How do you solve Complement of Base 10 Integer on LeetCode?

Complement of Base 10 Integer (LeetCode #1009) can be solved using Brute Force or Optimal Solution. The optimal approach is Optimal Solution with O(1) time complexity and O(1) space complexity. Key insight: The complement operation is closely related to binary representation and bit manipulation.

What is the brute force solution for Complement of Base 10 Integer?

The brute force approach for Complement of Base 10 Integer is Brute Force, with O(n) time complexity and O(n) space complexity. The brute-force approach involves converting the integer to its binary representation, flipping each bit, and converting it back to decimal. This is straightforward but not efficient for larger numbers. The optimal Optimal Solution approach improves this to O(1).

What algorithm or data structure is used to solve Complement of Base 10 Integer?

Complement of Base 10 Integer uses the following concepts: Bit Manipulation. The recommended patterns to study are: Bit Manipulation, Masking.

What are the interview tips for Complement of Base 10 Integer?

Always clarify if there are any edge cases, such as n = 0. Explain your thought process as you work through the problem to demonstrate your understanding. Practice converting between binary and decimal, as this is a common requirement in bit manipulation problems.

What are common mistakes when solving Complement of Base 10 Integer?

Forgetting to handle the case when n is 0, which should return 1. Not considering the bit length when creating the mask, leading to incorrect results.

#1009

Complement of Base 10 Integer

Easy

Bit ManipulationBit ManipulationMasking

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n)	O(1)
Space	O(n)	O(1)

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Intuition

Time O(1)Space O(1)

The optimal solution leverages the property that the complement of a number plus the number itself equals a number with all bits set to 1. By calculating this directly, we avoid unnecessary conversions.

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Algorithm

3 steps

1Step 1: Calculate the bit length of n to determine how many bits are needed.
2Step 2: Create a mask with all bits set to 1 for the length of n.
3Step 3: Subtract n from the mask to get the complement.

solution.py3 lines

1def findComplement(n):
2    mask = (1 << n.bit_length()) - 1
3    return mask - n

ℹ

Complexity note: The time complexity is O(1) because it involves constant time operations regardless of the size of n. The space complexity is also O(1) since we are using a fixed amount of space.

1The complement operation is closely related to binary representation and bit manipulation.
2Understanding how to create a mask can simplify many problems involving binary operations.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.