Added Radix Tree in data structures (#6616)

* added radix tree to data structures

* added doctests

* solved flake8

* added type hints

* added description for delete function

* Update data_structures/trie/radix_tree.py

* Update radix_tree.py

* Update radix_tree.py

* Update radix_tree.py

Co-authored-by: Alex de la Cruz <[email protected]>
Co-authored-by: Christian Clauss <[email protected]>

Author: 3 people

Diff for: data_structures/trie/radix_tree.py

@@ -0,0 +1,223 @@
+"""
+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")
+        """
+        # Case 1: If the word is the prefix of the node
+        # Solution: We set the current node as leaf
+        if self.prefix == word:
+            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)
+            else:
+                # If it is not a leaf, we don't have to delete
+                if 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 = list(self.nodes.values())[0]
+                            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 = list(incoming_node.nodes.values())[0]
+                        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()