Number Complement

Number Complement - Problem

Bit Manipulation Easy

The complement of an integer is the integer you get when you flip all the 0's to 1's and all the 1's to 0's in its binary representation.

For example, the integer 5 is "101" in binary and its complement is "010" which is the integer 2.

Given an integer num, return its complement.

Input & Output

Example 1 — Basic Case

$ Input: num = 5

› Output: 2

💡 Note: 5 in binary is 101. Flipping each bit: 1→0, 0→1, 1→0 gives us 010, which is 2 in decimal.

Example 2 — Single Bit

$ Input: num = 1

› Output: 0

💡 Note: 1 in binary is 1. Flipping the bit: 1→0 gives us 0.

Example 3 — Larger Number

$ Input: num = 7

› Output: 0

💡 Note: 7 in binary is 111. Flipping each bit: 1→0, 1→0, 1→0 gives us 000, which is 0 in decimal.

Constraints

1 ≤ num ≤ 2³¹ - 1

Visualization

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Asked in

G Google 15 a Amazon 12 M Microsoft 8 Apple 6

The key insight is to use bit manipulation with XOR operation. Create a mask of all 1's matching the number's bit length, then XOR with the original number to flip all bits efficiently. Best approach is XOR with Mask. Time: O(log n), Space: O(1)

Common Approaches

✓ String Manipulation

⏱️ Time: O(log n) Space: O(log n)

Convert the number to its binary string representation, iterate through each character flipping '0' to '1' and '1' to '0', then convert the result back to an integer.

XOR with Mask

⏱️ Time: O(log n) Space: O(1)

Find the position of the most significant bit, create a mask with all 1's up to that position, then XOR the original number with this mask to flip all relevant bits.

String Manipulation — Algorithm Steps

Step 1: Convert number to binary string (without '0b' prefix)
Step 2: Iterate through each character and flip bits
Step 3: Convert flipped binary string back to integer

Visualization

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Step-by-Step Walkthrough

Convert to Binary

Convert number 5 to binary string "101"

Flip Each Bit

Change '1'→'0' and '0'→'1' to get "010"

Convert to Integer

Convert "010" back to integer 2

Code -

solution.c — C

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

int solution(int num) {
    char binaryStr[32];
    char flipped[32];
    
    // Convert to binary string
    int index = 0;
    int temp = num;
    while (temp > 0) {
        binaryStr[index++] = (temp % 2) + '0';
        temp /= 2;
    }
    binaryStr[index] = '\0';
    
    // Reverse the binary string
    int len = strlen(binaryStr);
    for (int i = 0; i < len / 2; i++) {
        char temp = binaryStr[i];
        binaryStr[i] = binaryStr[len - 1 - i];
        binaryStr[len - 1 - i] = temp;
    }
    
    // Flip each bit
    for (int i = 0; i < len; i++) {
        if (binaryStr[i] == '0') {
            flipped[i] = '1';
        } else {
            flipped[i] = '0';
        }
    }
    flipped[len] = '\0';
    
    // Convert back to integer
    int result = 0;
    int power = 1;
    for (int i = len - 1; i >= 0; i--) {
        if (flipped[i] == '1') {
            result += power;
        }
        power *= 2;
    }
    
    return result;
}

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

Time & Space Complexity

Time Complexity

⏱️

O(log n)

Converting to binary string and back takes O(log n) time where log n is the number of bits

⚡ Linearithmic

Space Complexity

O(log n)

Binary string storage requires O(log n) space for the bit representation

⚡ Linearithmic Space

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Input & Output

Constraints

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Related Problems

Common Approaches

String Manipulation — Algorithm Steps

Visualization

Code -

Time & Space Complexity

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