BST Search Operation in DSA Java - 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. For every node, all values in the left subtree are smaller, and all values in the right subtree are larger than the node's value.

beginner

How does the search operation work in a BST?

Start at the root. If the value equals the node's value, return true. If smaller, search the left subtree. If larger, search the right subtree. Repeat until found or reach a null (not found).

intermediate

What is the time complexity of searching in a BST?

The average time complexity is O(log n) because each step halves the search space. In the worst case (unbalanced tree), it can be O(n).

beginner

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

The search will continue down the tree until it reaches a null child, meaning the value is not present, and the operation returns false.

beginner

Show the Java method signature for searching a value in a BST node.

public boolean searchBST(TreeNode root, int val)

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

A Left subtree

B Right subtree

C Current node

D Root node

If the value is smaller, the search continues in the left subtree.

What is the best case time complexity of searching in a balanced BST with n nodes?

A O(1)

B O(log n)

C O(n)

D O(n log n)

Best case occurs when the target is the root node, taking O(1) time.

If the search reaches a null node, what does it mean?

A Search should restart

B Value found

C Tree is empty

D Value not found

Null means the value is not present in the BST.

Which property must hold true for every node in a BST?

A Left child > node, right child < node

B Children have no order

C Left child < node, right child > node

D Left child = right child

Left subtree nodes are smaller, right subtree nodes are larger.

What is the first step in searching a value in a BST?

A Check the leftmost node

B Check the root node

C Check the rightmost node

D Check all nodes simultaneously

Search always starts at the root node.

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

Think about how you look for a word in a dictionary.

Describe the time complexity of searching in a BST and why it varies.

Consider how balanced the tree is.

Practice

1. What is the main purpose of the search operation in a Binary Search Tree (BST)?

easy

A. To insert a new value into the BST

B. To find whether a given value exists in the BST

C. To delete a value from the BST

D. To traverse all nodes in the BST

Solution

1. Step 1: Understand the search operation

   The search operation checks if a specific value is present in the BST by comparing it with nodes.

2. Step 2: Differentiate from other operations

   Insertion adds new nodes, deletion removes nodes, and traversal visits all nodes. Search only checks presence.

3. Final Answer:

   To find whether a given value exists in the BST -> Option B

4. Quick Check:

   Search = Find value presence [OK]

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

Common Mistakes:

• Confusing search with insert or delete
• Thinking search returns all nodes
• Assuming search modifies the tree

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

easy

A. public boolean search(int value)

B. public void search(int value)

C. public int search(int value)

D. public String search(int value)

Solution

1. Step 1: Identify return type for search

   Search should return true or false, so return type must be boolean.

2. Step 2: Check method signature correctness

   Method takes an int value to search and returns boolean. public boolean search(int value) matches this.

3. Final Answer:

   public boolean search(int value) -> Option A

4. Quick Check:

   Return type boolean for search [OK]

Hint: Search returns true/false, so use boolean return type [OK]

Common Mistakes:

• Using void return type for search
• Returning int or String instead of boolean
• Incorrect method parameter types

3. Consider the following BST and the search code snippet:

class Node {
  int data;
  Node left, right;
  Node(int d) { data = d; left = right = null; }
}

public boolean search(Node root, int key) {
  if (root == null) return false;
  if (root.data == key) return true;
  if (key < root.data) return search(root.left, key);
  else return search(root.right, key);
}

// BST structure:
//       10
//      /  \
//     5    15
//    / \     \
//   3   7     20

What is the output of search(root, 7)?

medium

A. null

B. false

C. true

D. Runtime error

Solution

1. Step 1: Trace search for key 7 starting at root 10

   7 < 10, so search left subtree (node 5).

2. Step 2: Trace search at node 5

   7 > 5, so search right subtree (node 7).

3. Step 3: Trace search at node 7

   Node data equals key (7), so return true.

4. Final Answer:

   true -> Option C

5. Quick Check:

   7 found in BST = true [OK]

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

Common Mistakes:

• Stopping search too early
• Confusing left and right subtree directions
• Assuming search returns node instead of boolean

4. The following Java method is intended to search a BST for a key. What is the bug?

public boolean search(Node root, int key) {
  if (root == null) return false;
  if (root.data == key) return true;
  if (key > root.data) return search(root.left, key);
  else return search(root.right, key);
}

medium

A. The recursive calls for left and right subtrees are swapped

B. The base case is missing

C. The method should return int instead of boolean

D. The method does not handle null keys

Solution

1. Step 1: Analyze recursive calls for BST search

   For BST, if key < root.data, search left; if key > root.data, search right.

2. Step 2: Identify swapped calls

   Code calls search(root.left, key) when key > root.data, which is incorrect; left and right calls are swapped.

3. Final Answer:

   The recursive calls for left and right subtrees are swapped -> Option A

4. Quick Check:

   Left/right calls must match key comparison [OK]

Hint: Left subtree for smaller keys, right for larger keys [OK]

Common Mistakes:

• Swapping left and right recursive calls
• Missing base case for null root
• Returning wrong data type

5. Given a BST with nodes inserted in this order: 15, 10, 20, 8, 12, 17, 25. Which sequence of nodes will the search operation visit when searching for 12?

hard

A. 10 -> 15 -> 12

B. 15 -> 20 -> 17 -> 12

C. 15 -> 10 -> 8 -> 12

D. 15 -> 10 -> 12

Solution

1. Step 1: Build BST structure from insertion order

   Insert 15 as root; 10 left of 15; 20 right of 15; 8 left of 10; 12 right of 10; 17 left of 20; 25 right of 20.

2. Step 2: Trace search path for key 12

   Start at 15: 12 < 15, go left to 10; 12 > 10, go right to 12; found key.

3. Final Answer:

   15 -> 10 -> 12 -> Option D

4. Quick Check:

   Search path follows BST rules [OK]

Hint: Follow left if smaller, right if larger until found [OK]

Common Mistakes:

• Visiting nodes not on search path
• Confusing insertion order with search path
• Assuming search visits all nodes