Autocomplete System with Trie in DSA Python - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a Trie data structure?

A Trie is a tree-like data structure that stores a dynamic set of strings, where each node represents a character. It is used to efficiently search for words with common prefixes.

beginner

How does a Trie help in implementing an autocomplete system?

A Trie allows quick lookup of all words that start with a given prefix by traversing nodes corresponding to the prefix characters, then collecting all descendant words.

intermediate

What is the time complexity to insert a word of length n into a Trie?

The time complexity is O(n), where n is the length of the word, because each character is processed once while traversing or creating nodes.

intermediate

Describe the process to find all autocomplete suggestions for a prefix in a Trie.

First, traverse the Trie nodes matching the prefix characters. Then, perform a depth-first search from that node to collect all complete words that start with the prefix.

intermediate

Why is a Trie more efficient than a list for autocomplete lookups?

A Trie shares common prefixes among words, reducing repeated comparisons. This allows prefix searches in O(m) time (m = prefix length), faster than scanning a list of words.

What does each node in a Trie represent?

A A number

B A complete word

C A character of a word

D A sentence

Each node in a Trie represents a single character of a word.

What is the first step to find autocomplete suggestions for a prefix?

A Sort all words alphabetically

B Traverse Trie nodes matching the prefix

C Delete all words not matching prefix

D Reverse the prefix string

You first traverse the Trie nodes that match the prefix characters.

What is the time complexity to search for a prefix of length m in a Trie?

A O(m * n)

B O(n)

C O(log n)

D O(m)

Searching a prefix of length m in a Trie takes O(m) time.

Which of these is NOT a benefit of using a Trie for autocomplete?

A Memory efficient for large datasets

B Fast prefix search

C Stores words sharing prefixes efficiently

D Allows quick insertion of new words

Tries can use more memory than other structures, so memory efficiency is not always a benefit.

After reaching the prefix node in a Trie, what is done next to get suggestions?

A Perform depth-first search to collect words

B Delete all child nodes

C Insert new words

D Reverse the prefix

A depth-first search collects all words starting from the prefix node.

Explain how a Trie supports autocomplete functionality step-by-step.

Think about how you find words starting with a prefix in a tree.

Describe the advantages and disadvantages of using a Trie for autocomplete.

Consider speed and memory trade-offs.

Practice

1. What is the main purpose of using a Trie in an autocomplete system?

easy

A. To sort words alphabetically

B. To efficiently store and search prefixes of words

C. To count the total number of words

D. To encrypt the stored words

Solution

1. Step 1: Understand the role of Trie in prefix search

   A Trie is a tree-like data structure designed to store strings by their prefixes, allowing quick prefix-based searches.

2. Step 2: Connect Trie usage to autocomplete

   Autocomplete requires finding all words starting with a given prefix efficiently, which Trie supports by traversing nodes matching the prefix.

3. Final Answer:

   To efficiently store and search prefixes of words -> Option B

4. Quick Check:

   Trie = prefix search [OK]

Hint: Trie stores prefixes for fast autocomplete search [OK]

Common Mistakes:

• Thinking Trie sorts words alphabetically
• Confusing Trie with hash tables
• Assuming Trie encrypts data

2. Which of the following is the correct way to insert a word "cat" into a Trie node in Python?

easy

A. node['c'] = TrieNode()

B. node.insert('c')

C. node.add('c')

D. node.children['c'] = TrieNode()

Solution

1. Step 1: Understand Trie node structure

   Trie nodes typically have a dictionary called children to map characters to child nodes.

2. Step 2: Insert character as a key in children dictionary

   To insert 'c', assign a new TrieNode to node.children['c'].

3. Final Answer:

   node.children['c'] = TrieNode() -> Option D

4. Quick Check:

   Insert char in children dict = node.children['c'] = TrieNode() [OK]

Hint: Use children dictionary to add new character nodes [OK]

Common Mistakes:

• Trying to assign directly to node['c'] without children
• Using non-existent methods like add or insert
• Confusing list with dictionary for children

3. Given the following code snippet, what will be the output?

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

class Trie:
    def __init__(self):
        self.root = TrieNode()

    def insert(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

    def search_prefix(self, prefix):
        node = self.root
        for char in prefix:
            if char not in node.children:
                return False
            node = node.children[char]
        return True

trie = Trie()
trie.insert('dog')
trie.insert('deer')
print(trie.search_prefix('de'))
print(trie.search_prefix('do'))
print(trie.search_prefix('da'))

medium

A. True\nFalse\nFalse

B. False\nTrue\nFalse

C. True\nTrue\nFalse

D. False\nFalse\nFalse

Solution

1. Step 1: Insert words 'dog' and 'deer' into Trie

   Both words add nodes for their characters. 'dog' adds d->o->g, 'deer' adds d->e->e->r.

2. Step 2: Check prefixes 'de', 'do', and 'da'

   'de' exists as prefix in 'deer', so returns True. 'do' exists as prefix in 'dog', so True. 'da' does not exist, so False.

3. Final Answer:

   True True False -> Option C

4. Quick Check:

   Prefix 'de' and 'do' found, 'da' not found = True, True, False [OK]

Hint: Check prefix path existence in Trie children [OK]

Common Mistakes:

• Confusing search_prefix with full word search
• Assuming 'da' prefix exists
• Ignoring is_end flag for prefix search

4. The following code is intended to insert words into a Trie, but it raises an error. What is the error?

class TrieNode:
    def __init__(self):
        self.children = []
        self.is_end = False

class Trie:
    def __init__(self):
        self.root = TrieNode()

    def insert(self, word):
        node = self.root
        for char in word:
            if char not in node.children:
                node.children[char] = TrieNode()
            node = node.children[char]

medium

A. TypeError: list indices must be integers or slices, not str

B. AttributeError: 'TrieNode' object has no attribute 'children'

C. SyntaxError: invalid syntax

D. No error, code runs fine

Solution

1. Step 1: Identify data structure used for children

   The code uses a list for children, but tries to access it with string keys.

2. Step 2: Understand list indexing rules

   Lists require integer indices, but code uses node.children[char] where char is a string, causing TypeError.

3. Final Answer:

   TypeError: list indices must be integers or slices, not str -> Option A

4. Quick Check:

   Using list with string keys causes TypeError [OK]

Hint: Use dictionary, not list, for children to index by characters [OK]

Common Mistakes:

• Using list instead of dict for children
• Ignoring error message details
• Assuming code runs without error

5. You want to implement an autocomplete system that returns all words starting with a given prefix using a Trie. Which approach correctly collects all matching words after reaching the prefix node?

hard

A. Perform a depth-first search (DFS) from the prefix node, collecting words where is_end is True

B. Return all children keys of the prefix node without further traversal

C. Only return the prefix itself without searching deeper

D. Use breadth-first search (BFS) but ignore is_end flags

Solution

1. Step 1: Reach the node matching the prefix

   Traverse the Trie to the node representing the last character of the prefix.

2. Step 2: Collect all words starting from prefix node using DFS

   Use DFS to explore all child nodes recursively, collecting words where is_end is True to get complete words.

3. Final Answer:

   Perform a depth-first search (DFS) from the prefix node, collecting words where is_end is True -> Option A

4. Quick Check:

   DFS from prefix node with is_end check = correct autocomplete [OK]

Hint: Use DFS from prefix node, collect words at is_end True [OK]

Common Mistakes:

• Returning only immediate children keys
• Ignoring is_end flags and returning incomplete words
• Using BFS without checking word ends