Here is the implementation of a Trie.

In Python, creating a custom TrieNode class object for every single character in an entire dictionary leads to massive memory bloat due to Python's object overhead.

To highly optimize for memory efficiency, this implementation uses Nested Dictionaries combined with a Sentinel Key. By leveraging Python's highly optimized, C-underlying built-in dictionaries and completely avoiding custom class instantiations, we dramatically reduce memory usage.

The Code

from typing import List

class MemoryEfficientTrie:
    def __init__(self):
        # We use nested standard dicts over custom Node classes. 
        # Python 3.6+ dicts are highly optimized and memory-compact in C.
        self.root = {}
        # A sentinel key used to designate the end of a word.
        self._end = '#'

    def insert(self, word: str) -> None:
        """Inserts a word into the trie."""
        node = self.root
        for char in word:
            # If the character isn't a child, create a new dictionary
            if char not in node:
                node[char] = {}
            node = node[char]
        
        # Mark the end of a word with the sentinel key
        node[self._end] = True

    def search(self, word: str) -> bool:
        """Returns True if the word is fully present in the trie."""
        node = self.root
        for char in word:
            if char not in node:
                return False
            node = node[char]
            
        # The word must end exactly here
        return self._end in node

    def autocomplete(self, prefix: str) -> List[str]:
        """Returns a list of all words with the given prefix."""
        node = self.root
        # Step 1: Traverse down to the end of the prefix
        for char in prefix:
            if char not in node:
                return [] # Prefix doesn't exist
            node = node[char]

        results = []
        # Step 2: Use Depth First Search to find all branches leading to words
        self._dfs(node, prefix, results)
        return results

    def _dfs(self, node: dict, current_word: str, results: List[str]) -> None:
        """Helper method to deeply search for word ends."""
        # If we hit the sentinel value, this path is a valid word
        if self._end in node:
            results.append(current_word)
            
        # Iterate through remaining children
        for char, child_node in node.items():
            if char != self._end:
                self._dfs(child_node, current_word + char, results)

# ==========================================
# Example Usage:
# ==========================================
if __name__ == "__main__":
    trie = MemoryEfficientTrie()
    
    words = ["app", "apple", "applet", "application", "bat", "batch", "car"]
    for w in words:
        trie.insert(w)

    print("Search 'apple':", trie.search("apple"))       # True
    print("Search 'app':", trie.search("app"))           # True
    print("Search 'appli':", trie.search("appli"))       # False

    print("\nAutocomplete 'app':\n", trie.autocomplete("app")) 
    # ['app', 'apple', 'applet', 'application']
    
    print("\nAutocomplete 'ba':\n", trie.autocomplete("ba"))   
    # ['bat', 'batch']

How the Memory Optimizations Work:

1. Avoidance of Object Overhead: A typical implementation instantiates a class TrieNode for every letter. In Python, an empty custom object usually carries around ~100+ bytes of metadata overhead (like standard __dict__ and garbage collection headers). By using nested primitive dicts, we bypass Python object initiation metadata, saving large amounts of memory.
2. Eliminating the is_end_of_word attribute: Instead of tying up memory with a boolean attribute on every node, we simply insert a sentinel character (#). Because Python interns small strings and booleans, inserting '#': True only takes up standard dict pointer space without allocating new memory for the boolean.
3. C-Level Optimization: Modern Python (3.6+) dictionaries use a compressed array layout written in C. Because of this, using deeply nested dictionaries is unexpectedly one of the most mechanically memory-efficient ways to write tree-structures without leaving pure Python.

Architectural Steps to Optimize Further (If Needed):

If you are dealing with millions of words and memory becomes an absolute bottleneck, you would move away from a standard Trie and use these variations:

• Radix Tree (Patricia Trie): Merges nodes with only one child. If inserting "apple" and "applet", instead of storing a-p-p-l-e as single nodes, you store app-l-e-[... ], cutting node count significantly.
• DAWG (Directed Acyclic Word Graph): If your dictionary is static (you don't add words at runtime), you can reuse identical suffixes. E.g., prefixes "read" and "listen" can both point to the exact same pointer for the "ing" suffix.

Trie Data Structure with Memory Optimization

Here's a comprehensive implementation of a trie with insert, search, and autocomplete functionality, followed by multiple memory optimization strategies.

1. Basic Trie Implementation

class TrieNode:
    def __init__(self):
        self.children = {}
        self.is_end_of_word = False

class Trie:
    def __init__(self):
        self.root = TrieNode()
    
    def insert(self, word: str) -> None:
        """Insert a word into the trie."""
        node = self.root
        for char in word:
            if char not in node.children:
                node.children[char] = TrieNode()
            node = node.children[char]
        node.is_end_of_word = True
    
    def search(self, word: str) -> bool:
        """Search for a complete word in the trie."""
        node = self._find_node(word)
        return node is not None and node.is_end_of_word
    
    def starts_with(self, prefix: str) -> bool:
        """Check if any word in the trie starts with the given prefix."""
        return self._find_node(prefix) is not None
    
    def _find_node(self, prefix: str):
        """Helper to find the node corresponding to a prefix."""
        node = self.root
        for char in prefix:
            if char not in node.children:
                return None
            node = node.children[char]
        return node
    
    def autocomplete(self, prefix: str, limit: int = 10) -> list:
        """Return up to `limit` words that start with the given prefix."""
        node = self._find_node(prefix)
        if not node:
            return []
        
        results = []
        self._dfs(node, prefix, results, limit)
        return results
    
    def _dfs(self, node, current_word, results, limit):
        """Depth-first search to collect words."""
        if len(results) >= limit:
            return
        if node.is_end_of_word:
            results.append(current_word)
        for char, child_node in sorted(node.children.items()):
            self._dfs(child_node, current_word + char, results, limit)

2. Memory-Optimized Trie with __slots__

class TrieNodeOptimized:
    __slots__ = ['children', 'is_end_of_word']
    
    def __init__(self):
        self.children = {}
        self.is_end_of_word = False

class TrieOptimized:
    def __init__(self):
        self.root = TrieNodeOptimized()
    
    def insert(self, word: str) -> None:
        node = self.root
        for char in word:
            if char not in node.children:
                node.children[char] = TrieNodeOptimized()
            node = node.children[char]
        node.is_end_of_word = True
    
    def search(self, word: str) -> bool:
        node = self._find_node(word)
        return node is not None and node.is_end_of_word
    
    def starts_with(self, prefix: str) -> bool:
        return self._find_node(prefix) is not None
    
    def _find_node(self, prefix: str):
        node = self.root
        for char in prefix:
            if char not in node.children:
                return None
            node = node.children[char]
        return node
    
    def autocomplete(self, prefix: str, limit: int = 10) -> list:
        node = self._find_node(prefix)
        if not node:
            return []
        
        results = []
        self._dfs(node, prefix, results, limit)
        return results
    
    def _dfs(self, node, current_word, results, limit):
        if len(results) >= limit:
            return
        if node.is_end_of_word:
            results.append(current_word)
        for char, child_node in sorted(node.items()):
            self._dfs(child_node, current_word + char, results, limit)
    
    def get_memory_usage(self) -> dict:
        """Estimate memory usage of the trie."""
        import sys
        def count_nodes(node):
            count = 1
            size = sys.getsizeof(node)
            for child in node.children.values():
                c, s = count_nodes(child)
                count += c
                size += s
            return count, size
        
        node_count, total_size = count_nodes(self.root)
        return {
            'node_count': node_count,
            'estimated_size_bytes': total_size,
            'estimated_size_mb': total_size / (1024 * 1024)
        }

3. Radix Trie (Compressed Trie) for Maximum Memory Efficiency

class RadixTrieNode:
    __slots__ = ['children', 'is_end_of_word']
    
    def __init__(self):
        self.children = {}
        self.is_end_of_word = False

class RadixTrie:
    def __init__(self):
        self.root = RadixTrieNode()
    
    def insert(self, word: str) -> None:
        if not word:
            return
        self._insert(self.root, word, 0)
    
    def _insert(self, node, word, index):
        if index == len(word):
            node.is_end_of_word = True
            return
        
        char = word[index]
        if char not in node.children:
            new_node = RadixTrieNode()
            node.children[char] = (word[index:], new_node)
            new_node.is_end_of_word = (index == len(word) - 1)
            return
        
        edge, child_node = node.children[char]
        i = 0
        while i < len(edge) and index + i < len(word) and edge[i] == word[index + i]:
            i += 1
        
        if i == len(edge):
            self._insert(child_node, word, index + i)
        elif i == len(word) - index:
            new_node = RadixTrieNode()
            new_node.is_end_of_word = True
            node.children[char] = (word[index:index + i], new_node)
            new_node.children[edge[i]] = (edge[i:], child_node)
        else:
            new_node = RadixTrieNode()
            node.children[char] = (edge[:i], new_node)
            new_node.children[edge[i]] = (edge[i:], child_node)
            new_node.children[word[index + i]] = (word[index + i:], RadixTrieNode())
            new_node.children[word[index + i]][1].is_end_of_word = True
    
    def search(self, word: str) -> bool:
        node = self._find_node(word)
        return node is not None and node.is_end_of_word
    
    def starts_with(self, prefix: str) -> bool:
        return self._find_node(prefix) is not None
    
    def _find_node(self, word):
        node = self.root
        index = 0
        while index < len(word) and node:
            char = word[index]
            if char not in node.children:
                return None
            edge, child_node = node.children[char]
            if not word[index:].startswith(edge):
                return None
            index += len(edge)
            node = child_node
        return node if index == len(word) else None
    
    def autocomplete(self, prefix: str, limit: int = 10) -> list:
        node = self._find_node(prefix)
        if not node:
            return []
        results = []
        self._dfs(node, prefix, results, limit)
        return results
    
    def _dfs(self, node, current_word, results, limit):
        if len(results) >= limit:
            return
        if node.is_end_of_word:
            results.append(current_word)
        for char, (edge, child_node) in sorted(node.children.items()):
            self._dfs(child_node, current_word + edge, results, limit)
    
    def get_memory_usage(self) -> dict:
        import sys
        def count_nodes(node):
            count = 1
            size = sys.getsizeof(node)
            for edge, child in node.children.values():
                size += sys.getsizeof(edge)
                c, s = count_nodes(child)
                count += c
                size += s
            return count, size
        node_count, total_size = count_nodes(self.root)
        return {
            'node_count': node_count,
            'estimated_size_bytes': total_size,
            'estimated_size_mb': total_size / (1024 * 1024)
        }

4. Flat Dictionary Trie (Most Memory Efficient)

class FlatTrie:
    def __init__(self):
        self.nodes = {}  # (node_id, char) -> node_id
        self.ends = set()  # node_ids that end a word
        self.next_id = 1
        self.root = 0
    
    def insert(self, word: str) -> None:
        node_id = self.root
        for char in word:
            key = (node_id, char)
            if key not in self.nodes:
                self.nodes[key] = self.next_id
                self.next_id += 1
            node_id = self.nodes[key]
        self.ends.add(node_id)
    
    def search(self, word: str) -> bool:
        node_id = self._find_node(word)
        return node_id is not None and node_id in self.ends
    
    def starts_with(self, prefix: str) -> bool:
        return self._find_node(prefix) is not None
    
    def _find_node(self, prefix):
        node_id = self.root
        for char in prefix:
            key = (node_id, char)
            if key not in self.nodes:
                return None
            node_id = self.nodes[key]
        return node_id
    
    def autocomplete(self, prefix: str, limit: int = 10) -> list:
        node_id = self._find_node(prefix)
        if node_id is None:
            return []
        results = []
        self._dfs(node_id, prefix, results, limit)
        return results
    
    def _dfs(self, node_id, current_word, results, limit):
        if len(results) >= limit:
            return
        if node_id in self.ends:
            results.append(current_word)
        for (nid, char), child_id in sorted(self.nodes.items()):
            if nid == node_id:
                self._dfs(child_id, current_word + char, results, limit)
    
    def get_memory_usage(self) -> dict:
        import sys
        size = (
            sys.getsizeof(self.nodes) +
            sys.getsizeof(self.ends) +
            sum(sys.getsizeof(k) + sys.getsizeof(v) for k, v in self.nodes.items()) +
            sum(sys.getsizeof(nid) for nid in self.ends)
        )
        return {
            'node_count': self.next_id,
            'estimated_size_bytes': size,
            'estimated_size_mb': size / (1024 * 1024)
        }

5. Usage Example and Comparison

def compare_implementations():
    words = [
        "apple", "application", "apply", "appreciate",
        "banana", "band", "bandana", "bank",
        "cat", "catch", "category", "caterpillar"
    ]
    
    implementations = [
        ("Basic Trie", Trie),
        ("Optimized Trie", TrieOptimized),
        ("Radix Trie", RadixTrie),
        ("Flat Trie", FlatTrie)
    ]
    
    for name, TrieClass in implementations:
        trie = TrieClass()
        for word in words:
            trie.insert(word)
        
        print(f"\n{name}:")
        print(f"  Search 'apple': {trie.search('apple')}")
        print(f"  Search 'app': {trie.search('app')}")
        print(f"  Starts with 'app': {trie.starts_with('app')}")
        print(f"  Autocomplete 'app': {trie.autocomplete('app', 5)}")
        
        if hasattr(trie, 'get_memory_usage'):
            mem = trie.get_memory_usage()
            print(f"  Nodes: {mem['node_count']}, Memory: {mem['estimated_size_mb']:.2f} MB")

if __name__ == "__main__":
    compare_implementations()

Memory Optimization Summary

Strategy	Memory Savings	Trade-offs
__slots__	~40–50% per node	Slightly less flexible
Radix Trie	~30–60% nodes	More complex insert logic
Flat Dictionary Trie	~50–70% total	Less intuitive, harder to extend
Remove is_end_of_word	Small savings	Need alternate word-end tracking
Array-based children	Good for fixed alphabets	Wasteful for sparse data

Recommendation

• Use TrieOptimized for most cases — balanced performance and memory.
• Use RadixTrie for large datasets with many shared prefixes.
• Use FlatTrie when memory is the top priority and simplicity is less critical.

Choose the implementation that best suits your use case's performance and memory constraints.