""" A Radix Tree is a data structure that represents a space-optimized trie (prefix tree) in whicheach node that is the only child is merged with its parent [https://en.wikipedia.org/wiki/Radix_tree] """ class RadixNode: def __init__(self, prefix: str = "", is_leaf: bool = False) -> None: # Mapping from the first character of the prefix of the node self.nodes: dict[str, RadixNode] = {} # A node will be a leaf if the tree contains its word self.is_leaf = is_leaf self.prefix = prefix def match(self, word: str) -> tuple[str, str, str]: """Compute the common substring of the prefix of the node and a word Args: word (str): word to compare Returns: (str, str, str): common substring, remaining prefix, remaining word >>> RadixNode("myprefix").match("mystring") ('my', 'prefix', 'string') """ x = 0 for q, w in zip(self.prefix, word): if q != w: break x += 1 return self.prefix[:x], self.prefix[x:], word[x:] def insert_many(self, words: list[str]) -> None: """Insert many words in the tree Args: words (list[str]): list of words >>> RadixNode("myprefix").insert_many(["mystring", "hello"]) """ for word in words: self.insert(word) def insert(self, word: str) -> None: """Insert a word into the tree Args: word (str): word to insert >>> RadixNode("myprefix").insert("mystring") >>> root = RadixNode() >>> root.insert_many(['myprefix', 'myprefixA', 'myprefixAA']) >>> root.print_tree() - myprefix (leaf) -- A (leaf) --- A (leaf) """ # Case 1: If the word is the prefix of the node # Solution: We set the current node as leaf if self.prefix == word and not self.is_leaf: self.is_leaf = True # Case 2: The node has no edges that have a prefix to the word # Solution: We create an edge from the current node to a new one # containing the word elif word[0] not in self.nodes: self.nodes[word[0]] = RadixNode(prefix=word, is_leaf=True) else: incoming_node = self.nodes[word[0]] matching_string, remaining_prefix, remaining_word = incoming_node.match( word ) # Case 3: The node prefix is equal to the matching # Solution: We insert remaining word on the next node if remaining_prefix == "": self.nodes[matching_string[0]].insert(remaining_word) # Case 4: The word is greater equal to the matching # Solution: Create a node in between both nodes, change # prefixes and add the new node for the remaining word else: incoming_node.prefix = remaining_prefix aux_node = self.nodes[matching_string[0]] self.nodes[matching_string[0]] = RadixNode(matching_string, False) self.nodes[matching_string[0]].nodes[remaining_prefix[0]] = aux_node if remaining_word == "": self.nodes[matching_string[0]].is_leaf = True else: self.nodes[matching_string[0]].insert(remaining_word) def find(self, word: str) -> bool: """Returns if the word is on the tree Args: word (str): word to check Returns: bool: True if the word appears on the tree >>> RadixNode("myprefix").find("mystring") False """ incoming_node = self.nodes.get(word[0], None) if not incoming_node: return False else: matching_string, remaining_prefix, remaining_word = incoming_node.match( word ) # If there is remaining prefix, the word can't be on the tree if remaining_prefix != "": return False # This applies when the word and the prefix are equal elif remaining_word == "": return incoming_node.is_leaf # We have word remaining so we check the next node else: return incoming_node.find(remaining_word) def delete(self, word: str) -> bool: """Deletes a word from the tree if it exists Args: word (str): word to be deleted Returns: bool: True if the word was found and deleted. False if word is not found >>> RadixNode("myprefix").delete("mystring") False """ incoming_node = self.nodes.get(word[0], None) if not incoming_node: return False else: matching_string, remaining_prefix, remaining_word = incoming_node.match( word ) # If there is remaining prefix, the word can't be on the tree if remaining_prefix != "": return False # We have word remaining so we check the next node elif remaining_word != "": return incoming_node.delete(remaining_word) # If it is not a leaf, we don't have to delete elif not incoming_node.is_leaf: return False else: # We delete the nodes if no edges go from it if len(incoming_node.nodes) == 0: del self.nodes[word[0]] # We merge the current node with its only child if len(self.nodes) == 1 and not self.is_leaf: merging_node = next(iter(self.nodes.values())) self.is_leaf = merging_node.is_leaf self.prefix += merging_node.prefix self.nodes = merging_node.nodes # If there is more than 1 edge, we just mark it as non-leaf elif len(incoming_node.nodes) > 1: incoming_node.is_leaf = False # If there is 1 edge, we merge it with its child else: merging_node = next(iter(incoming_node.nodes.values())) incoming_node.is_leaf = merging_node.is_leaf incoming_node.prefix += merging_node.prefix incoming_node.nodes = merging_node.nodes return True def print_tree(self, height: int = 0) -> None: """Print the tree Args: height (int, optional): Height of the printed node """ if self.prefix != "": print("-" * height, self.prefix, " (leaf)" if self.is_leaf else "") for value in self.nodes.values(): value.print_tree(height + 1) def test_trie() -> bool: words = "banana bananas bandana band apple all beast".split() root = RadixNode() root.insert_many(words) assert all(root.find(word) for word in words) assert not root.find("bandanas") assert not root.find("apps") root.delete("all") assert not root.find("all") root.delete("banana") assert not root.find("banana") assert root.find("bananas") return True def pytests() -> None: assert test_trie() def main() -> None: """ >>> pytests() """ root = RadixNode() words = "banana bananas bandanas bandana band apple all beast".split() root.insert_many(words) print("Words:", words) print("Tree:") root.print_tree() if __name__ == "__main__": main()