​
Core Implementation

​
Basic Trie

class TrieNode:
    def __init__(self):
        self.children = {}
        self.is_end = False
        self.count = 0  # Number of words ending here
        self.prefix_count = 0  # Number of words using this prefix

class Trie:
    def __init__(self):
        self.root = TrieNode()
    
    def insert(self, word):
        node = self.root
        for char in word:
            node.prefix_count += 1
            if char not in node.children:
                node.children[char] = TrieNode()
            node = node.children[char]
        node.prefix_count += 1
        node.is_end = True
        node.count += 1
    
    def search(self, word):
        node = self._traverse(word)
        return node is not None and node.is_end
    
    def starts_with(self, prefix):
        node = self._traverse(prefix)
        return node is not None
    
    def _traverse(self, prefix):
        node = self.root
        for char in prefix:
            if char not in node.children:
                return None
            node = node.children[char]
        return node
    
    def count_words_with_prefix(self, prefix):
        node = self._traverse(prefix)
        return node.prefix_count if node else 0

​
Implementation Variations

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1. Compressed Trie (Radix Tree)

class CompressedTrieNode:
    def __init__(self):
        self.children = {}  # {string: node} pairs
        self.is_end = False

class CompressedTrie:
    def __init__(self):
        self.root = CompressedTrieNode()
    
    def insert(self, word):
        node = self.root
        
        while word:
            # Find matching prefix in children
            matched_prefix = None
            matched_child = None
            
            for prefix, child in node.children.items():
                for i in range(min(len(word), len(prefix))):
                    if word[i] != prefix[i]:
                        break
                    if i == min(len(word), len(prefix)) - 1:
                        matched_prefix = prefix
                        matched_child = child
                        break
            
            if not matched_prefix:
                # No match found, create new node
                node.children[word] = CompressedTrieNode()
                node.children[word].is_end = True
                break
            
            if len(matched_prefix) > len(word):
                # Split existing node
                new_node = CompressedTrieNode()
                new_node.children = matched_child.children
                new_node.is_end = matched_child.is_end
                
                node.children[word] = CompressedTrieNode()
                node.children[word].is_end = True
                node.children[matched_prefix[len(word):]] = new_node
                del node.children[matched_prefix]
                break
            
            if len(word) > len(matched_prefix):
                # Continue with remaining substring
                node = matched_child
                word = word[len(matched_prefix):]
            else:
                matched_child.is_end = True
                break

​
2. Ternary Search Tree

class TSTNode:
    def __init__(self, char):
        self.char = char
        self.left = None
        self.right = None
        self.equal = None
        self.is_end = False

class TST:
    def __init__(self):
        self.root = None
    
    def insert(self, word):
        self.root = self._insert_recursive(self.root, word, 0)
    
    def _insert_recursive(self, node, word, index):
        char = word[index]
        
        if not node:
            node = TSTNode(char)
        
        if char < node.char:
            node.left = self._insert_recursive(node.left, word, index)
        elif char > node.char:
            node.right = self._insert_recursive(node.right, word, index)
        elif index < len(word) - 1:
            node.equal = self._insert_recursive(node.equal, word, index + 1)
        else:
            node.is_end = True
        
        return node

​
Time Complexities

OperationStandard TrieCompressed TrieTST
InsertO(m)O(m)O(m)
SearchO(m)O(m)O(m)
Prefix SearchO(p)O(p)O(p)
DeleteO(m)O(m)O(m)
Space ComplexityO(ALPHABET_SIZE * m * n)O(n)O(n)

where m = length of word, p = length of prefix, n = number of words

​
Space Complexities

ImplementationSpace ComplexityAdditional Notes
Standard TrieO(ALPHABET_SIZE * m * n)More space for faster lookups
Compressed TrieO(n)Space efficient but slower updates
TSTO(n)Best for sparse datasets

​
Common Data Structure Patterns

  1. Autocomplete Systems

    • Prefix matching
    • Top-k suggestions
    • Fuzzy search

  2. Spell Checkers

    • Word validation
    • Suggestion generation
    • Edit distance

  3. String Matching

    • Pattern matching
    • Wildcard matching
    • Regex operations

  4. IP Routing Tables

    • Longest prefix matching
    • Route aggregation
    • Next hop lookup

  5. Dictionary Operations

    • Word insertion
    • Deletion
    • Lookup

  6. Phone Directory

    • Contact search
    • Partial matching
    • Prefix based search

​
Edge Cases to Consider

  1. Empty String
def insert_empty(self):
    if not word:
        self.root.is_end = True
        return
  1. Single Character
def handle_single_char(self, char):
    if len(char) == 1:
        node = self.root
        if char not in node.children:
            node.children[char] = TrieNode()
        node.children[char].is_end = True
  1. Duplicate Words
def insert_with_count(self, word):
    node = self.root
    for char in word:
        if char not in node.children:
            node.children[char] = TrieNode()
        node = node.children[char]
    node.is_end = True
    node.count += 1  # Track duplicates

​
Optimization Techniques

  1. Array-based Children
class OptimizedTrieNode:
    def __init__(self):
        self.children = [None] * 26  # For lowercase English letters
        self.is_end = False
    
    def get_index(self, char):
        return ord(char) - ord('a')
    
    def get_child(self, char):
        return self.children[self.get_index(char)]
    
    def set_child(self, char, node):
        self.children[self.get_index(char)] = node
  1. Bit Vector Implementation
class BitVectorTrie:
    def __init__(self):
        self.children = 0  # Use bits to represent children
        self.child_nodes = []
        self.is_end = False
    
    def has_child(self, char):
        return bool(self.children & (1 << (ord(char) - ord('a'))))
    
    def add_child(self, char):
        self.children |= (1 << (ord(char) - ord('a')))
  1. Path Compression
class CompressedNode:
    def __init__(self):
        self.path = ""  # Store complete path segment
        self.children = {}
        self.is_end = False

​
Memory Management

  1. Memory Pool
class TrieNodePool:
    def __init__(self, size=1000):
        self.pool = [TrieNode() for _ in range(size)]
        self.available = list(range(size))
    
    def get_node(self):
        if self.available:
            return self.pool[self.available.pop()]
        return TrieNode()
    
    def return_node(self, node):
        if len(self.available) < len(self.pool):
            node.children.clear()
            node.is_end = False
            self.available.append(self.pool.index(node))
  1. Lazy Loading
class LazyTrie:
    def __init__(self, word_file):
        self.root = TrieNode()
        self.word_file = word_file
        self.loaded = False
    
    def ensure_loaded(self):
        if not self.loaded:
            with open(self.word_file) as f:
                for word in f:
                    self.insert(word.strip())
            self.loaded = True

​
Performance Considerations

  1. Batch Operations
def bulk_insert(self, words):
    # Sort words for better cache locality
    words.sort()
    for word in words:
        self.insert(word)
  1. Prefix Caching
class CachedTrie(Trie):
    def __init__(self):
        super().__init__()
        self.prefix_cache = {}
    
    def find_with_prefix(self, prefix):
        if prefix in self.prefix_cache:
            return self.prefix_cache[prefix]
        
        results = self._find_words(self._traverse(prefix), prefix)
        self.prefix_cache[prefix] = results
        return results

​
Common Pitfalls

  1. Memory Leak in Deletion
# Wrong
def delete_wrong(self, word):
    node = self._traverse(word)
    if node:
        node.is_end = False  # Memory leak, nodes still exist

# Correct
def delete(self, word):
    def _delete_recursive(node, word, depth=0):
        if not node:
            return None
        
        if depth == len(word):
            node.is_end = False
            if not node.children:
                return None
            return node
        
        char = word[depth]
        node.children[char] = _delete_recursive(node.children.get(char), word, depth + 1)
        
        if not node.children[char]:
            del node.children[char]
        
        if not node.children and not node.is_end:
            return None
        return node
    
    self.root = _delete_recursive(self.root, word)
  1. Incorrect Prefix Counting
# Wrong
def count_prefix_wrong(self, prefix):
    node = self._traverse(prefix)
    return 1 if node else 0  # Doesn't count all words with prefix

# Correct
def count_prefix(self, prefix):
    def _count_recursive(node):
        count = node.count if node.is_end else 0
        for child in node.children.values():
            count += _count_recursive(child)
        return count
    
    node = self._traverse(prefix)
    return _count_recursive(node) if node else 0
  1. Inefficient Space Usage
# Wrong (wastes space)
class InefficientTrieNode:
    def __init__(self):
        self.children = [{} for _ in range(26)]  # Unnecessary nesting

# Better
class EfficientTrieNode:
    def __init__(self):
        self.children = {}  # Only create what's needed
GraphDisjoint set union