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.

方法：backtracking（可惜一开始没有想到用这个方法）

思路：用一个set来记录所有出现过的substring，backtrack来处理所有可能得到的结果。然后取最大值。（感觉也有点像是brute force）

time complexity：O(2^N) 

class Solution:
    def maxUniqueSplit(self, s: str) -> int:
        if not s or len(s) == 0: return 0 
        
        self.res = 0 
        
        self.dfs(s, 0, 0, set())
        
        return self.res 
    
    def dfs(self, s, p, length, visited):
        if length == len(s):
            self.res = max(self.res, len(visited))
            return 
        
        for i in range(p, len(s)):
            if s[p:i+1] not in visited:
                visited.add(s[p:i+1])
                self.dfs(s, i+1, length+i+1-p, visited)
                visited.remove(s[p:i+1])