BST Search Operation in DSA C++ - Build from Scratch

BST Search Operation

📖 Scenario: You are working with a phone book application that stores contacts in a Binary Search Tree (BST). Each contact has a unique phone number. You want to find if a particular phone number exists in the phone book.

🎯 Goal: Build a simple BST and write code to search for a given phone number in it.

📋 What You'll Learn

Create a BST node structure with integer phone numbers

Manually create a BST with given phone numbers

Write a function to search for a phone number in the BST

Print whether the phone number is found or not

💡 Why This Matters

🌍 Real World

BSTs are used in phone books, contact lists, and databases to quickly find information by key.

💼 Career

Understanding BST search is fundamental for software engineers working with data storage, retrieval, and optimization.

1

Create BST Node Structure and Root Node

Create a struct called Node with an int data, and two pointers left and right of type Node*. Then create a Node* variable called root and initialize it with a new node containing the value 50.

DSA C++

// Define struct Node and create root node with value 50
// Your code here

Hint

Think of a tree node as a box holding a number and two pointers to other boxes.

2

Add Left and Right Child Nodes to Root

Add two child nodes to root: set root->left to a new node with value 30 and root->right to a new node with value 70. Both children should have their left and right pointers set to nullptr.

DSA C++

struct Node {
    int data;
    Node* left;
    Node* right;
};

Node* root = new Node{50, nullptr, nullptr};
// Add left child with value 30 and right child with value 70 to root
// Your code here

Hint

Attach smaller number to the left and bigger number to the right of root.

3

Write a Function to Search for a Value in BST

Write a function called searchBST that takes a Node* called root and an int key. It should return true if key is found in the BST, otherwise false. Use the BST property to decide whether to search left or right.

DSA C++

struct Node {
    int data;
    Node* left;
    Node* right;
};

Node* root = new Node{50, nullptr, nullptr};
root->left = new Node{30, nullptr, nullptr};
root->right = new Node{70, nullptr, nullptr};

// Write searchBST function below
// Your code here

Hint

Check if current node is null or matches key. If not, go left if key is smaller, else right.

4

Search for a Phone Number and Print Result

Call searchBST with root and the key 70. Print "Found" if the function returns true, otherwise print "Not Found".

DSA C++

struct Node {
    int data;
    Node* left;
    Node* right;
};

Node* root = new Node{50, nullptr, nullptr};
root->left = new Node{30, nullptr, nullptr};
root->right = new Node{70, nullptr, nullptr};

bool searchBST(Node* root, int key) {
    if (root == nullptr) {
        return false;
    }
    if (root->data == key) {
        return true;
    } else if (key data) {
        return searchBST(root->left, key);
    } else {
        return searchBST(root->right, key);
    }
}

// Call searchBST with key 70 and print "Found" or "Not Found"
// Your code here

Hint

Use an if statement to print "Found" if searchBST returns true, else "Not Found".

Practice

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

easy

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

B. To insert a new node in the BST

C. To delete a node from the BST

D. To traverse all nodes in the BST

Solution

1. Step 1: Understand the purpose of search in BST

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

2. Step 2: Differentiate from other operations

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

3. Final Answer:

   To find 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 insertion
• Thinking search modifies the tree
• Mixing search with traversal

2. Which of the following is the correct syntax to start a recursive search function in C++ for a BST node pointer root and integer key?

easy

A. void search(Node root, int key) { ... }

B. bool search(Node* root, int key) { ... }

C. int search(Node* root, int key) { ... }

D. Node search(Node* root, int key) { ... }

Solution

1. Step 1: Identify return type for search

   Search returns true/false if key found, so return type should be bool.

2. Step 2: Check parameter types

   Root is a pointer to Node, key is int. So signature is bool search(Node* root, int key).

3. Final Answer:

   bool search(Node* root, int key) { ... } -> Option B

4. Quick Check:

   Return bool and pointer param [OK]

Hint: Search returns bool, takes Node pointer and key [OK]

Common Mistakes:

• Using void return type for search
• Passing Node by value instead of pointer
• Returning Node instead of bool

3. Consider the following BST and the search function call search(root, 15). What will be the output?

struct Node {
  int data;
  Node* left;
  Node* right;
};

bool search(Node* root, int key) {
  if (!root) 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    20
//         /  \
//        15  30

// Call:
// bool found = search(root, 15);
// std::cout << (found ? "Found" : "Not Found");

medium

A. Found

B. Not Found

C. Compilation Error

D. Runtime Error

Solution

1. Step 1: Trace search path for key 15

   Start at root 10, 15 > 10, go right to 20. Then 15 < 20, go left to 15.

2. Step 2: Check node data at 15

   Node data matches key 15, so function returns true and prints "Found".

3. Final Answer:

   Found -> Option A

4. Quick Check:

   Key found in BST = Found [OK]

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

Common Mistakes:

• Stopping search too early
• Confusing left and right child directions
• Assuming key not found when present

4. Identify the error in the following BST search function and choose the correct fix:

bool search(Node* root, int key) {
  if (root == nullptr) 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. Remove base case for nullptr

B. Change return type to int

C. Swap left and right in recursive calls; should be key < root->data for left

D. Add print statements for debugging

Solution

1. Step 1: Analyze recursive calls logic

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

2. Step 2: Identify incorrect direction

   Code searches left when key > root->data, which is wrong. Left subtree has smaller values.

3. Step 3: Correct the recursive calls

   Swap left and right calls: if (key < root->data) search left; else search right.

4. Final Answer:

   Swap left and right in recursive calls; should be key < root->data for left -> Option C

5. Quick Check:

   BST property fixes search direction [OK]

Hint: Left subtree < node, right subtree > node [OK]

Common Mistakes:

• Mixing left and right subtree directions
• Ignoring base case
• Changing return type unnecessarily

5. Given a BST with nodes inserted in this order: 25, 15, 50, 10, 22, 35, 70. You want to search for the value 22. How many nodes will the search function visit before finding 22?

hard

A. 2

B. 5

C. 4

D. 3

Solution

1. Step 1: Build BST structure from insertion order

   Insert 25 (root), then 15 (left of 25), 50 (right of 25), 10 (left of 15), 22 (right of 15), 35 (left of 50), 70 (right of 50).

2. Step 2: Trace search path for 22

   Start at 25 (visit 1), 22 < 25 go left to 15 (visit 2), 22 > 15 go right to 22 (visit 3), found key.

3. Final Answer:

   3 -> Option D

4. Quick Check:

   Nodes visited = 3 [OK]

Hint: Count nodes visited following BST search path [OK]

Common Mistakes:

• Counting nodes not visited
• Misplacing nodes in BST
• Stopping count before finding key