Binary Search Recursive Approach in DSA Python - Build from Scratch

Binary Search Recursive Approach

📖 Scenario: You have a sorted list of book titles in a library catalog. You want to find if a specific book is available using a fast search method.

🎯 Goal: Build a recursive binary search function to check if a book title exists in the sorted list.

📋 What You'll Learn

Create a sorted list of book titles

Define variables for the search range (start and end indexes)

Write a recursive function for binary search

Print the result of searching for a specific book

💡 Why This Matters

🌍 Real World

Binary search is used in many software systems to quickly find data in sorted lists, such as searching for a contact in a phone book or a product in an online store.

💼 Career

Understanding binary search helps in technical interviews and is fundamental for efficient data retrieval in software development roles.

1

Create the sorted list of book titles

Create a list called books with these exact titles in this order: 'Algorithms', 'Data Structures', 'Machine Learning', 'Python', 'Web Development'

DSA Python

# Create the list of books
# Your code here

Hint

Remember to keep the list sorted alphabetically.

2

Set the start and end index variables

Create two variables called start and end. Set start to 0 and end to the last index of the books list.

DSA Python

books = ['Algorithms', 'Data Structures', 'Machine Learning', 'Python', 'Web Development']
# Set start and end indexes
# Your code here

Hint

Use len(books) - 1 to get the last index.

3

Write the recursive binary search function

Define a function called binary_search that takes four parameters: books, start, end, and target. Implement the recursive binary search logic inside this function using if and else statements. Use mid = (start + end) // 2 to find the middle index. Return True if target is found, otherwise return False.

DSA Python

books = ['Algorithms', 'Data Structures', 'Machine Learning', 'Python', 'Web Development']
start = 0
end = len(books) - 1

# Define the recursive binary_search function
# Your code here

Hint

Remember the base case is when start is greater than end.

4

Search for a book and print the result

Call the binary_search function with books, start, end, and the target book 'Python'. Store the result in a variable called found. Then print found.

DSA Python

books = ['Algorithms', 'Data Structures', 'Machine Learning', 'Python', 'Web Development']
start = 0
end = len(books) - 1

def binary_search(books, start, end, target):
    if start > end:
        return False
    mid = (start + end) // 2
    if books[mid] == target:
        return True
    elif books[mid] < target:
        return binary_search(books, mid + 1, end, target)
    else:
        return binary_search(books, start, mid - 1, target)

# Call binary_search for 'Python' and print the result
# Your code here

Hint

Use print(found) to show if the book was found.

Practice

1. What is the main idea behind the binary search recursive approach?

easy

A. Search every element one by one from start to end

B. Sort the list first and then search linearly

C. Divide the list into halves and search recursively in the half where the target may exist

D. Use a queue to store elements and search iteratively

Solution

1. Step 1: Understand binary search logic

   Binary search works by dividing the list into two halves and deciding which half to search next based on comparison with the middle element.

2. Step 2: Recognize recursive approach

   The recursive approach calls the same function on the half where the target could be, reducing the search space each time.

3. Final Answer:

   Divide the list into halves and search recursively in the half where the target may exist -> Option C

4. Quick Check:

   Binary search = divide and conquer [OK]

Hint: Think divide and conquer, search half recursively [OK]

Common Mistakes:

• Searching all elements linearly instead of dividing
• Not reducing the search space correctly
• Confusing iterative with recursive approach

2. Which of the following is the correct base case for a recursive binary search function in Python?

easy

A. if low > high: return -1

B. if low == high: return mid

C. if mid == target: return low

D. if high < low: return mid

Solution

1. Step 1: Identify base case condition

   The base case occurs when the search space is empty, meaning low index is greater than high index.

2. Step 2: Confirm correct return value

   When low > high, the target is not found, so return -1 to indicate failure.

3. Final Answer:

   if low > high: return -1 -> Option A

4. Quick Check:

   Empty search space means return -1 [OK]

Hint: Base case: low index passes high index means not found [OK]

Common Mistakes:

• Returning mid when low == high without checking target
• Using wrong comparison operators in base case
• Returning wrong index or value in base case

3. What will be the output of the following code?

def binary_search(arr, low, high, target):
    if low > high:
        return -1
    mid = (low + high) // 2
    if arr[mid] == target:
        return mid
    elif arr[mid] > target:
        return binary_search(arr, low, mid - 1, target)
    else:
        return binary_search(arr, mid + 1, high, target)

arr = [2, 4, 6, 8, 10]
print(binary_search(arr, 0, len(arr) - 1, 6))

medium

A. 1

B. 2

C. -1

D. 3

Solution

1. Step 1: Trace initial call

   Call binary_search(arr, 0, 4, 6). mid = (0+4)//2 = 2. arr[2] = 6 matches target 6.

2. Step 2: Return mid index

   Since arr[mid] == target, function returns 2 immediately.

3. Final Answer:

   2 -> Option B

4. Quick Check:

   Target 6 found at index 2 [OK]

Hint: Check middle element first, return index if match [OK]

Common Mistakes:

• Calculating mid incorrectly
• Returning wrong index
• Confusing target value with index

4. Find the error in the following recursive binary search code:

def binary_search(arr, low, high, target):
    if low >= high:
        return -1
    mid = (low + high) // 2
    if arr[mid] == target:
        return mid
    elif arr[mid] > target:
        return binary_search(arr, low, mid - 1, target)
    else:
        return binary_search(arr, mid + 1, high, target)

medium

A. Recursive calls should swap low and high parameters

B. Mid calculation should be 'mid = (low + high + 1) // 2'

C. Return value should be 'None' instead of '-1'

D. Base case condition should be 'if low > high' instead of 'if low >= high'

Solution

1. Step 1: Analyze base case condition

   The base case incorrectly uses 'if low >= high', which misses the case when low == high and target is at that index.

2. Step 2: Correct base case to 'if low > high'

   Changing to 'if low > high' allows checking the last element when low == high before returning -1.

3. Final Answer:

   Base case condition should be 'if low > high' instead of 'if low >= high' -> Option D

4. Quick Check:

   Base case must allow checking last element [OK]

Hint: Base case: low > high means search ended [OK]

Common Mistakes:

• Using >= instead of > in base case
• Incorrect mid calculation
• Returning wrong value on failure

5. Given a sorted list arr = [1, 3, 5, 7, 9, 11, 13], write a recursive binary search function to find the index of the target 10. What will be the final output?

hard

A. -1

B. 4

C. 5

D. 6

Solution

1. Step 1: Trace recursive calls for target 10

   Initial call: low=0, high=6, mid=3, arr[3]=7 < 10, search right half (4 to 6). Next mid=5, arr[5]=11 > 10, search left half (4 to 4). Next mid=4, arr[4]=9 < 10, search right half (5 to 4). Now low=5 > high=4, base case reached.

2. Step 2: Return -1 as target not found

   Since low > high, function returns -1 indicating target 10 is not in the list.

3. Final Answer:

   -1 -> Option A

4. Quick Check:

   Target 10 not in list returns -1 [OK]

Hint: If target not found, recursive calls end with -1 [OK]

Common Mistakes:

• Assuming closest smaller element index is returned
• Not handling base case properly
• Confusing index with value