BST Search Operation in DSA Go - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is a Binary Search Tree (BST)?

A Binary Search Tree is a tree data structure where each node has at most two children. The left child contains values less than the node, and the right child contains values greater than the node.

beginner

How does the search operation work in a BST?

Start at the root. If the value equals the node's value, return it. If the value is less, search the left subtree. If greater, search the right subtree. Repeat until found or reach a null node.

intermediate

What is the time complexity of searching in a BST?

The average time complexity is O(log n) when the tree is balanced. In the worst case (skewed tree), it can be O(n).

intermediate

Show the Go code snippet for searching a value in a BST.

func searchBST(root *TreeNode, val int) *TreeNode { if root == nil || root.Val == val { return root } if val < root.Val { return searchBST(root.Left, val) } return searchBST(root.Right, val) }

beginner

What happens if the searched value is not in the BST?

The search will continue down the tree until it reaches a null node, then it returns nil indicating the value is not found.

In a BST, where do you search if the target value is less than the current node's value?

A Root node only

B Right subtree

C Both subtrees

D Left subtree

In a BST, values less than the current node are in the left subtree.

What is the best case time complexity for searching in a balanced BST?

A O(log n)

B O(n)

C O(1)

D O(n log n)

Balanced BST search takes O(log n) time because it halves the search space each step.

What does the search function return if the value is not found in the BST?

A Nil (null)

B The last visited node

C The root node

D An error

If the value is not found, the search reaches a null node and returns nil.

Which of these is true about BST search?

A Search visits nodes randomly

B Search always visits every node

C Search only visits nodes along one path from root

D Search visits nodes in level order

Search in BST follows one path from root to leaf based on comparisons.

If the BST is skewed (like a linked list), what is the search time complexity?

A O(log n)

B O(n)

C O(1)

D O(n log n)

In a skewed BST, search time degrades to O(n) because it behaves like a linked list.

Explain how the search operation works in a Binary Search Tree step-by-step.

Think about how you decide which way to go at each node.

Describe the impact of tree shape on the efficiency of BST search.

Consider how many nodes you visit in best vs worst cases.

Practice

1. What does the search operation in a Binary Search Tree (BST) do?

easy

A. Finds whether a given value exists in the BST

B. Deletes a node from the BST

C. Inserts a new node into the BST

D. Traverses all nodes in the BST

Solution

1. Step 1: Understand the purpose of BST search

   The search operation is designed to check if a specific value is present in the BST.

2. Step 2: Differentiate from other operations

   Insertion adds nodes, deletion removes nodes, and traversal visits nodes. Search only checks for existence.

3. Final Answer:

   Finds whether a given value exists in the BST -> Option A

4. Quick Check:

   Search = Find value [OK]

Hint: Search checks presence, not insertion or deletion [OK]

Common Mistakes:

• Confusing search with insert or delete
• Thinking search returns the node always
• Assuming search traverses all nodes

2. Which of the following is the correct Go function signature for a BST search method that returns a boolean indicating if a value exists?

easy

A. func Search(val int) *Node

B. func (root *Node) Search(val int) bool

C. func (root Node) Search(val string) bool

D. func Search(root Node, val int) int

Solution

1. Step 1: Identify method receiver and return type

   BST search is usually a method on a pointer to Node and returns bool for found or not.

2. Step 2: Check parameter types and return type

   func (root *Node) Search(val int) bool uses pointer receiver, int parameter, and bool return which matches the expected signature.

3. Final Answer:

   func (root *Node) Search(val int) bool -> Option B

4. Quick Check:

   Pointer receiver + bool return = func (root *Node) Search(val int) bool [OK]

Hint: Search returns bool, uses pointer receiver for tree nodes [OK]

Common Mistakes:

• Using value receiver instead of pointer
• Wrong parameter or return types
• Confusing method vs function signatures

3. Given the BST below and the Go code snippet, what will be the output? BST structure: ``` 10 / \ 5 15 / 3 ``` Go code:

found := root.Search(3)
fmt.Println(found)

medium

A. true

B. false

C. nil

D. runtime error

Solution

1. Step 1: Trace the search for value 3 in the BST

   Starting at root 10, 3 < 10, go left to 5; 3 < 5, go left to 3; found node with value 3.

2. Step 2: Understand the returned value and print output

   Search returns true because 3 exists; printing true outputs 'true'.

3. Final Answer:

   true -> Option A

4. Quick Check:

   3 found in BST = true [OK]

Hint: Follow BST left/right rules to find value [OK]

Common Mistakes:

• Assuming search returns node instead of bool
• Confusing true/false output
• Ignoring BST structure when tracing

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

func (root *Node) Search(val int) bool {
    if root == nil {
        return false
    }
    if root.Value == val {
        return true
    }
    if val < root.Value {
        return root.Search(val)
    } else {
        return root.Search(val)
    }
}

medium

A. Base case for nil root is missing

B. Uses value receiver instead of pointer

C. Returns int instead of bool

D. Recursive calls do not move to left or right child nodes

Solution

1. Step 1: Analyze recursive calls in search method

   Both recursive calls use root.Search(val) without moving to root.Left or root.Right, causing infinite recursion.

2. Step 2: Identify correct recursive calls

   Should call root.Left.Search(val) if val < root.Value, else root.Right.Search(val) to move down the tree.

3. Final Answer:

   Recursive calls do not move to left or right child nodes -> Option D

4. Quick Check:

   Recursive calls must move down tree [OK]

Hint: Recursive calls must go to left or right child [OK]

Common Mistakes:

• Calling search on same node causing infinite loop
• Missing base case for nil
• Wrong return types

5. You want to search for a value in a BST but also count how many nodes you visited during the search. Which modification to the search function is best?

hard

A. Use a global variable to count nodes visited during search

B. Return the node instead of bool and count nodes outside the function

C. Add a counter parameter passed by pointer and increment it on each node visited

D. Modify the BST to store counts in each node

Solution

1. Step 1: Understand the need to count nodes during search

   Counting nodes visited requires tracking each node checked during recursion.

2. Step 2: Choose method to count nodes visited

   Passing a pointer to a counter variable and incrementing it at each node visit allows accurate counting without side effects.

3. Final Answer:

   Add a counter parameter passed by pointer and increment it on each node visited -> Option C

4. Quick Check:

   Pass counter pointer to track visits [OK]

Hint: Pass counter pointer to track nodes visited [OK]

Common Mistakes:

• Using global variables causing side effects
• Counting outside search missing recursive visits
• Changing BST structure unnecessarily