Trie Search Operation in DSA Go - Time & Space Complexity

Time Complexity: Trie Search Operation

O(n)

Understanding Time Complexity

We want to know how long it takes to find a word in a trie.

How does the search time change when the word gets longer?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

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

This code checks if a word exists in the trie by following each character step-by-step.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

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

How Execution Grows With Input

Each extra character means one more step to check in the trie.

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

Pattern observation: The number of steps grows directly with the word length.

Final Time Complexity

Time Complexity: O(n)

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

Common Mistake

[X] Wrong: "Searching a trie depends on the total number of words stored."

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

Interview Connect

Knowing trie search time helps you explain efficient word lookups and autocomplete features clearly.

Self-Check

"What if we changed the trie to store only lowercase letters instead of all characters? How would the time complexity change?"

Practice

1. What does the search operation in a Trie data structure check for?

easy

A. The number of words stored in the Trie

B. If the Trie is empty

C. If a given word exists in the Trie

D. The length of the longest word in the Trie

Solution

1. Step 1: Understand the purpose of Trie search

   The search operation in a Trie is designed to check if a specific word is stored in the Trie.

2. Step 2: Differentiate from other Trie operations

   Other operations like counting words or checking emptiness are not the purpose of search.

3. Final Answer:

   If a given word exists in the Trie -> Option C

4. Quick Check:

   Trie search checks word existence [OK]

Hint: Search checks if the exact word is stored [OK]

Common Mistakes:

• Confusing search with counting words
• Thinking search checks Trie emptiness
• Assuming search returns word length

2. Which of the following is the correct way to check if a character node exists in a Trie map in Go?

easy

A. if node.children[char] != nil

B. if node.children[char] == nil

C. if node.children.contains(char)

D. if node.children.has(char)

Solution

1. Step 1: Recall Go map access syntax

   In Go, to check if a key exists in a map, you check if the value is not nil (for pointer or map values).

2. Step 2: Apply to Trie children map

   Trie children are stored in a map from rune to *TrieNode, so checking if node.children[char] != nil confirms existence.

3. Final Answer:

   if node.children[char] != nil -> Option A

4. Quick Check:

   Go map key exists check [OK]

Hint: Check map key by comparing to nil in Go [OK]

Common Mistakes:

• Using contains or has methods (not in Go maps)
• Checking for equality to nil incorrectly
• Confusing map key existence with value presence

3. Consider the following Go code snippet for searching a word in a Trie:

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

What will be the output of Search("cat") if the Trie contains the words "car", "cat", and "cap"?

medium

A. compilation error

B. true

C. runtime error

D. false

Solution

1. Step 1: Trace the search for "cat" in the Trie

   The loop checks each character 'c', 'a', 't' in order. Since "cat" is inserted, all nodes exist and node.isEnd is true at 't'.

2. Step 2: Return value after traversal

   Because node.isEnd is true at the last character, the function returns true.

3. Final Answer:

   true -> Option B

4. Quick Check:

   Word "cat" exists in Trie = true [OK]

Hint: Search returns true if last node marks word end [OK]

Common Mistakes:

• Ignoring isEnd flag and returning true always
• Assuming false if any child exists
• Confusing runtime errors with nil checks

4. The following Go code for Trie search has a bug. What is the error?

func (t *Trie) Search(word string) bool {
    node := t.root
    for i := 0; i <= len(word); i++ {
        ch := rune(word[i])
        if node.children[ch] == nil {
            return false
        }
        node = node.children[ch]
    }
    return node.isEnd
}

medium

A. Missing check for empty Trie root

B. Incorrect rune conversion for characters

C. Returning wrong boolean value

D. Index out of range error due to loop condition

Solution

1. Step 1: Analyze the loop condition

   The loop runs from i = 0 to i <= len(word), which means it tries to access word[len(word)] causing index out of range error.

2. Step 2: Correct loop boundary

   The loop should run with i < len(word) to avoid accessing beyond the string length.

3. Final Answer:

   Index out of range error due to loop condition -> Option D

4. Quick Check:

   Loop boundary error causes runtime panic [OK]

Hint: Use i < len(word), not i <= len(word) in loops [OK]

Common Mistakes:

• Using <= instead of < in loop
• Ignoring string length limits
• Assuming rune conversion causes error

5. You want to modify the Trie search function to support prefix search (check if any word starts with the given prefix). Which change is correct?

hard

A. Return true immediately after traversing all prefix characters without checking isEnd

B. Return true only if isEnd is true at last prefix character

C. Return false if any character node is missing, else return false always

D. Return true only if prefix length equals word length stored

Solution

1. Step 1: Understand prefix search goal

   Prefix search should return true if the prefix exists as a path in the Trie, regardless of isEnd flag.

2. Step 2: Modify search to return true after prefix traversal

   After checking all prefix characters exist, return true immediately without checking isEnd.

3. Final Answer:

   Return true immediately after traversing all prefix characters without checking isEnd -> Option A

4. Quick Check:

   Prefix search ignores isEnd, returns true if path exists [OK]

Hint: For prefix, return true after full prefix traversal [OK]

Common Mistakes:

• Checking isEnd for prefix search
• Returning false even if prefix path exists
• Confusing prefix length with word length