Trie Insert Operation in DSA Go - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a Trie data structure?

A Trie is a tree-like data structure used to store a dynamic set of strings where keys are usually strings. Each node represents a character, and paths down the tree represent words.

beginner

What does the insert operation do in a Trie?

The insert operation adds a word to the Trie by creating nodes for each character if they don't exist and marking the end of the word.

beginner

In Trie insertion, what does marking the end of a word mean?

It means setting a flag (usually a boolean) in the last node of the inserted word to indicate that this path represents a complete word.

intermediate

Why do we create new nodes only if the character path does not exist during insertion?

Because existing nodes represent prefixes of other words already stored, so we reuse them to save space and avoid duplication.

intermediate

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

The time complexity is O(n), where n is the length of the word, because we process each character once.

What does each node in a Trie typically represent?

A A character

B A whole word

C An integer value

D A number of children

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

During insertion, if a character node already exists, what should the algorithm do?

A Delete the existing node

B Create a new node anyway

C Reuse the existing node

D Stop insertion

The algorithm reuses existing nodes to represent shared prefixes.

What flag is set to mark the end of a word in a Trie node?

A isWordEnd

B isLeaf

C isRoot

D isVisited

The isWordEnd flag marks that the path to this node forms a complete word.

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

A O(1)

B O(log n)

C O(n^2)

D O(n)

Insertion requires processing each character once, so O(n).

If you insert the words 'cat' and 'car' into a Trie, how many nodes will be shared?

A 0

B 2

C 1

D 3

The nodes for 'c' and 'a' are shared, so 2 nodes.

Explain step-by-step how to insert the word 'dog' into an empty Trie.

Think about creating nodes for each character and marking the last node.

Describe why Tries are efficient for prefix-based searches and how insertion supports this.

Focus on how shared prefixes reduce space and speed up searches.

Practice

1. What is the main purpose of the Insert operation in a Trie data structure?

easy

A. To delete a word from the Trie

B. To add a new word by creating nodes for each character

C. To search for a word in the Trie

D. To count the total words stored in the Trie

Solution

1. Step 1: Understand the Insert operation

   The Insert operation adds a word by creating nodes for each character if they don't exist.

2. Step 2: Differentiate from other operations

   Deleting removes words, searching finds words, counting totals words. Insert specifically adds words.

3. Final Answer:

   To add a new word by creating nodes for each character -> Option B

4. Quick Check:

   Insert = Add word nodes [OK]

Hint: Insert means adding nodes for each character [OK]

Common Mistakes:

• Confusing insert with search or delete
• Thinking insert counts words
• Assuming insert modifies existing words

2. Which of the following is the correct way to declare a Trie node struct in Go for insertion?

easy

A. type TrieNode struct { children map[rune]*TrieNode; isEnd bool }

B. type TrieNode struct { children []int; isEnd int }

C. type TrieNode struct { children map[string]int; isEnd string }

D. type TrieNode struct { children []string; isEnd bool }

Solution

1. Step 1: Identify correct children type for TrieNode

   Children should map characters (rune) to TrieNode pointers for branching.

2. Step 2: Check isEnd type

   isEnd is a boolean indicating if node ends a word.

3. Final Answer:

   type TrieNode struct { children map[rune]*TrieNode; isEnd bool } -> Option A

4. Quick Check:

   Children map[rune]*TrieNode and isEnd bool [OK]

Hint: Children map with rune keys and bool isEnd [OK]

Common Mistakes:

• Using slice instead of map for children
• Wrong data types for children or isEnd
• Using string keys instead of rune

3. What will be the output after inserting the words "cat" and "car" into an empty Trie and then checking if the node for 'a' under 'c' has children?

medium

A. nil

B. false

C. true

D. runtime error

Solution

1. Step 1: Insert "cat" and "car" into Trie

   Both words share prefix 'c' -> 'a'. After insertion, node 'a' has children 't' and 'r'.

2. Step 2: Check if node 'a' under 'c' has children

   Since 'a' node has two children nodes ('t' and 'r'), it has children, so true.

3. Final Answer:

   true -> Option C

4. Quick Check:

   Shared prefix node has children = true [OK]

Hint: Shared prefix nodes have children after insert [OK]

Common Mistakes:

• Assuming node 'a' has no children
• Confusing node existence with children presence
• Expecting nil or error instead of true

4. Given this Go code snippet for inserting a word into a Trie, what is the bug?

func (t *TrieNode) Insert(word string) {
    node := t
    for _, ch := range word {
        if node.children[ch] == nil {
            node.children[ch] = &TrieNode{}
        }
        node = node.children[ch]
    }
    node.isEnd = true
}

medium

A. children map is not initialized before use

B. Loop variable ch should be int, not rune

C. isEnd should be set before loop

D. Function should return a value

Solution

1. Step 1: Check initialization of children map

   The children map must be initialized (e.g., make(map[rune]*TrieNode)) before inserting nodes.

2. Step 2: Identify impact of missing initialization

   Without initialization, accessing children[ch] causes runtime panic (nil map assignment).

3. Final Answer:

   children map is not initialized before use -> Option A

4. Quick Check:

   Uninitialized map causes runtime error [OK]

Hint: Always initialize map before inserting keys [OK]

Common Mistakes:

• Ignoring map initialization
• Misunderstanding rune vs int for keys
• Thinking isEnd needs early assignment

5. You want to insert the words ["go", "gone", "guild"] into a Trie. After insertion, how many children does the root node have, and why?

hard

A. 0, because root has no children

B. 3, because there are three words

C. 2, because 'go' and 'guild' share 'g' but 'gone' differs

D. 1, because all words start with 'g'

Solution

1. Step 1: Analyze first characters of all words

   All words start with the letter 'g', so root node will have one child for 'g'.

2. Step 2: Understand Trie root children count

   Root children count equals distinct first letters of inserted words, here only 'g'.

3. Final Answer:

   1, because all words start with 'g' -> Option D

4. Quick Check:

   Root children = distinct first letters = 1 [OK]

Hint: Root children = unique first letters of words [OK]

Common Mistakes:

• Counting words instead of unique first letters
• Assuming root has no children
• Confusing shared prefixes with root children count