Kth Smallest Element in BST in DSA Python - Build from Scratch

Kth Smallest Element in BST

📖 Scenario: You are working with a simple phone book application that stores contacts in a special tree structure called a Binary Search Tree (BST). Each contact has a unique number. You want to find the contact with the kth smallest number quickly.

🎯 Goal: Build a program that creates a BST with given numbers, sets a value for k, and finds the kth smallest number in the BST.

📋 What You'll Learn

Create a BST by inserting nodes with given values

Set a variable k to specify which smallest element to find

Write a function to find the kth smallest element using in-order traversal

Print the kth smallest element

💡 Why This Matters

🌍 Real World

Finding the kth smallest element is useful in databases, search engines, and ranking systems where sorted data retrieval is needed.

💼 Career

Understanding BSTs and traversal algorithms is important for software engineers working on data storage, retrieval, and optimization tasks.

1

Create the BST Node class and insert nodes

Create a class called Node with an __init__ method that takes val and sets self.val, self.left, and self.right to None. Then create a function called insert that takes root and val and inserts a new node with val into the BST. Finally, create a BST by inserting these values in order: 5, 3, 6, 2, 4, 1. Store the root in a variable called root.

DSA Python

# Define Node class and insert function
# Insert values 5, 3, 6, 2, 4, 1 into BST and assign root
# Your code here

Hint

Remember, the insert function places smaller values to the left and larger or equal values to the right.

2

Set the value of k

Create a variable called k and set it to 3 to find the 3rd smallest element in the BST.

DSA Python

class Node:
    def __init__(self, val):
        self.val = val
        self.left = None
        self.right = None

def insert(root, val):
    if root is None:
        return Node(val)
    if val < root.val:
        root.left = insert(root.left, val)
    else:
        root.right = insert(root.right, val)
    return root

root = None
for v in [5, 3, 6, 2, 4, 1]:
    root = insert(root, v)

# Set k to 3
# Your code here

Hint

Just create a variable k and assign it the value 3.

3

Write function to find kth smallest element

Write a function called kth_smallest that takes root and k. Use an inner helper function called inorder to do an in-order traversal of the BST. Keep track of visited nodes in a list called elements. Return the kth smallest element from elements.

DSA Python

class Node:
    def __init__(self, val):
        self.val = val
        self.left = None
        self.right = None

def insert(root, val):
    if root is None:
        return Node(val)
    if val < root.val:
        root.left = insert(root.left, val)
    else:
        root.right = insert(root.right, val)
    return root

root = None
for v in [5, 3, 6, 2, 4, 1]:
    root = insert(root, v)

k = 3

# Define kth_smallest function below
# Your code here

Hint

Use in-order traversal to visit nodes in ascending order and collect their values in a list.

4

Print the kth smallest element

Use print to display the result of calling kth_smallest(root, k).

DSA Python

class Node:
    def __init__(self, val):
        self.val = val
        self.left = None
        self.right = None

def insert(root, val):
    if root is None:
        return Node(val)
    if val < root.val:
        root.left = insert(root.left, val)
    else:
        root.right = insert(root.right, val)
    return root

root = None
for v in [5, 3, 6, 2, 4, 1]:
    root = insert(root, v)

k = 3

def kth_smallest(root, k):
    elements = []
    def inorder(node):
        if node is None:
            return
        inorder(node.left)
        elements.append(node.val)
        inorder(node.right)
    inorder(root)
    return elements[k-1]

# Print the kth smallest element
# Your code here

Hint

Call the function and print its result to see the kth smallest value.

Practice

1. What does the term Kth Smallest Element in BST mean?

easy

A. The element that is the Kth largest in the BST

B. The element that is the Kth in ascending order in the BST

C. The root element of the BST

D. The element with value K in the BST

Solution

1. Step 1: Understand BST ordering

   A Binary Search Tree (BST) stores elements so that left child is smaller and right child is larger.

2. Step 2: Define Kth smallest element

   The Kth smallest element is the element that appears in the Kth position when all elements are sorted ascending.

3. Final Answer:

   The element that is the Kth in ascending order in the BST -> Option B

4. Quick Check:

   Kth smallest means sorted order position [OK]

Hint: Kth smallest means counting nodes in ascending order [OK]

Common Mistakes:

• Confusing Kth smallest with Kth largest
• Thinking it means the root node
• Assuming K is the value, not position

2. Which of the following Python function signatures is correct to find the Kth smallest element in a BST?

easy

A. def kth_smallest(root: Optional[TreeNode], k: int) -> int:

B. def kth_smallest(k: int, root: TreeNode) -> int:

C. def kth_smallest(root: TreeNode, k: str) -> int:

D. def kth_smallest(root: TreeNode) -> int:

Solution

1. Step 1: Check parameter order and types

   The function should take the root node and an integer k to find the Kth smallest element.

2. Step 2: Validate correct typing and order

   def kth_smallest(root: Optional[TreeNode], k: int) -> int: correctly uses root as TreeNode (or Optional) and k as int, returning int.

3. Final Answer:

   def kth_smallest(root: Optional[TreeNode], k: int) -> int: -> Option A

4. Quick Check:

   Correct parameter order and types [OK]

Hint: Root node first, k as int second in function parameters [OK]

Common Mistakes:

• Swapping parameter order
• Using wrong type for k (like string)
• Missing k parameter

3. Given the BST below and k = 3, what is the output of the function kth_smallest(root, 3)?

       5
      / \
     3   7
    / \   \
   2   4   8

medium

A. 4

B. 5

C. 3

D. 7

Solution

1. Step 1: List BST elements in ascending order

   Inorder traversal gives: 2, 3, 4, 5, 7, 8.

2. Step 2: Identify the 3rd smallest element

   The 3rd element in this list is 4.

3. Final Answer:

   4 -> Option A

4. Quick Check:

   Inorder 3rd element = 4 [OK]

Hint: Inorder traversal lists nodes ascending; pick Kth [OK]

Common Mistakes:

• Choosing root or random node instead of Kth
• Counting nodes incorrectly
• Confusing Kth smallest with Kth largest

4. The following code tries to find the Kth smallest element in a BST but has a bug. What is the bug?

def kth_smallest(root, k):
    stack = []
    while True:
        while root:
            stack.append(root)
            root = root.right  # Bug here
        root = stack.pop()
        k -= 1
        if k == 0:
            return root.val
        root = root.left

medium

A. Stack should be initialized with root

B. Return statement is missing

C. k should be incremented, not decremented

D. It should go to the left child first, not right

Solution

1. Step 1: Analyze traversal direction

   For Kth smallest, we do inorder traversal: left -> node -> right. The code wrongly goes right first.

2. Step 2: Identify correct child to traverse first

   It should go to the left child first to get smallest elements first.

3. Final Answer:

   It should go to the left child first, not right -> Option D

4. Quick Check:

   Inorder traversal starts with left child [OK]

Hint: Inorder traversal: always left child first [OK]

Common Mistakes:

• Going right child first in inorder
• Not using stack properly
• Incorrect decrement of k

5. You have a BST with nodes: 10, 5, 15, 3, 7, 12, 18. You want to find the 5th smallest element. Which approach below correctly finds it efficiently?

hard

A. Use preorder traversal and return the 5th node visited

B. Traverse only right subtree and pick the 5th node

C. Perform inorder traversal and return the 5th visited node

D. Return the root node value directly

Solution

1. Step 1: Understand traversal types

   Inorder traversal visits nodes in ascending order in BST.

2. Step 2: Apply inorder traversal to find Kth smallest

   Perform inorder traversal and stop at the 5th node visited to get the 5th smallest element.

3. Final Answer:

   Perform inorder traversal and return the 5th visited node -> Option C

4. Quick Check:

   Inorder traversal gives sorted order [OK]

Hint: Use inorder traversal to get sorted nodes [OK]

Common Mistakes:

• Using preorder or postorder which are not sorted
• Ignoring left subtree nodes
• Assuming root is always Kth smallest