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  • Analyze Multiple Sources: While our analyses provide valuable insights,<|end_of_document|>[0]: #!/usr/bin/env python [1]: """ [2]: Given an input string s and a dictionary of words dict, [3]: add spaces in s to construct a sentence where each word is a valid dictionary word. [4]: Return all such possible sentences. [5]: For example, given [6]: s = "catsanddog", [7]: dict = ["cat", "cats", "and", "sand", "dog"]. [8]: A solution is ["cats and dog", "cat sand dog"]. [9]: """ [10]: import sys [11]: class Solution: [12]: def wordBreak(self, s: str, wordDict): [13]: # write your code here [14]: self.wordDict = set(wordDict) [15]: self.result = [] [16]: self.dfs(s) [17]: return self.result [18]: def dfs(self, s): [19]: if len(s) == 0: [20]: self.result.append("") [21]: for i in range(1,len(s)+1): [22]: if s[:i] not in self.wordDict: [23]: continue [24]: if i == len(s): [25]: self.result.append(s[:]) [26]: else: [27]: temp = self.dfs(s[i:]) [28]: for j in range(len(temp)): [29]: if j !=0: [30]: temp[j] = ' ' + temp[j] [31]: temp[j] = s[:i] + temp[j] def main(): print(Solution().wordBreak("catsanddog", ["cat", "cats", "and", "sand", "dog"])) print(Solution().wordBreak("pineapplepenapple", ["apple", "pen", "applepen", "pine", "pineapple"])) print(Solution().wordBreak("catsandog", ["cats", "dog", "sand", "and", "cat"])) print(Solution().wordBreak("", [])) print(Solution().wordBreak("aaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaabaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaaa", ["a","aa","aaa","aaaa","aaaaa","aaaaaa","aaaaaaa","aaaaaaaa","aaaaaaaaa","aaaaaaaaaa"])) if __name__ == "__main__": sys.exit(main()) ***** Tag Data ***** ID: 1 description: Depth-First Search (DFS) based recursive function to solve word break problem. start line: 18 end line: 31 dependencies: - type: Method name: wordBreak start line: 12 end line: 17 - type: Class name: Solution start line: 11 end line: 31 context description: This DFS function is central to solving the word break problem. It recursively attempts to break down the string `s` using words from `wordDict`, appending valid combinations to `self.result`. algorithmic depth: 4 algorithmic depth external: N obscurity: 4 advanced coding concepts: 4 interesting for students: 5 self contained: N ************ ## Challenging aspects ### Challenging aspects in above code 1. **Recursive Depth-First Search (DFS)**: - The implementation uses recursion extensively which requires careful handling of base cases (`len(s) ==0`) and recursive calls (`self.dfs(s[i:])`). Recursive solutions need efficient termination conditions and memory management. 2. **String Manipulation**: - The code involves intricate string slicing (`s[:i]`) and concatenation operations which must be handled efficiently. 3. **State Management**: - Managing state across recursive calls is non-trivial here since results from deeper recursive calls must be correctly merged (`temp[j] = ' ' + temp[j]`). 4. **Dictionary Lookup**: - Efficiently checking membership (`s[:i] not in self.wordDict`) using sets (`self.wordDict = set(wordDict)`), leveraging O(1) average time complexity lookups. 5. **Result Aggregation**: - Properly aggregating results across different branches of recursion requires careful handling (`self.result.append(...)`). ### Extension 1. **Dynamic Word Dictionary**: - Handle scenarios where `wordDict` can dynamically change during execution (words can be added or removed). 2. **Partial Matches**: - Allow partial matches where some segments of `s` might not fully belong to `wordDict` but should be