C++ Bitset and its Application

Bitset is a container that represents a fixed-size sequence of bits. A bitset allows you to manipulate individual bits efficiently, making it useful in problems related to bitwise operations, such as checking flags, implementing binary representations.

Bitset is defined as the std::bitset class template inside the <bitset> header file.

Syntax of Bitset

bitset<n> name;

where, n is the number of bits to allocate, and name is the name assigned.

Initializing

By default, when a bitset of a given size is created, all of its bits are unset i.e. 0. We can initialize it to some value simply by passing it to its constructor.

#include <bits/stdc++.h>
using namespace std;

int main() {
    
    // Default Initialization
    bitset<5> bnum(18);
    cout << bnum;
    return 0;
}

Here, the bitset bnum is of size 5 bits and stores the decimal value 18 in binary form.

Binary numbers are also represented as strings, so bitset also provide facility to initialize itself from the strings.

#include <bits/stdc++.h>
using namespace std;

int main() {
    
    // Initialize bitset with value
    bitset<5> bs2("10010");

    cout << bs2 << endl;
    return 0;
}

The string should represent a valid binary number i.e. all characters should be 0 or 1. Otherwise, an error may occur.

Accessing Individual Bits

We can access individual bits in a bitset using the [] operator, just like an array.

Example:

#include <bits/stdc++.h>
using namespace std;

int main() {
    
    // 18 = (10010)
    bitset<5> bs(18);
    
    // Check 3rd bit
    cout << bs[2] << endl;
    
    // Check 5th bit
    cout << bs.test(4);
    return 0;
}

0
1

Setting, Resetting and Flipping

Setting means making the bit at particular position 1 and resetting means making it 0. These operations can be done using set() and reset() function. The flip() function can be used to set the bit if it's not set and unset if it is set.

Example:

#include <bits/stdc++.h>
using namespace std;

int main() {
    bitset<5> bs(18);
    
    // Set 1st bit
    bs.set(0);
    cout << bs << endl;
    
    // Reset 2nd bit 
    bs.reset(1);
    cout << bs << endl;
    
    // Flip 5th bit
    bs.flip(4);
    cout << bs;
    return 0;
}

10011
10001
00001

Bitset Operators

Bitset objects can work with all the bitwise operators to provide seamless replacement integration in the code.

Example:

#include <bits/stdc++.h>
using namespace std;

int main() {

    // 18 = (10010)
    bitset<5> bs1(18);
    
    // 5 = (00101)
    bitset<5> bs2(5);
    
    // AND Operator 
    cout << (bs1 & bs2) << endl;
    
    // OR Operator
    cout << (bs1 | bs2) << endl;
    
    // XOR operator
    cout << (bs1 ^ bs2);
    return 0;
}

00000
10111
10111

Why Bitset is Preferred

• Memory Efficient- Stores bits compactly using less space than arrays of bools.
• Fast Operations- Bitwise operations like AND, OR, XOR are very fast.
• Easy to Use- Provides built-in functions like count(), any(), none(), and indexing with[].

Difference between std::bitset and std::vector<bool> and an array of bool

Vector of bool and array of bool can also be implemented to store a sequence of boolean values like bitset but there are some differences between each implementation: