Solution {
      private Set<String> vis = new HashSet<>();
      private int ans = 1;
      private String s;
  
      public int maxUniqueSplit(String s) {
          this.s = s;
          dfs(0, 0);
          return ans;
      }
  
      private void dfs(int i, int t) {
          if (i >= s.length()) {
              ans = Math.max(ans, t);
              return;
          }
          for (int j = i + 1; j <= s.length(); ++j) {
              String x = s.substring(i, j);
              if (vis.add(x)) {
                  dfs(j, t + 1);
                  vis.remove(x);
              }
          }
      }
  }
  

• // OJ: https://leetcode.com/problems/split-a-string-into-the-max-number-of-unique-substrings/
  // Time: O(2^N)
  // Space: O(N)
  class Solution {
      unordered_set<string> m;
      int ans = 0;
      void dfs(string &s, int i) {
          if (i == s.size()) {
              ans = max(ans, (int)m.size());
              return;
          }
          for (int j = i; j < s.size(); ++j) {
              string sub = s.substr(i, j - i + 1);
              if (m.count(sub)) continue;
              m.insert(sub);
              dfs(s, j + 1);
              m.erase(sub);
          }
      }
  public:
      int maxUniqueSplit(string s) {
          dfs(s, 0);
          return ans;
      }
  };
  

• class Solution:
      def maxUniqueSplit(self, s: str) -> int:
          def dfs(i, t):
              if i >= len(s):
                  nonlocal ans
                  ans = max(ans, t)
                  return
              for j in range(i + 1, len(s) + 1):
                  if s[i:j] not in vis:
                      vis.add(s[i:j])
                      dfs(j, t + 1)
                      vis.remove(s[i:j])
  
          vis = set()
          ans = 1
          dfs(0, 0)
          return ans
  
  ############
  
  # 1593. Split a String Into the Max Number of Unique Substrings
  # https://leetcode.com/problems/split-a-string-into-the-max-number-of-unique-substrings/
  
  class Solution:
      def maxUniqueSplit(self, S: str) -> int:
          def backtrack(S, seen):
              res = 0
              for i in range(1,len(S)+1):
                  s = S[:i]
                  if s not in seen:
                      seen.add(s)
                      res = max(res, 1 + backtrack(S[i:], seen))
                      seen.remove(s)
              
              return res
          
          seen = set()
          return backtrack(S, seen)
      
          
                  
          
  

• func maxUniqueSplit(s string) int {
  	ans := 1
  	vis := map[string]bool{}
  
  	var dfs func(i, t int)
  	dfs = func(i, t int) {
  		if i >= len(s) {
  			ans = max(ans, t)
  			return
  		}
  		for j := i + 1; j <= len(s); j++ {
  			x := s[i:j]
  			if !vis[x] {
  				vis[x] = true
  				dfs(j, t+1)
  				vis[x] = false
  			}
  		}
  	}
  	dfs(0, 0)
  	return ans
  }
  
  func max(a, b int) int {
  	if a > b {
  		return a
  	}
  	return b
  }
  

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