Word Search in Trie in DSA Go - Time & Space Complexity

Time Complexity: Word Search in Trie

O(n)

Understanding Time Complexity

We want to understand how long it takes to search for a word in a Trie data structure.

The question is: how does the search time grow as the word length increases?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

func (t *TrieNode) Search(word string) bool {
    current := t
    for _, ch := range word {
        if current.children[ch-'a'] == nil {
            return false
        }
        current = current.children[ch-'a']
    }
    return current.isEnd
}
    

This code checks if a given word exists in the Trie by following nodes for each letter.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Looping through each character of the word.
• How many times: Exactly once per character in the word (word length).

How Execution Grows With Input

As the word gets longer, the search checks one more node for each letter.

Input Size (n)	Approx. Operations
10	10 checks
100	100 checks
1000	1000 checks

Pattern observation: The operations grow linearly with the word length.

Final Time Complexity

Time Complexity: O(n)

This means the search time grows directly with the length of the word you are looking for.

Common Mistake

[X] Wrong: "Searching a word in a Trie takes time proportional to the number of words stored."

[OK] Correct: The search depends only on the length of the word, not how many words are in the Trie.

Interview Connect

Knowing this helps you explain why Tries are efficient for prefix and word searches, a common topic in coding interviews.

Self-Check

"What if the Trie stored Unicode characters instead of only lowercase letters? How would the time complexity change?"

Practice

1. What is the main purpose of using a Trie data structure in word search problems?

easy

A. To reverse words quickly

B. To sort words alphabetically

C. To store words efficiently for quick prefix-based searches

D. To count the frequency of words

Solution

1. Step 1: Understand Trie structure

   A Trie stores characters of words in a tree form, sharing prefixes.

2. Step 2: Identify Trie use in word search

   This structure allows fast prefix checks and word existence queries.

3. Final Answer:

   To store words efficiently for quick prefix-based searches -> Option C

4. Quick Check:

   Trie = prefix search efficiency [OK]

Hint: Trie is best for prefix-based word searches [OK]

Common Mistakes:

• Confusing Trie with sorting structures
• Thinking Trie counts word frequency
• Assuming Trie reverses words

2. Which of the following Go code snippets correctly initializes an empty Trie node struct with a children map and end-of-word flag?

easy

A. type TrieNode struct { children map[string]TrieNode; isEnd bool }
root := TrieNode{children: map[string]TrieNode{}, isEnd: false}

B. type TrieNode struct { children []TrieNode; isEnd int }
root := TrieNode{children: []TrieNode{}, isEnd: 0}

C. type TrieNode struct { children map[rune]TrieNode; isEnd bool }
root := &TrieNode{children: make(map[rune]TrieNode), isEnd: false}

D. type TrieNode struct { children map[rune]*TrieNode; isEnd bool }
root := &TrieNode{children: make(map[rune]*TrieNode), isEnd: false}

Solution

1. Step 1: Check struct field types

   Children should be a map from rune to pointer to TrieNode for dynamic nodes.

2. Step 2: Verify initialization syntax

   Use make(map[rune]*TrieNode) and isEnd as bool with false initial value.

3. Final Answer:

   type TrieNode struct { children map[rune]*TrieNode; isEnd bool } root := &TrieNode{children: make(map[rune]*TrieNode), isEnd: false} -> Option D

4. Quick Check:

   Correct map and pointer usage = type TrieNode struct { children map[rune]*TrieNode; isEnd bool } root := &TrieNode{children: make(map[rune]*TrieNode), isEnd: false} [OK]

Hint: Use map[rune]*TrieNode and make() to initialize children [OK]

Common Mistakes:

• Using slice instead of map for children
• Using non-pointer TrieNode in map values
• Incorrect map key type (string instead of rune)

3. Given the following Go code snippet for searching a word in a Trie, what will be the output if the word "cat" is searched after inserting "car" and "cat"?

func (t *TrieNode) Search(word string) bool {
    node := t
    for _, ch := range word {
        if _, ok := node.children[ch]; !ok {
            return false
        }
        node = node.children[ch]
    }
    return node.isEnd
}

medium

A. true

B. false

C. Compilation error

D. Runtime panic

Solution

1. Step 1: Understand insertion of "car" and "cat"

   Both words share prefix 'ca', nodes created for 'c', 'a', then separate nodes for 'r' and 't' with isEnd true.

2. Step 2: Trace search for "cat"

   Traverse nodes for 'c', 'a', 't' successfully, last node has isEnd true, so returns true.

3. Final Answer:

   true -> Option A

4. Quick Check:

   Word inserted and found = true [OK]

Hint: Search returns true if last node's isEnd is true [OK]

Common Mistakes:

• Assuming search returns true for prefixes only
• Confusing isEnd flag usage
• Thinking search returns true if partial path exists

4. Identify the bug in the following Go code snippet for searching a word in a Trie:

func (t *TrieNode) Search(word string) bool {
    node := t
    for _, ch := range word {
        if node.children[ch] == nil {
            return false
        }
        node = node.children[ch]
    }
    return true
}

medium

A. Returns true even if the word is only a prefix, not a full word

B. Panics if children map is nil

C. Does not check for nil children map before access

D. Incorrect loop variable type causes compilation error

Solution

1. Step 1: Analyze search return condition

   Function returns true after traversing all characters without checking isEnd flag.

2. Step 2: Understand consequence of missing isEnd check

   Words that are prefixes but not complete words will incorrectly return true.

3. Final Answer:

   Returns true even if the word is only a prefix, not a full word -> Option A

4. Quick Check:

   Missing isEnd check causes false positives [OK]

Hint: Always check isEnd after traversal to confirm full word [OK]

Common Mistakes:

• Forgetting to check isEnd flag
• Assuming traversal success means word exists
• Ignoring nil map checks (not in this code)

5. You have a list of words: ["apple", "app", "application", "bat", "bath", "baton"]. You want to build a Trie and then search for the word "bat". Which of the following statements is true about the search result and the Trie structure after insertion?

hard

A. Searching "bat" returns false because "bat" is a prefix of "bath" and "baton"

B. Searching "bat" returns true; nodes for 'b', 'a', 't' share prefixes with other words

C. Trie stores each word as a separate branch without shared nodes

D. Searching "bat" returns true only if "bat" is inserted last

Solution

1. Step 1: Insert all words into Trie

   Words share prefixes: "app" and "apple" share 'app', "bat", "bath", "baton" share 'bat'.

2. Step 2: Search for "bat"

   Since "bat" is inserted, its node's isEnd is true, so search returns true.

3. Final Answer:

   Searching "bat" returns true; nodes for 'b', 'a', 't' share prefixes with other words -> Option B

4. Quick Check:

   Shared prefix nodes and isEnd true = Searching "bat" returns true; nodes for 'b', 'a', 't' share prefixes with other words [OK]

Hint: Shared prefixes save space; isEnd marks full words [OK]

Common Mistakes:

• Thinking prefix words are not found
• Assuming separate branches for each word
• Believing insertion order affects search result