When working with binary numbers, it is sometimes necessary to find the previous permutation of a given number. In C++, the std::bitset class provides a convenient way to work with binary numbers. However, there is no built-in method to find the previous permutation of a bitset. In this blog post, we will explore how to find the previous permutation of a bitset in C++.

Understanding Bitset

A std::bitset is a container in C++ that stores a fixed-size sequence of bits. It provides a convenient interface to manipulate individual bits within the sequence. By default, all bits in a bitset are initialized to zero. You can also initialize a bitset with a specific pattern by passing an integer or a string of zeroes and ones during its construction.

Finding the Previous Permutation

To find the previous permutation of a bitset, we need to follow these steps:

1. Start from the least significant bit (LSB).
2. Find the first occurrence of two consecutive ‘1’ bits starting from the LSB. Let’s call the rightmost bit as i and the next bit as j.
3. Flip the i-th bit and all the bits to its right.
4. Set all the bits to the left of bit i to ‘1’.
5. The resulting bitset is the previous permutation.

Let’s see an example implementation in C++:

#include <iostream>
#include <bitset>

std::bitset<4> previousPermutation(std::bitset<4> bs) {
    int i = 0;
    while (i < bs.size() - 1 && bs[i] != 1 || bs[i + 1] != 0) {
        i++;
    }

    bs.flip(i);
    bs.reset(i + 1);
    bs.set();

    return bs;
}

int main() {
    std::bitset<4> bs("1010");
    std::bitset<4> previous = previousPermutation(bs);
    std::cout << previous << std::endl; // Output: 1001

    return 0;
}

In the example above, we start with a bitset initialized as “1010”, which represents the decimal number 10. The previous permutation of this bitset is “1001”, which represents the decimal number 9. The function previousPermutation takes a bitset as input and returns the previous permutation using the algorithm we described earlier.

Conclusion

While there is no built-in method to find the previous permutation of a bitset, we can achieve it by following a simple algorithm. By flipping bits and adjusting their values, we can efficiently find the previous permutation. The code snippet provided in this blog post demonstrates how to find the previous permutation of a bitset in C++. Remember to handle the edge case where no previous permutation exists.

#programming #C++