Number Complement - Practice Coding Problems

Number Complement - Problem

Bit Manipulation Easy

Binary Number Complement Challenge

In the world of binary operations, every number has an alter ego - its complement! Your mission is to find this binary opposite.

Given an integer num, you need to flip every bit in its binary representation:
• Convert all 0s to 1s
• Convert all 1s to 0s

Example: The number 5 in binary is 101. Flipping the bits gives us 010, which equals 2 in decimal.

Note: We only consider the significant bits (ignore leading zeros in the original number).

Input & Output

example_1.py — Basic Case

$ Input: num = 5

› Output: 2

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

example_2.py — Single Bit

$ Input: num = 1

› Output: 0

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

example_3.py — Larger Number

$ Input: num = 7

› Output: 0

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

Constraints

1 ≤ num ≤ 2³¹ - 1
The input is guaranteed to be a positive integer
Only consider the significant bits (no leading zeros)

Visualization

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Understanding the Visualization

Identify Bit Pattern

Look at the binary representation of the input number

Create Universal Flipper

Make a mask with all 1s that covers exactly the same bit positions

Flip All Switches

XOR the number with the mask to flip every bit simultaneously

Key Takeaway

🎯 Key Insight: XOR with a mask of all 1s efficiently flips every bit in the significant portion of the number

Asked in

G Google 15 a Amazon 12 ⊞ Microsoft 8 Apple 6

The optimal solution uses bit manipulation with an XOR operation. Create a mask with all 1s for the significant bits using (1 << bitLength) - 1, then XOR with the original number to flip all bits in O(1) time.

Common Approaches

Approach	Time	Space	Notes
✓ Brute Force (Bit by Bit)	O(log n)	O(log n)	Convert to binary string, flip each character, convert back to integer
Bit Mask XOR (Optimal)	O(1)	O(1)	Create a mask with all 1s for significant bits, then XOR with the original number

Brute Force (Bit by Bit) — Algorithm Steps

Convert the number to binary string (without '0b' prefix)
Create an empty result string
Iterate through each character in the binary string
For each bit, flip it: '0' becomes '1', '1' becomes '0'
Convert the flipped binary string back to integer

Visualization

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Step-by-Step Walkthrough

Convert to Binary

Convert input number 5 to binary string '101'

Flip Each Bit

Go through each character: '1'→'0', '0'→'1', '1'→'0' = '010'

Convert Back

Convert binary string '010' back to decimal: 2

Code -

solution.c — C

#include <stdio.h>
#include <string.h>
#include <math.h>

int findComplement(int num) {
    // Convert to binary string
    char binaryStr[32];
    int index = 0;
    int temp = num;
    
    while (temp > 0) {
        binaryStr[index++] = (temp % 2) + '0';
        temp /= 2;
    }
    
    // Reverse the string
    for (int i = 0; i < index / 2; i++) {
        char temp = binaryStr[i];
        binaryStr[i] = binaryStr[index - 1 - i];
        binaryStr[index - 1 - i] = temp;
    }
    binaryStr[index] = '\0';
    
    // Flip each bit and convert back to integer
    int result = 0;
    for (int i = 0; i < index; i++) {
        int bit = (binaryStr[i] == '0') ? 1 : 0;
        result = result * 2 + bit;
    }
    
    return result;
}

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

Time & Space Complexity

Time Complexity

⏱️

O(log n)

Need to process each bit of the number, which is log n bits

⚡ Linearithmic

Space Complexity

O(log n)

Store binary representation as string, which takes log n space

⚡ Linearithmic Space

78.0K Views

Medium Frequency

~8 min Avg. Time

2.4K Likes

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Smart Actions

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Input & Output

Constraints

Visualization

Related Problems

Common Approaches

Brute Force (Bit by Bit) — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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