Check if Number is Power of Two in DSA Python - Build from Scratch

Check if Number is Power of Two

📖 Scenario: Imagine you are working with a system that needs to quickly check if certain numbers are powers of two. This is common in computer memory allocation and optimization tasks.

🎯 Goal: You will build a simple program that checks if a given number is a power of two and prints the result.

📋 What You'll Learn

Create a variable to store the number to check

Create a variable to store the result of the power of two check

Use a condition to check if the number is a power of two

Print the result as True or False

💡 Why This Matters

🌍 Real World

Checking if a number is a power of two is useful in computer memory management, graphics, and optimization tasks where sizes and capacities are often powers of two.

💼 Career

Understanding bitwise operations and conditional checks is important for software developers, especially those working in systems programming, embedded systems, and performance-critical applications.

1

Create the number variable

Create a variable called number and set it to 16.

DSA Python

# Create a variable called number and set it to 16
# Your code here

Hint

Use the assignment operator = to set the value.

2

Create the result variable

Create a variable called is_power_of_two and set it to False initially.

DSA Python

number = 16
# Create a variable called is_power_of_two and set it to False
# Your code here

Hint

Initialize the result variable before checking the condition.

3

Check if the number is a power of two

Use an if statement to check if number is greater than zero and if number & (number - 1) == 0. If true, set is_power_of_two to True.

DSA Python

number = 16
is_power_of_two = False
# Use if statement to check if number is power of two
# Your code here

Hint

This is a common bitwise trick to check powers of two.

4

Print the result

Print the value of is_power_of_two.

DSA Python

number = 16
is_power_of_two = False
if number > 0 and (number & (number - 1)) == 0:
    is_power_of_two = True
# Print the result
# Your code here

Hint

Use the print() function to show the result.

Practice

1. Which of the following numbers is a power of two?

easy

A. 16

B. 18

C. 20

D. 22

Solution

1. Step 1: Understand powers of two

   Powers of two are numbers like 1, 2, 4, 8, 16, 32, etc., where each is 2 raised to an integer.

2. Step 2: Check each option

   16 = 2^4, so it is a power of two. Others like 18, 20, 22 are not powers of two.

3. Final Answer:

   16 -> Option A

4. Quick Check:

   16 = 2^4 [OK]

Hint: Only numbers with one '1' bit in binary are powers of two [OK]

Common Mistakes:

• Confusing even numbers with powers of two
• Thinking any multiple of 2 is a power of two

2. Which of the following Python expressions correctly checks if n is a power of two?

easy

A. n | (n - 1) == 0

B. n & (n - 1) == 0

C. n ^ (n - 1) == 0

D. n + (n - 1) == 0

Solution

1. Step 1: Understand bitwise AND check

   For powers of two, binary form has only one '1'. n & (n-1) clears the lowest set bit. If result is 0, n is power of two.

2. Step 2: Analyze options

   n & (n - 1) == 0 uses correct bitwise AND check. Others use OR, XOR, or addition which do not correctly check power of two.

3. Final Answer:

   n & (n - 1) == 0 -> Option B

4. Quick Check:

   Bitwise AND check is standard for power of two [OK]

Hint: Use n & (n-1) == 0 to check power of two [OK]

Common Mistakes:

• Using OR or XOR instead of AND
• Forgetting to check n > 0 before this test

3. What is the output of the following code?

def is_power_of_two(n):
    return n > 0 and (n & (n - 1)) == 0

print(is_power_of_two(32))
print(is_power_of_two(45))

medium

A. False\nFalse

B. False\nTrue

C. True\nFalse

D. True\nTrue

Solution

1. Step 1: Check 32

   32 is 2^5, so n > 0 and n & (n-1) == 0 is True.

2. Step 2: Check 45

   45 is not a power of two, so n & (n-1) != 0, returns False.

3. Final Answer:

   True\nFalse -> Option C

4. Quick Check:

   32 power of two = True, 45 not = False [OK]

Hint: Check output for known powers of two and non-powers [OK]

Common Mistakes:

• Ignoring n > 0 condition
• Assuming all even numbers are powers of two

4. Find the error in this code snippet that checks if a number is a power of two:

def check_power(n):
    if n & (n - 1) == 0:
        return True
    else:
        return False

print(check_power(0))

medium

A. Missing check for n > 0 before bitwise operation

B. No error, code works fine

C. Should use OR instead of AND

D. Return values should be strings 'True' or 'False'

Solution

1. Step 1: Analyze bitwise check

   n & (n-1) == 0 works only if n > 0. For n=0, it returns True incorrectly.

2. Step 2: Identify missing condition

   Code lacks n > 0 check, so 0 incorrectly returns True.

3. Final Answer:

   Missing check for n > 0 before bitwise operation -> Option A

4. Quick Check:

   Always check n > 0 before bitwise test [OK]

Hint: Always check n > 0 before bitwise power of two test [OK]

Common Mistakes:

• Not handling zero or negative inputs
• Using wrong bitwise operators

5. You want to filter a list to keep only numbers that are powers of two. Which code snippet correctly does this?

nums = [0, 1, 2, 3, 4, 5, 8, 16, 18]

A) result = [x for x in nums if x & (x - 1) == 0]
B) result = [x for x in nums if x > 0 and x & (x - 1) == 0]
C) result = [x for x in nums if x | (x - 1) == 0]
D) result = [x for x in nums if x > 0 or x & (x - 1) == 0]

hard

A. result = [x for x in nums if x & (x - 1) == 0]

B. result = [x for x in nums if x > 0 or x & (x - 1) == 0]

C. result = [x for x in nums if x | (x - 1) == 0]

D. result = [x for x in nums if x > 0 and x & (x - 1) == 0]

Solution

1. Step 1: Understand filtering condition

   We must check x > 0 to avoid zero or negative numbers passing the test.

2. Step 2: Analyze each option

   result = [x for x in nums if x > 0 and x & (x - 1) == 0] correctly uses x > 0 and bitwise check. result = [x for x in nums if x & (x - 1) == 0] misses x > 0, so 0 passes incorrectly. Options C and D use wrong operators or logic.

3. Final Answer:

   result = [x for x in nums if x > 0 and x & (x - 1) == 0] -> Option D

4. Quick Check:

   Filter with x > 0 and bitwise AND check [OK]

Hint: Filter with x > 0 and x & (x-1) == 0 for powers of two [OK]

Common Mistakes:

• Not filtering out zero
• Using OR instead of AND in condition
• Using bitwise OR instead of AND