Complement of Base 10 Integer - Practice Coding Problems

Complement of Base 10 Integer - Problem

Bit Manipulation Easy

Ever wondered what happens when you flip every bit in a number's binary representation? That's exactly what we're doing in this fascinating bit manipulation problem!

The Challenge: Given an integer n, find its complement by flipping all the bits in its binary representation. This means every 0 becomes a 1, and every 1 becomes a 0.

Key Examples:

The number 5 in binary is 101
Flipping the bits gives us 010
Which equals 2 in decimal

Important Note: We only consider the significant bits (no leading zeros in the original number). For example, 5 is represented as 101, not 00000101.

Goal: Return the decimal value of the complement.

Input & Output

example_1.py — Simple Case

$ Input: n = 5

› Output: 2

💡 Note: 5 in binary is 101. The complement flips all bits: 101 → 010, which equals 2 in decimal.

example_2.py — Single Bit

$ Input: n = 1

› Output: 0

💡 Note: 1 in binary is 1. The complement flips the single bit: 1 → 0, which equals 0 in decimal.

example_3.py — Power of 2 Minus 1

$ Input: n = 7

› Output: 0

💡 Note: 7 in binary is 111. The complement flips all bits: 111 → 000, which equals 0 in decimal.

Constraints

1 ≤ n ≤ 2³¹ - 1
The input is guaranteed to be a positive integer
No leading zeros in the binary representation

Visualization

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Understanding the Visualization

Identify Pattern

Recognize that we need to flip exactly the significant bits

Create Mask

Build a mask with 1s in all positions we want to flip

Apply XOR

Use XOR operation to flip all bits simultaneously

Get Result

The XOR result is our complement

Key Takeaway

🎯 Key Insight: The XOR operation with a carefully crafted mask flips exactly the bits we want - it's like having a master switch that controls all the individual switches at once!

Asked in

G Google 45 a Amazon 38 ⊞ Microsoft 32 Apple 28

The optimal solution uses bit manipulation with XOR operation. Create a mask with 1s in all significant bit positions, then XOR the original number with this mask to flip all bits simultaneously. Time complexity: O(1), Space complexity: O(1).

Common Approaches

Approach	Time	Space	Notes
✓ Bit Manipulation with Mask	O(1)	O(1)	Use bit operations to flip all bits at once with a carefully crafted mask

Bit Manipulation with Mask — Algorithm Steps

Find the number of bits in the input number
Create a mask with all 1s for those bit positions
XOR the original number with the mask to flip all bits
Return the result

Visualization

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Step-by-Step Walkthrough

Original Number

Start with number 5 = 101 in binary

Create Mask

Create mask 111 (3 ones for 3 bits)

XOR Operation

101 XOR 111 = 010

Result

010 in binary = 2 in decimal

Code -

solution.c — C

#include <stdio.h>

int findComplement(int num) {
    // Find the number of bits in num
    int bitLength = 0;
    int temp = num;
    while (temp > 0) {
        bitLength++;
        temp >>= 1;
    }
    
    // Create a mask with all 1s for the significant bits
    int mask = (1 << bitLength) - 1;
    
    // XOR with mask to flip all bits
    return num ^ mask;
}

int main() {
    int num;
    scanf("%d", &num);
    printf("%d\n", findComplement(num));
    return 0;
}

Time & Space Complexity

Time Complexity

⏱️

O(1)

Bit operations are constant time, and finding bit length is O(log n) but practically constant for 32-bit integers

✓ Linear Growth

Space Complexity

O(1)

Only uses a few integer variables

✓ Linear Space

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Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Bit Manipulation with Mask — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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