Search in a Binary Search Tree

This problem can be solved using a simple recursive strategy because we’re working with a Binary Search Tree (BST). We will leverage the property of a BST where for any given node, all nodes in its left subtree have a value less than the node, and all nodes in its right subtree have a value greater than the node.

Here’s the step-by-step approach:

  1. Check the current node. If it is None, return None because the value doesn’t exist in the BST.
  2. If the current node’s value equals the target value, return the current node because we have found our target in the BST.
  3. If the current node’s value is greater than the target value, we search the left subtree. This is because in a BST, all nodes with a value less than the current node’s value are in the left subtree.
  4. If the current node’s value is less than the target value, we search the right subtree. This is because in a BST, all nodes with a value greater than the current node’s value are in the right subtree.

Here’s the Python code:

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class Solution:
    def searchBST(self, root: Optional[TreeNode], val: int) -> Optional[TreeNode]:
        if root is None: 
            # Value does not exist in the BST
            return None

        if root.val == val: 
            # Found the node
            return root 

        elif root.val > val: 
            # Search the left subtree
            return self.searchBST(root.left, val)

        else: 
            # Search the right subtree
            return self.searchBST(root.right, val)

This function starts at the root and traverses down the tree until it either finds the target value or reaches a leaf node. It narrows down the search area by choosing the correct subtree based on the comparison between the current node’s value and the target value.

Identifying Problem Isomorphism

“Search in a Binary Search Tree” can be mapped to “Insert into a Binary Search Tree”.

“Search in a Binary Search Tree” requires us to find a node in a Binary Search Tree (BST) that matches a certain value and return the subtree that starts from that node.

“Insert into a Binary Search Tree” is about inserting a node into a BST. We need to find the correct location where the new node should be inserted, which involves searching the BST to find the appropriate place for the new node.

Both problems involve traversing a Binary Search Tree and making decisions based on the binary tree property: left child node is less than the parent, and the right child node is greater than the parent.

“Search in a Binary Search Tree” is simpler because it only involves finding a node and returning the corresponding subtree. “Insert into a Binary Search Tree” not only involves searching for the right place but also updating the tree structure by inserting the new node, which adds an extra level of complexity.

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class Solution:
    def searchBST(self, root: TreeNode, val: int) -> TreeNode:
        if not root:
            return
        if root.val==val:
            return root
        if root.val < val:
            return self.searchBST(root.right,val)
        else:
            return self.searchBST(root.left,val)

Problem Classification

The problem falls under the Data Structures domain with a focus on binary search trees.

“What” Components:

  1. “Root of a binary search tree (BST)”: This indicates that we have a data structure, specifically a binary search tree, as the initial input.

  2. “An integer val”: This tells us that there is another input, a specific integer value, that we need to search for within the binary search tree.

  3. “Find the node in the BST”: The task involves searching for a specific value within the given binary search tree.

  4. “Node’s value equals val”: The criteria for the search operation is defined here - the node’s value should equal the provided integer.

  5. “Return the subtree rooted with that node”: Once the node is found, the desired output is the subtree that takes the found node as the root.

  6. “If such a node does not exist, return null”: This provides the return value in case the provided integer value is not found within the tree.

This problem can be classified as a Tree Search problem, specifically within a Binary Search Tree. It involves traversing the tree in a specific way to find a node with a certain value and then returning a part of the tree (subtree). If the node does not exist, it involves returning a null value. The key to solving this problem lies in understanding the properties of binary search trees and how to traverse them effectively.

Language Agnostic Coding Drills

  1. Dissecting the Code:

    a. Class Definition: The code defines a Python class Solution, which is used to encapsulate the solution method.

    b. Function Definition: The method searchBST is defined within the class, which accepts a root of a binary tree and an integer value as parameters.

    c. Conditional Checking: The function has several if conditions to direct the flow of the program based on the value at a node, or the absence of a node (null check).

    d. Recursion: The solution uses recursive calls to traverse the binary search tree.

    e. Binary Search Tree Traversal: The problem solution requires knowledge of BST properties and how to use them to optimize search operations.

  2. Coding Concepts in Order of Increasing Difficulty:

    a. Conditional Checking (Beginner): The ability to use if statements to control the program’s flow based on certain conditions.

    b. Function Definition (Beginner): Understanding how to define a function, specify parameters, and return values.

    c. Class Definition (Intermediate): The understanding of how to define and use classes in Python.

    d. Recursion (Intermediate): A somewhat advanced concept where a function calls itself to solve smaller instances of the same problem.

    e. Binary Search Tree Traversal (Advanced): This requires an understanding of binary search tree properties and how to perform a search operation efficiently. This is considered an advanced topic as it requires prerequisite knowledge of data structures and specific properties of BSTs.

  3. Problem-Solving Approach:

    The problem-solving approach here is centered on understanding the properties of a binary search tree (BST). In a BST, all nodes to the left of a node have values lesser than the node, and all nodes to the right have values greater.

    Start from the root and compare the node’s value with the target value. If they are equal, return the node. If the node’s value is less than the target value, you know that you need to go to the right subtree because, in a BST, all values on the right are larger. Conversely, if the node’s value is greater than the target, go to the left subtree.

    This search operation is recursively repeated until the target is found or it is confirmed that the target does not exist in the BST (when we hit a None or leaf node).

    The coding concepts identified each play a part in this solution - function definition allows the encapsulation of our logic, conditional checking allows the decision-making process to take place, recursion enables efficient tree traversal, and binary search tree traversal principles guide the overall approach.

Targeted Drills in Python

  1. Python Coding Drills for Identified Concepts:

    a. Conditional Checking:

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    # If Statement
x = 10
if x > 5:
    print("x is greater than 5")

    b. Function Definition:

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    # Defining a simple function
def greet(name):
    return f"Hello, {name}!"
print(greet("Alice"))

    c. Class Definition:

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    # Defining a simple class
class Dog:
    def __init__(self, name):
        self.name = name
    def bark(self):
        return "Woof!"
my_dog = Dog("Fido")
print(my_dog.bark())

    d. Recursion:

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    # Factorial using recursion
def factorial(n):
    if n == 0:
        return 1
    else:
        return n * factorial(n-1)
print(factorial(5))

    e. Binary Search Tree Traversal:

    Note: This is an advanced concept, for which we need a binary search tree data structure.

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    # Simple Binary Search Tree
class Node:
    def __init__(self, key):
        self.left = None
        self.right = None
        self.val = key

# A utility function to do inorder tree traversal
def printInorder(root):
    if root:
        printInorder(root.left)
        print(root.val),
        printInorder(root.right)

  2. Problem-Specific Concepts:

    The problem-specific concept here is the use of recursion to traverse the binary search tree. This approach is used to traverse down the tree using the property of binary search tree. This concept is critical as the problem requires us to locate a specific node in the tree, which is efficiently achievable using this method.

  3. Integrating the Coding Drills:

    Once each of the drills has been understood, they can be combined to form the solution to the problem. The integration of the drills would follow these steps:

    a. Begin with the class definition drill, creating a class Solution.

    b. Inside the class, use the function definition drill to create a method searchBST(self, root, val).

    c. Inside this function, apply the conditional checking drill to check if root is None. If so, return None.

    d. If root is not None, check if root.val is equal to val. If so, return root.

    e. If root.val is not equal to val, use the conditional checking drill again to check if root.val is less than val.

    f. If root.val is less than val, apply the recursion drill by calling self.searchBST(root.right, val).

    g. If root.val is greater than val, apply the recursion drill by calling self.searchBST(root.left, val).

    h. As a final step, understand that the recursion and BST traversal drills go hand-in-hand. The recursion is what allows the BST traversal to occur, making this an important combination of the identified concepts.

This way, the individual drills contribute to the final solution in a systematic and structured manner, leading to an efficient solution for the given problem.