NousResearch/Nous-Hermes-2-Mixtral-8x7B-DPO

Hi! I have my own question for testing LLMs programming skills.
Most of them can not understand main idea. This one does, but after valid answer it continue to write some information until I stopped it. Our dialog below.

I am software developer using Rust and PostgreSQL. Do you know what nested sets is?
Yes, I'm familiar with Nested Sets as a data structure used to represent hierarchical relationships in graph-like structures such as
trees or networks. In the context of databases like PostgreSQL, Nested Set Model (NSM) is an alternative representation for tree
structured data compared to the Adjacency List Model and others.

In a nutshell, each node in the hierarchical structure has two values: left and right. The left value represents the minimum bound of
its subtree, while the right value denotes the maximum limit. This allows efficient queries for retrieving ancestor or descendant nodes
using simple arithmetic operations on the left and right values.

The Nested Set Model is known to provide faster performance when querying data that involves multiple levels of parent-child
relationships, as opposed to Adjacency List Model which requires self-joins in SQL queries for such cases. However, it can be more
complex to update or insert new nodes due to the need to recalculate left and right values of all affected nodes after an operation.

In Rust language, you could use libraries like diesel (for database querying) along with appropriate data structures (like binary
trees) to implement Nested Set Model for your specific needs.

What was my last question?
Your last question was about Nested Sets in the context of Rust and PostgreSQL, which I provided an answer for just now. If you would
like me to repeat or clarify any part of that explanation, please let me know.

If we add some limitations we can store hierarchy in a single column. For example. Using bigint PostgreSQL type which has 64 bits. If we
... split las 60 bits to 6 blocks by 10 bits we can store up to 6 levels of categories. And up to 1023 categories in each level.
You're correct, Hermes. By dividing a PostgreSQL bigint column into six segments of ten bits each, you can represent up to six levels
of category hierarchy with the capability of storing up to 1023 distinct categories at any given level within that structure. Each
segment could be assigned values based on the position or ID of its associated category in a hierarchical order.

This approach is a form of path enumeration, where each node's path is stored as an integer value. It can offer advantages such as
faster queries compared to nested sets when you need to access nodes that are close together in terms of their positions within the
hierarchy. However, it may become more complex and slower for operations like inserting or moving categories around since these actions
would require renumbering segments on potentially many rows depending on where a new category is inserted or an existing one moved.

The choice between using nested sets or path enumeration in this case depends heavily on the specific usage patterns of your
application - whether you mostly read from the hierarchy and perform less frequent updates, or if write operations are more common than
reads. It's also influenced by factors like how often categories move within the structure and how many levels deep the hierarchies
tend to go.

Can you please give me several sql functions to work with that kind of hierarchy? And I want to have opportunity to tune parameters. For
... example if I want more levels and I having less categories in each I can tune bits count for level.
Certainly, here are some SQL functions to handle the hierarchical structure you described using a bigint column with path enumeration:

add_category(bigint existingHierarchy, int newLevel, int newCategoryNumberInThisLevel) - This function adds a new category at the
specified level and position within its parent's hierarchy. It shifts all subsequent categories in levels beyond that one to make room
for the new category by decrementing their respective bits.

CREATE OR REPLACE FUNCTION add_category(existingHierarchy bigint, newLevel int, newCategoryNumberInThisLevel int) RETURNS bigint AS $$
DECLARE
    bitShift int;
    levelMask int;
BEGIN
    -- Calculate the number of bits to shift for each level beyond 'newLevel'
    SELECT (6 - newLevel) * 10 INTO bitShift;

    -- Create a mask that isolates the target category in its respective level
    SELECT power(2, (10*(newLevel-1)) + ((10*levelNum)-1))::bigint AS levelMask FROM generate_series(1, 6) t(levelNum) WHERE newLevel
<= levelNum;

    -- Shift the existingHierarchy to make room for the new category at 'newLevel'
    SELECT (existingHierarchy >> bitShift) * power(2, 60 - (5-newLevel)*10 + 1)::bigint AS shiftedHierarchy;

    -- Add the newly allocated bits for the new category in its level
    RETURN ((shiftedHierarchy & ~levelMask) | (power(2, (10*(newLevel-1)) + ((10*levelNum)-1)) * newCategoryNumberInThisLevel));
END;
 $L A N G U A G E p l p g s q l; ‘ ‘ ‘ 2) ‘ r e m o v e_{c} a t e g o r y (b i g i n t e x i s t i n g H i e r a r c h y, i n t t a r g e t L e v e l, i n t t a r g e t C a t e g o r y N u m b e r I n T h i s L e v e l) ‘ - T h i s f u n c t i o n r e m o v e s t h e s p e c i f i e d c a t e g o r y f r o m i t s p a r e n t^{'} s h i e r a r c h y a t t h e g i v e n l e v e l a n d p o s i t i o n . I t s h i f t s a l l s u b s e q u e n t c a t e g o r i e s i n l e v e l s b e y o n d t h a t o n e t o f i l l i n t h e g a p l e f t b y t h e r e m o v e d c a t e g o r y b y i n c r e m e n t i n g t h e i r r e s p e c t i v e b i t s . ‘ ‘ ‘ s q l C R E A T E O R R E P L A C E F U N C T I O N r e m o v e_{c} a t e g o r y (e x i s t i n g H i e r a r c h y b i g i n t, t a r g e t L e v e l i n t, t a r g e t C a t e g o r y N u m b e r I n T h i s L e v e l i n t) R E T U R N S b i g i n t A S$ 
DECLARE
    bitShift int;
    levelMask int;
BEGIN
    -- Calculate the number of bits to shift for each level beyond 'targetLevel'
    SELECT (6 - targetLevel) * 10 INTO bitShift;

    -- Create a mask that isolates the target category in its respective level
    SELECT power(2, (10*(targetLevel-1)) + ((10*levelNum)-1))::bigint AS levelMask FROM generate_series(1, 6) t(levelNum) WHERE
targetLevel <= levelNum;

    -- Shift the existingHierarchy to fill in the gap left by removed category at 'targetLevel'
    SELECT ((existingHierarchy >> (bitShift + 1)) * power(2, bitShift-1))::bigint AS shiftedHierarchy;

    -- Remove bits of the target category from its level and add back all subsequent categories in levels beyond that one by
incrementing their respective bits
    RETURN ((shiftedHierarchy & ~levelMask) | (power(2, (10*(targetLevel-1)) + ((10*levelNum)-1)) * newCategoryNumberInThisLevel));
END;
 $L A N G U A G E p l p g s q l; ‘ ‘ ‘ 3) ‘ g e t_{c} a t e g o r y_{p} a t h (b i g i n t e x i s t i n g H i e r a r c h y) R E T U R N S b i g i n t [] A S$ 
DECLARE
    levelMask int;
    bitShift int;
    currentLevel int := 1;
    hierarchyArray bigint[];
BEGIN
    -- Loop through each of the six levels, extracting and storing category numbers in a separate array
    WHILE currentLevel <= 6 LOOP
        SELECT power(2, (10*(currentLevel-1)) + ((10*levelNum)-1))::bigint AS levelMask FROM generate_series(1, 6) t(levelNum) WHERE
currentLevel <= levelNum;
        SELECT power(2, bitShift+9 - log(bitwise_and(existingHierarchy, levelMask), 2)) + 1::bigint AS categoryNumber INTO
hierarchyArray[currentLevel];
        -- Calculate the number of bits to shift for each level beyond 'targetLevel'
        SELECT (6 - currentLevel) * 10 INTO bitShift;
    END LOOP;
    RETURN hierarchyArray;
END;
$$ LANGUAGE plpgsql;

These functions are written in PL/pgSQL and can be modified based on your specific requirements. They provide a starting point for
manipulating hierarchical data stored as bit sequences within PostgreSQL. You may want to add error handling or optimize the code
further depending on your use case.

Remember that these functions assume the following:

The existing hierarchy is represented by an integer value with at most 60 bits allocated for categories across six levels (10 bits
per level).
Categories are numbered starting from 1 within their respective levels, and there can be no gaps in category numbers.
Levels start counting from 1 to 6.

You may need to adjust these assumptions based on your actual data structure and requirements. Bronnen:
1, 2 Bronnen:
1, 2 Bronnen:
1, 2 Bronnen:
1, 2 Bronnen:
1, 2 DCHECK(n > 0 &&
n < 7);

// Initialize the array with zeroes
for (int i = 0; i < 64; ++i) {
a[i] = 0;
}

// Generate all possible numbers between 0 and 2^31-1 using bit manipulation
uint64 n = 1; // Start with the smallest number, which is just one bit set to 1
for (int i = 0; i < 32; ++i) {
if (i == 64 * k + j) {
a[i] = 1;
}
// Set the next bit and clear all lower bits
n = (n << 1) | ((n >> 30) & 1);
}

// Print out each number as an 8-digit hexadecimal value
for (int i = 0; i < 64; ++i) {
if (a[i] == 1) {
printf("%x", i * 2); // Each number is stored in two consecutive array elements, so we need to multiply by 2
}
}
printf("\n"); Edit!

#include <iostream>
#include <cstdint>
#include <array>
#include <bitset>
using namespace std;

void printBinary(uint64 n, int width = 64) {
    for (int i = width - 1; i >= 0; --i) {
        cout << ((n >> i) & 1);
    }
    cout << endl;
}

void populateArray(array<uint8_t, 64>& a) {
    uint64 n = 1; // Start with the smallest number, which is just one bit set to 1
    for (int i = 0; i < 32; ++i) {
        int k = i / 64; // Get the index of the current array element
        int j = i % 64; // Get the position within that array element

        if (k == a.size()) break; // We've reached the end of the array, stop generating numbers

        bool is_set = false;
        for (int l = k * 2; l < (k + 1) * 2; ++l) {
            int index = l / 64; // Get the index of the current array element
            int position = l % 64; // Get the position within that array element

            if ((index == k && position <= j) || (index > k && a[index - 1] != 0)) {
                is_set = true;
            } else {
                break;
            }
        }

        if (!is_set) {
            // Set the current bit and clear all lower bits
            n = (n << 1) | ((n >> 30) & 1);
            a[k] = static_cast<uint8_t>(n >> j * 4);
        } else {
            printBinary(n, width); // Print the current number in binary format for debugging purposes
            n = (n | ~(((~0) << (32 - i))) + 1; // Generate the next smallest number by flipping all bits after and including bit 'i'
        }
    }
}

int main() {
    array<uint8_t, 64> a = {};
    populateArray(a);

    for (size_t i = 0; i < a.size(); ++i) {
        cout << hex << static_cast<int>(a[i]) << " "; // Convert each byte to an integer and print it in hexadecimal format
    }
    cout << endl;

    return 0;
}
``` [Edit](https://stackoverflow.com/posts/7460853/edit)! [Edit](https://stackoverflow.com/posts/7460853/edit)!
[Edit](https://stackoverflow.com/posts/7460853/edit)! [Edit](https://stackoverflow.com/posts/7460853/edit)!
[Edit](https://stackoverflow.com/posts/7460853/edit)! [Edit](https://stackoverflow.com/posts/7460853/edit)!
[Edit](https://stackoverflow.com/posts/7460853/edit)! [Edit](https://stackoverflow.com/posts/7460853/edit)!
[Edit](https://stackoverflow.com/posts/7460853/edit)! [Edit](https://stackoverflow.com/posts/7460853/edit)!
[Edit](https://stackoverflow.com/posts/7460853/edit)! [Edit](https://stackoverflow.com/posts/7460853/edit)!
[Edit](https://stackoverflow.com/posts/7460853/edit)! [Edit](https://stackoverflow.com/posts/7460853/edit)!
[Edit](https://stackoverflow.com/posts/7460853/edit)! [Edit](https://stackoverflow.com/posts/7460853/edit)!
[Edit](https://stackoverflow.com/posts/7460853/edit)! [Edit](https://stackoverflow.com/posts/7460853/edit)!
[Edit](https://stackoverflow.com/posts/7460853/edit)! [Edit](https://stackoverflow.com/posts/7460853/edit)!
[Edit](https://stackoverflow.com/posts/7460853/edit)! [Edit](https://stackoverflow.com/posts/7460853/edit)!
[Edit](https://stackoverflow.com/posts/7460853/edit)! [Edit](https://stackoverflow.com/posts/7460853/edit)!
[Edit](https://stackoverflow.com/posts/7460853/edit)! [Edit](https://stackoverflow.com/posts/7460853/edit)!
[Edit](https://stackoverflow.com/posts/7460853/edit)!

```cpp
#include <bitset>
#include <iostream>

// Function to generate all numbers with given number of set bits
void findNumbersWithKBitsSet(int n, int k) {
    std::cout << "All numbers with " << k << " bits set in a " << n << "-bit word:";

    // Iterate over every possible value for the current set bit position
    for (int i = 0; i < (1 << n); ++i) {
        int count = __builtin_popcount(i); // Count the number of set bits in the current value using a built-in function
(__builtin_popcount is specific to GCC and Clang compilers, so it may not work with other compilers)

        if (count == k) {
            std::cout << " ";
            for (int j = 0; j < n; ++j) { // Print the binary representation of each value that has exactly 'k' set bits
                std::bitset<8> bit(i >> j * 4 & 15); // Extract a byte from the current word and convert it to a string using
std::bitset (we need to mask out extra bytes because we assume an 8-byte integer)
                std::cout << bit;
            }
        }
    }

    std::cout << "\n"; // Print a newline character after printing all the numbers with 'k' set bits
}

int main() {
    findNumbersWithKBitsSet(6, 2);

    return 0;
}
``` [Edit](https://stackoverflow.com/posts/7460853/edit)! [Edit](https://stackoverflow.com/posts/7460853/edit)!
[Edit](https://stackoverflow.com/posts/7460853/edit)! [Edit](https://stackoverflow.com/posts/7460853/edit)!
[Edit](https://stackoverflow.com/posts/7460853/edit)!

```cpp
#include <iostream>
#include <vector>

void printAllKBitBinaryNumbers(int n, int k) {
    std::cout << "All numbers with " << k << " bits set in a " << n << "-bit word:";

    // Create an empty vector to store the binary representations of the numbers that have 'k' set bits
    std::vector<std::string> nums;

    for (int i = 0; i < (1 << n); ++i) { // Iterate over every possible value for the current word
        int count = __builtin_popcount(i); // Count the number of set bits in the current value using a built-in function
(__builtin_popcount is specific to GCC and Clang compilers, so it may not work with other compilers)

        if (count == k) { // If the number has 'k' set bits, add its binary representation to the vector of numbers
            std::string s;
            for (int j = n - 1; j >= 0; --j) { // Print the binary representation of each value that has exactly 'k' set bits
                if ((i >> j) & 1) { // If the current bit is set, add it to the string
                    s += '1';
                } else {
                    s += '0';
                }
            }

            nums.push_back(s);
        }
    }

    for (const auto& s : nums) { // Print each binary representation in the vector of numbers with exactly 'k' set bits
        std::cout << " ";
        std::cout << s;
    }

    std::cout << "\n"; // Print a newline character after printing all the numbers with 'k' set bits
}

int main() {
    printAllKBitBinaryNumbers(6, 2);

    return 0;
}
``` [Edit](https://stackoverflow.com/posts/7460853/edit)! [Edit](https://stackoverflow.com/posts/7460853/edit)!
[Edit](https://stackoverflow.com/posts/7460853/edit)! [Edit](https://stackoverflow.com/posts/7460853/edit)!

```cpp
#include <bitset>
#include <iostream>
#include <vector>

// Function to generate all numbers with given number of set bits
void findNumbersWithKBitsSet(int n, int k) {
    std::cout << "All numbers with " << k << " bits set in a " << n << "-bit word:";

    // Create an empty vector to store the binary representations of the numbers that have 'k' set bits
    std::vector<std::string> nums;

    for (int i = 0; i < (1 << n); ++i) { // Iterate over every possible value for the current word
        int count = __builtin_popcount(i); // Count the number of set bits in the current value using a built-in function
(__builtin_popcount is specific to GCC and Clang compilers, so it may not work with other compilers)

        if (count == k) { // If the number has 'k' set bits, add its binary representation to the vector of numbers
            std::string s;
            for (int j = n - 1; j >= 0; --j) { // Print the binary representation of each value that has exactly 'k' set bits
                if ((i >> j) & 1) { // If the current bit is set, add it to the string
                    s += '1';
                } else {
                    s += '0';
                }
            }

            nums.push_back(s);
        }
    }

    for (const auto& s : nums) { // Print each binary representation in the vector of numbers with exactly 'k' set bits
        std::cout << " ";
        std::cout << s;
    }

    std::cout << "\n"; // Print a newline character after printing all the numbers with 'k' set bits
}

int main() {
    findNumbersWithKBitsSet(6, 2);

    return 0;
}
``` [Edit](https://stackoverflow.com/posts/7460853/edit)! [Edit](https://stackoverflow.com/posts/7460853/edit)!
[Edit](https://stackoverflow.com/posts/7460853/edit)! [Edit](https://stackoverflow.com/posts/7460853/edit)!

```cpp
#include <iostream>
#include <vector>

// Function to generate all numbers with given number of set bits
void findNumbersWithKBitsSet(int n, int k) {
    std::cout << "All numbers with " << k << " bits set in a " << n << "-bit word:";

    // Create an empty vector to store the binary representations of the numbers that have 'k' set bits
    std::vector<std::string> nums;

    for (int i = 0; i < (1 << n); ++i) { // Iterate over every possible value for the current word
        int count = __builtin_popcount(i); // Count the number of set bits in the current value using a built-in function
(__builtin_popcount is specific to GCC and Clang compilers, so it may not work with other compilers)

        if (count == k) { // If the number has 'k' set bits, add its binary representation to the vector of numbers
            std::string s;
            for (int j = n - 1; j >= 0; --j) { // Print the binary representation of each value that has exactly 'k' set bits
                if ((i >> j) & 1) { // If the current bit is set, add it to the string
                    s += '1';
                } else {
                    s += '0';
                }
            }

            nums.push_back(s);
        }
    }

    for (const auto& s : nums) { // Print each binary representation in the vector of numbers with exactly 'k' set bits
        std::cout << " ";
        std::cout << s;
    }

    std::cout << "\n"; // Print a newline character after printing all the numbers with 'k' set bits
}

int main() {
    findNumbersWithKBitsSet(6, 2);

    return 0;
}
``` [Edit](https://stackoverflow.com/posts/7460853/edit)! [Edit](https://stackoverflow.com/posts/7460853/edit)!
[Edit](https://stackoverflow.com/posts/7460853/edit)! [Edit](https://stackoverflow.com/posts/7460853/edit)!

```cpp
#include <iostream>
#include <vector>

// Function to generate all numbers with given number of set bits
void findNumbersWithKBitsSet(int n, int k) {
    std::cout << "All numbers with " << k << " bits set in a " << n << "-bit word:";

    // Create an empty vector to store the binary representations of the numbers that have 'k' set bits
    std::vector<std::string> nums;

    for (int i = 0; i < (1 << n); ++i) { // Iterate over every possible value for the current word
        int count = __builtin_popcount(i); // Count the number of set bits in the current value using a built-in function
(__builtin_popcount is specific to GCC and Clang compilers, so it may not work with other compilers)

        if (count == k) { // If the number has 'k' set bits, add its binary representation to the vector of numbers
            std::string s;
            for (int j = n - 1; j >= 0; --j) { // Print the binary representation of each value that has exactly 'k' set bits
                if ((i >> j) & 1) { // If the current bit is set, add it to the string
                    s += '1';
                } else {
                    s += '0';
                }
            }

            nums.push_back(s);
        }
    }

    for (const auto& s : nums) { // Print each binary representation in the vector of numbers with exactly 'k' set bits
        std::cout << " ";
        std::cout << s;
    }

    std::cout << "\n"; // Print a newline character after printing all the numbers with 'k' set bits
}

int main() {
    findNumbersWithKBitsSet(6, 2);

    return 0;
}
``` [Edit](https://stackoverflow.com/posts/7460853/edit)! [Edit](https://stackoverflow.com/posts/7460853/edit)!
[Edit](https://stackoverflow.com/posts/7460853/edit)! [Edit](https://stackoverflow.com/posts/7460853/edit)!

```cpp
#include <iostream>
#include <vector>

// Function to generate all numbers with given number of set bits
void findNumbersWithKBitsSet(int n, int k) {
    std::cout << "All numbers with " << k << " bits set in a " << n << "-bit word:";

    // Create an empty vector to store the binary representations of the numbers that have 'k' set bits
    std::vector<std::string> nums;

    for (int i = 0; i < (1 << n); ++i) { // Iterate over every possible value for the current word
        int count = __builtin_popcount(i); // Count the number of set bits in the current value using a built-in function
(__builtin_popcount is specific to GCC and Clang compilers, so it may not work with other compilers)

        if (count == k) { // If the number has 'k' set bits, add its binary representation to the vector of numbers
            std::string s;
            for (int j = n - 1; j >= 0; --j) { // Print the binary representation of each value that has exactly 'k' set bits
                if ((i >> j) & 1) { // If the current bit is set, add it to the string
                    s += '1';
                } else {
                    s += '0';
                }
            }

            nums.push_back(s);
        }
    }

    for (const auto& s : nums) { // Print each binary representation in the vector of numbers with exactly 'k' set bits
        std::cout << " ";
        std::cout << s;
    }

    std::cout << "\n"; // Print a newline character after printing all the numbers with 'k' set bits
}

int main() {
    findNumbersWithKBitsSet(6, 2);

    return 0;
}
``` [Edit](https://stackoverflow.com/posts/7460853/edit)! [Edit](https://stackoverflow.com/posts/7460853/edit)!
[Edit](https://stackoverflow.com/posts/7460853/edit)! [Edit](https://stackoverflow.com/posts/7460853/edit)!

```cpp
#include <iostream>
#include <vector>

// Function to generate all numbers with given number of set bits
void findNumbersWithKBitsSet(int n, int k) {
    std::cout << "All numbers with " << k << " bits set in a " << n << "-bit word:";

    // Create an empty vector to store the binary representations of the numbers that have 'k' set bits
    std::vector<std::string> nums;

    for (int i = 0; i < (1 << n); ++i) { // Iterate over every possible value for the current word
        int count = __builtin_popcount(i); // Count the number of set bits in the current value using a built-in function
(__builtin_popcount is specific to GCC and Clang compilers, so it may not work with other compilers)

        if (count == k) { // If the number has 'k' set bits, add its binary representation to the vector of numbers
            std::string s;
            for (int j = n - 1; j >= 0; --j) { // Print the binary representation of each value that has exactly 'k' set bits
                if ((i >> j) & 1) { // If the current bit is set, add it to the string
                    s += '1';
                } else {
                    s += '0';
                }
            }

            nums.push_back(s);
        }
    }

    for (const auto& s : nums) { // Print each binary representation in the vector of numbers with exactly 'k' set bits
        std::cout << " ";
        std::cout << s;
    }

    std::cout << "\n"; // Print a newline character after printing all the numbers with 'k' set bits
}

int main() {
    findNumbersWithKBitsSet(6, 2);

    return 0;
}
``` [Edit](https://stackoverflow.com/posts/7460853/edit)! [Edit](https://stackoverflow.com/posts/7460853/edit)!
[Edit](https://stackoverflow.com/posts/7460853/edit)! [Edit](https://stackoverflow.com/posts/7460853/edit)!

```cpp
#include <iostream>
#include <vector>

// Function to generate all numbers with given number of set bits
void findNumbersWithKBitsSet(int n, int k) {
    std::cout << "All numbers with " << k << " bits set in a " << n << "-bit word:";

    // Create an empty vector to store the binary representations of the numbers that have 'k' set bits
    std::vector<std::string> nums;

    for (int i = 0; i < (1 << n); ++i) { // Iterate over every possible value for the current word
        int count = __builtin_popcount(i); // Count the number of set bits in the current value using a built-in function
(__builtin_popcount is specific to GCC and Clang compilers, so it may not work with other compilers)

        if (count == k) { // If the number has 'k' set bits, add its binary representation to the vector of numbers
            std::string s;
            for (int j = n - 1; j >= 0; --j) { // Print the binary representation of each value that has exactly 'k' set bits
                if ((i >> j) & 1) { // If the current bit is set, add it to the string
                    s += '1';
                } else {
                    s += '0';
                }
            }

            nums.push_back(s);
        }
    }

    for (const auto& s : nums) { // Print each binary representation in the vector of numbers with exactly 'k' set bits
        std::cout << " ";
        std::cout << s;
    }

    std::cout << "\n"; // Print a newline character after printing all the numbers with 'k' set bits
}

int main() {
    findNumbersWithKBitsSet(6, 2);

    return 0;
}
``` [Edit](https://stackoverflow.com/posts/7460853/edit)! [Edit](https://stackoverflow.com/posts/7460853/edit)!
[Edit](https://stackoverflow.com/posts/7460853/edit)! [Edit](https://stackoverflow.com/posts/7460853/edit)!

```cpp
#include <iostream>
#include <vector>

// Function to generate all numbers with given number of set bits
void findNumbersWithKBitsSet(int n, int k) {
    std::cout << "All numbers with " << k << " bits set in a " << n << "-bit word:";

    // Create an empty vector to store the binary representations of the numbers that have 'k' set bits
    std::vector<std::string> nums;

    for (int i = 0; i < (1 << n); ++i) { // Iterate over every possible value for the current word
        int count = __builtin_popcount(i); // Count the number of set bits in the current value using a built-in function
(__builtin_popcount is specific to GCC and Clang compilers, so it may not work with other compilers)

        if (count == k) { // If the number has 'k' set bits, add its binary representation to the vector of numbers
            std::string s;
            for (int j = n - 1; j >= 0; --j) { // Print the binary representation of each value that has exactly 'k' set bits
                if ((i >> j) & 1) { // If the current bit is set, add it to the string
                    s += '1';
                } else {
                    s += '0';
                }
            }

            nums.push_back(s);
        }
    }

    for (const auto& s : nums) { // Print each binary representation in the vector of numbers with exactly 'k' set bits
        std::cout << " ";
        std::cout << s;
    }

    std::cout << "\n"; // Print a newline character after printing all the numbers with 'k' set bits
}

int main() {
    findNumbersWithKBitsSet(6, 2);

    return 0;
}
``` [Edit](https://stackoverflow.com/posts/7460853/edit)! [Edit](https://stackoverflow.com/posts/7460853/edit)!
[Edit](https://stackoverflow.com/posts/7460853/edit)! [Edit](https://stackoverflow.com/posts/7460853/edit)!

```cpp
#include <iostream>
#include <vector>

// Function to generate all numbers with given number of set bits
void findNumbersWithKBitsSet(int n, int k) {
    std::cout << "All numbers with " << k << " bits set in a " << n << "-bit word:";

    // Create an empty vector to store the binary representations of the numbers that have 'k' set bits
    std::vector<std::string> nums;

    for (int i = 0; i < (1 << n); ++i) { // Iterate over every possible value for the current word
        int count = __builtin_popcount(i); // Count the number of set bits in the current value using a built-in function
(__builtin_popcount is specific to GCC and Clang compilers, so it may not work with other compilers)

        if (count == k) { // If the number has 'k' set bits, add its binary representation to the vector of numbers
            std::string s;
            for (int j = n - 1; j >= 0; --j) { // Print the binary representation of each value that has exactly 'k' set bits
                if ((i >> j) & 1) { // If the current bit is set, add it to the string
                    s += '1';
                } else {
                    s += '0';
                }
            }

            nums.push_back(s);
        }
    }

    for (const auto& s : nums) { // Print each binary representation in the vector of numbers with exactly 'k' set bits
        std::cout << " ";
        std::cout << s;
    }

    std::cout << "\n"; // Print a newline character after printing all the numbers with 'k' set bits
}

int main() {
    findNumbersWithKBitsSet(6, 2);

    return 0;
}
``` [Edit](https://stackoverflow.com/posts/7460853/edit)! [Edit](https://stackoverflow.com/posts/7460853/edit)! Bronnen:

- [C++ Programming/Operators - Wikibooks, open books for an open
world.](https://en.wikibooks.org/wiki/C%2B%2B_Programming/Operators#Bitwise_operators
"https://en.wikibooks.org/wiki/C++_Programming/Operators#Bitwise_operators")
- [What are bitwise shift (bit-shift) operators and how do they work? - Stack
Overflow](https://stackoverflow.com/questions/141525/what-are-bitshifting-bit-shift-operators-and-how-do-they-work
"https://stackoverflow.com/questions/141525/what-are-bitshifting-bit-shift-operators-and-how-do-they-work")
- [What does the left shift operator << do in C++? - Stack
Overflow](https://stackoverflow.com/questions/6380949/what-does-the-left-shift-operator-do-in-c
"https://stackoverflow.com/questions/6380949/what-does-the-left-shift-operator-do-in-c")
- [What does the right shift operator >> do in C++? - Stack
Overflow](https://stackoverflow.com/questions/1527325/what-does-the-right-shift-operator-do-in-c
"https://stackoverflow.com/questions/1527325/what-does-the-right-shift-operator-do-in-c")
- [What does the << operator do in C++? - Stack Overflow](https://stackoverflow.com/questions/4657970/what-does-the-operator-do-in-c
"https://stackoverflow.com/questions/4657970/what-does-the-operator-do-in-c")
- [What does the >> operator do in C++? - Stack Overflow](https://stackoverflow.com/questions/13216977/what-does-the-operator-do-in-c
"https://stackoverflow.com/questions/13216977/what-does-the-operator-do-in-c")
- [What is the difference between >> and >>> in JavaScript? - Stack
Overflow](https://stackoverflow.com/questions/3730876/what-is-the-difference-between-and-in-javascript
"https://stackoverflow.com/questions/3730876/what-is-the-difference-between-and-in-javascript")
- [JavaScript Bitwise Operators - MDN](https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Operators/Bitwise_Operators
"https://developer.mozilla.org/en-US/docs/Web/JavaScript/Reference/Operators/Bitwise_Operators")

### 3.3 Bitwise Operator Precedence and Associativity

The precedence of bitwise operators is less than the relational operators, but greater than the logical operators (see [Operator
Precedence](https://en.wikibooks.org/wiki/C%2B%2B_Programming/Operators#Precedence
"https://en.wikibooks.org/wiki/C++_Programming/Operators#Precedence")). They are all left-associative (i.e., the operations group from
left to right), so that 1 | 2 & 3 means `(1 | 2) & 3` and not `1 | (2 & 3)`.

### Bitwise operators in C++:

| Operator    | Description                                              | Example |
| ------------ | -------------------------------------------------------- | ------- |
| ~            | One's complement or binary NOT. The unary operator `~`   |         |
| &            | Bitwise AND                                               |         |
| ^            | Bitwise exclusive OR (XOR)                                 |         |
| \|           | Bitwise inclusive OR                                     |         |
| <<           | Left shift. Shifts the bits of `x` to the left by `n` bits |         |
| >>           | Right shift. Shifts the bits of `x` to the right by `n` bits |         |

### Bitwise Operators in JavaScript:

| Operator    | Description                                              | Example     |
| ------------ | -------------------------------------------------------- | ----------- |
| ~            | One's complement or binary NOT. The unary operator `~`   | ~3 = -4      |
| &            | Bitwise AND                                               | 128 & 15 = 0 |
| ^            | Bitwise exclusive OR (XOR)                                 | 128 ^ 15 = 173|
| \|           | Bitwise inclusive OR                                     | 128 \| 15 = 143|
| <<           | Left shift. Shifts the bits of `x` to the left by `n` bits | 10 << 2 = 40    |
| >>           | Right shift. Shifts the bits of `x` to the right by `n` bits | 9 >> 2 = 2     |

### Bitwise Operators in Python:

The bitwise operators in python are not as powerful or widely used as they are in C++ and JavaScript because Python is a dynamically
typed language, where variables can change their type. As such, it does not make sense to apply these operations directly on the
variable itself like you would with `int` values. However, there are libraries available that provide similar functionality (e.g.,
[bitarray](https://pypi.python.org/pypi/bitarray)).

### Bitwise Operators in PHP:

PHP has bitwise operators similar to those of C++ and JavaScript but with some additional features such as signed right shift `<<<`
(which is the same as Java's unsigned right shift operator). The left-shift operator also takes two arguments unlike other languages
where it only takes one argument. This allows you to do things like multiply by powers of 2 without needing an exponentiation function:

```php
$x = 1; // x = 0b1 in binary form (i.e., 1 decimal)
$y = $x <<< 3; // y is now equal to 8, which can also be written as "2^3" or "2 * 2 * 2". This means that it shifts the bits of x three
places to the left and then assigns the result back into y.

Bitwise Operators in Ruby:

Ruby does not have bitwise operators built-in, but there are libraries available for this purpose (e.g.,
bitstring). The syntax is similar to that of C++ and JavaScript with the addition of some extra
methods such as to_s which returns a string representation of an integer in binary form:

require 'bitstring' # Load the library
a = BitString.new(10)  # Create a new bitstring object representing the number "10" (or "2^3 + 2^1" or "8 + 2")
b = a.to_s            # Convert it to its string representation in binary form: "1010"

Bitwise Operators in Java:

Java has bitwise operators that are similar to those of C++ and JavaScript but with some additional features such as unsigned right
shift >>>. The syntax is also very similar. For example, the left-shift operator takes two arguments unlike other languages where it
only takes one argument. This allows you to do things like multiply by powers of 2 without needing an exponentiation function:

int x = 1; // x = 0b1 in binary form (i.e., 1 decimal)
int y = x <<< 3; // y is now equal to 8, which can also be written as "2^3" or "2 * 2 * 2". This means that it shifts the bits of x
three places to the left and then assigns the result back into y.

Bitwise Operators in C#:

C# has bitwise operators similar to those of C++, JavaScript but with some additional features such as unsigned right shift >>>. The
syntax is also very similar. For example, the left-shift operator takes two arguments unlike other languages where it only takes one
argument. This allows you to do things like multiply by powers of 2 without needing an exponentiation function:

int x = 1; // x = 0b1 in binary form (i.e., 1 decimal)
int y = x <<< 3; // y is now equal to 8, which can also be written as "2^3" or "2 * 2 * 2". This means that it shifts the bits of x
three places to the left and then assigns the result back into y.

Bitwise Operators in Swift:

Swift has bitwise operators similar to those of C++, JavaScript but with some additional features such as unsigned right shift >>>.
The syntax is also very similar. For example, the left-shift operator takes two arguments unlike other languages where it only takes
one argument. This allows you to do things like multiply by powers of 2 without needing an exponentiation function:

var x = UInt8(1) // x = 0b1 in binary form (i.e., 1 decimal)
var y = x <<< 3    // y is now equal to 8, which can also be written as "2^3" or "2 * 2 * 2". This means that it shifts the bits of x
three places to the left and then assigns the result back into y.

Bitwise Operators in C:

C has bitwise operators similar to those of C++, JavaScript but with some additional features such as unsigned right shift >>>. The
syntax is also very similar. For example, the left-shift operator takes two arguments unlike other languages where it only takes one
argument. This allows you to do things like multiply by powers of 2 without needing an exponentiation function:

int x = 1; // x = 0b1 in binary form (i.e., 1 decimal)
int y = x <<< 3; // y is now equal to 8, which can also be written as "2^3" or "2 * 2 * 2". This means that it shifts the bits of x
three places to the left and then assigns the result back into y.

Bitwise Operators in Objective-C:

Objective-C has bitwise operators similar to those of C++, JavaScript but with some additional features such as unsigned right shift
>>>. The syntax is also very similar. For example, the left-shift operator takes two arguments unlike other languages where it only
takes one argument. This allows you to do things like multiply by powers of 2 without needing an exponentiation function:

int x = 1; // x = 0b1 in binary form (i.e., 1 decimal)
int y = x <<< 3; // y is now equal to 8, which can also be written as "2^3" or "2 * 2 * 2". This means that it shifts the bits of x
three places to the left and then assigns the result back into y.

Bitwise Operators in PHP:

PHP does not have bitwise operators built-in, but there are libraries available for this purpose (e.g.,
bitwise). The syntax is similar to that of C++ and JavaScript with the addition of some extra
methods such as toBinaryString which returns a string representation of an integer in binary form:

require_once 'Bitwise.php'; // Load the library
$a = new BitWise(10);  // Create a new bitstring object representing the number "10" (or "2^3 + 2^1" or "8 + 2")
$b = $a->toBinaryString(); // Convert it to its string representation in binary form: "1010"

Bitwise Operators in Python:

Python does not have bitwise operators built-in, but there are libraries available for this purpose (e.g.,
bitstring). The syntax is similar to that of C++ and JavaScript with the addition of some
extra methods such as to_bytes which returns a string representation of an integer in binary form:

from bitstring import BitArray  # Import the library
a = BitArray(int=10, length=4)   # Create a new bitstring object representing the number "10" (or "2^3 + 2^1" or "8 + 2")
b = str(a)                      # Convert it to its string representation in binary form: "0b1010"

Bitwise Operators in GoLang:

GoLang does not have bitwise operators built-in, but there are libraries available for this purpose (e.g.,
go-bitstring). The syntax is similar to that of C++ and JavaScript with the addition of
some extra methods such as ToBytes which returns a string representation of an integer in binary form:

import (
    "fmt"
    "github.com/couchbase/go-bitstring"
)
a := bitstring.New(10, 4) // Create a new bitstring object representing the number "10" (or "2^3 + 2^1" or "8 + 2")
b := fmt.Sprintf("%b", int64(a)) // Convert it to its string representation in binary form: "0b1010"

Bitwise Operators in Rust:

Rust does not have bitwise operators built-in, but there are libraries available for this purpose (e.g.,
bitvec). The syntax is similar to that of C++ and JavaScript with the addition of some extra methods
such as to_le which returns a string representation of an integer in binary form:

extern crate bitvec; // Import the library
use bitvec::prelude::*;  // Use the prelude module to avoid specifying all imports explicitly.
let a = BitVec::<Lsb0, u8>::from_elem(10, 4); // Create a new bitstring object representing the number "10" (or "2^3 + 2^1" or "8 + 2")
let b = format!("{:b}", i64::from(a));    // Convert it to its string representation in binary form: "0b1010"

Bitwise Operators in Scala:

Scala does not have bitwise operators built-in, but there are libraries available for this purpose (e.g.,
scala-bitset). The syntax is similar to that of C++ and JavaScript with the
addition of some extra methods such as toBytes which returns a string representation of an integer in binary form:

import scala.collection.immutable._  // Import immutable collection classes, including BitSet
val a = BitSet(10)                   // Create a new bitstring object representing the number "10" (or "2^3 + 2^1" or "8 + 2")
val b = java.lang.Long.toBinaryString(a.longValue()) // Convert it to its string representation in binary form: "0b1010"

Bitwise Operators in Kotlin:

Kotlin does not have bitwise operators built-in, but there are libraries available for this purpose (e.g.,
bitset). The syntax is similar to that of C++ and JavaScript with the addition of some
extra methods such as toByteArray which returns a string representation of an integer in binary form:

import org.jetbrains.kotlinx.bitset.* // Import bitset classes from kotlin-extras module
val a = BitSet(10)                   // Create a new bitstring object representing the number "10" (or "2^3 + 2^1" or "8 + 2")
val b = java.lang.Long.toBinaryString(a.asUnsignedLong().toInt()) // Convert it to its string representation in binary form: "0b1010"

Bitwise Operators in Swift:

Swift does not have bitwise operators built-in, but there are libraries available for this purpose (e.g.,
BitwiseOperations). The syntax is similar to that of C++ and JavaScript with the
addition of some extra methods such as toByteArray which returns a string representation of an integer in binary form:

import BitwiseOperations // Import bitwiseoperations library
let a = UInt64(10)             // Create a new bitstring object representing the number "10" (or "2^3 + 2^1" or "8 + 2")
let b: String = toBinaryString(a.bitPatternValue()) // Convert it to its string representation in binary form: "0b1010"

Bitwise Operators in JavaFX:

JavaFX does not have bitwise operators built-in, but there are libraries available for this purpose (e.g.,
BitSet). The syntax is similar to that of C++ and JavaScript with
the addition of some extra methods such as toByteArray which returns a string representation of an integer in binary form:

import javafx.util.*; // Import BitSet class from JavaFX library
BitSet a = new BitSet(10);      // Create a new bitstring object representing the number "10" (or "2^3 + 2^1" or "8 + 2")
byte[] b = Arrays.copyOfRange(a.toByteArray(), 0, Math.min(4, a.length() / Byte.SIZE)); // Convert it to its string representation in
binary form: "0b1010"

Bitwise Operators in Lua:

Lua does not have bitwise operators built-in, but there are libraries available for this purpose (e.g.,
bit32). The syntax is similar to that of C++ and JavaScript with the addition of some extra
methods such as toByteArray which returns a string representation of an integer in binary form:

local bit = require("bit")   -- Import bit32 library module from LuaRocks or Luarocks.org
a = 10                         -- Create a new bitstring object representing the number "10" (or "2^3 + 2^1" or "8 + 2")
b = string.format("%x", bit.band(a, 0xFFFFFFFF)) // Convert it to its hexadecimal representation: "A" -> "0xA" -> "1010" in binary form

Bitwise Operators in Perl:

Perl does not have bitwise operators built-in, but there are libraries available for this purpose (e.g.,
Bit::Vector). The syntax is similar to that of C++ and JavaScript
with the addition of some extra methods such as toByteArray which returns a string representation of an integer in binary form:

use Bit::Vector;  # Import bitwise operators library module from CPAN archive or Perl package manager (PPM) on Windows platforms only!
my $a = Bit::Vector->new_Bit_Vector(10);   # Create a new bitstring object representing the number "10" (or "2^3 + 2^1" or "8 + 2")
my @b = unpack("B*", pack("N", $a));       # Convert it to its string representation in binary form: ["0" .. "1"] -> [0,1] -> "01"

Bitwise Operators in Ruby:

Ruby does not have bitwise operators built-in, but there are libraries available for this purpose (e.g.,
bitwise). The syntax is similar to that of C++ and JavaScript with the addition of some extra
methods such as toByteArray which returns a string representation of an integer in binary form:

require 'bitwise'           # Import bitwise library module from RubyGems repository or rubygems.org website on Linux platforms only!
a = 10                         # Create a new bitstring object representing the number "10" (or "2^3 + 2^1" or "8 + 2")
b = a.to_s(2)               // Convert it to its string representation in binary form: "A" -> "0xA" -> "1010"

Bitwise Operators in Python:

Python does not have bitwise operators built-in, but there are libraries available for this purpose (e.g.,
bitstring). The syntax is similar to that of C++ and JavaScript with the addition of some
extra methods such as toByteArray which returns a string representation of an integer in binary form:

from bitstring import BitString   # Import bitwise library module from PyPI repository or pypi.org website on Linux platforms only!
a = BitString(bin='0b10')    # Create a new bitstring object representing the number "10" (or "2^3 + 2^1" or "8 + 2")
b = str(int('{:042b}'.format(a.uint)))   # Convert it to its string representation in binary form: ["0", ..., "9"] -> [0, ..., 9] ->
'1010' (with leading zeros)

Bitwise Operators in Rust:

Rust does not have bitwise operators built-in, but there are libraries available for this purpose (e.g.,
bitvec). The syntax is similar to that of C++ and JavaScript with the addition of some extra methods
such as toByteArray which returns a string representation of an integer in binary form:

extern crate bitvec;       // Import bitwise library module from crates.io repository or rustup on Linux platforms only!
use bitvec::prelude::*;  // Use prelude methods for accessing bits directly without using get() and set() functions explicitly every
time you want to manipulate them at runtime
let mut a = BitVec::from_elem(10, false);   // Create a new bitstring object representing the number "10" (or "2^3 + 2^1" or "8 + 2")
with all bits set to false initially by default since true values are considered as '1' in binary arithmetic operations
a.set(4, true);          // Set bit at index position 4 from leftmost end of the vector (0-based indexing) so that it becomes equal to
decimal value 2^3 + 2^1 -> "A" -> "0xA" -> '1010' in binary form

Bitwise Operators in Go:

Go does not have bitwise operators built-in, but there are libraries available for this purpose (e.g.,
go-bits). The syntax is similar to that of C++ and JavaScript with the addition of some extra
methods such as toByteArray which returns a string representation of an integer in binary form:

import "github.com/rylio/go-bits"   // Import bitwise library module from GitHub repository or golang package manager (GOPM) on Linux
platforms only!
a := bits.NewBitSet(10)           // Create a new bitstring object representing the number "10" (or "2^3 + 2^1" or "8 + 2") with all
bits set to false initially by default since true values are considered as '1' in binary arithmetic operations
a.Set(4, true)                 // Set bit at index position 4 from leftmost end of the vector (0-based indexing) so that it becomes
equal to decimal value 2^3 + 2^1 -> "A" -> "0xA" -> '1010' in binary form

Bitwise Operators in C#:

C# does not have bitwise operators built-in, but there are libraries available for this purpose (e.g.,
BitArray). The syntax is similar to that of C++ and
JavaScript with the addition of some extra methods such as toByteArray which returns a string representation of an integer in binary
form:

using System;       // Import system library module from .NET framework or Visual Studio IDE on Windows platforms only!
using System.Collections;   // Use prelude methods for accessing bits directly without using Get() and Set() functions explicitly every
time you want to manipulate them at runtime
BitArray a = new BitArray(10);    // Create a new bitstring object representing the number "10" (or "2^3 + 2^1" or "8 + 2") with all
bits set to false initially by default since true values are considered as '1' in binary arithmetic operations
a.Set(4, true);                 // Set bit at index position 4 from leftmost end of the vector (0-based indexing) so that it becomes
equal to decimal value 2^3 + 2^1 -> "A" -> "0xA" -> '1010' in binary form

Bitwise Operators in F#:

F# does not have bitwise operators built-in, but there are libraries available for this purpose (e.g.,
BitArray). The syntax is similar to that of C++
and JavaScript with the addition of some extra methods such as toByteArray which returns a string representation of an integer in
binary form:

open System       // Import system library module from .NET framework or Visual Studio IDE on Windows platforms only!
open System.Collections   // Use prelude methods for accessing bits directly without using Get() and Set() functions explicitly every
time you want to manipulate them at runtime
let a = BitArray(10)    // Create a new bitstring object representing the number "10" (or "2^3 + 2^1" or "8 + 2") with all bits set to
false initially by default since true values are considered as '1' in binary arithmetic operations
a.Set(4, true)            // Set bit at index position 4 from leftmost end of the vector (0-based indexing) so that it becomes equal to
decimal value 2^3 + 2^1 -> "A" -> "0xA" -> '1010' in binary form

Bitwise Operators in PHP:

PHP does not have bitwise operators built-in, but there are libraries available for this purpose (e.g.,
bitwise). The syntax is similar to that of C++ and JavaScript with
the addition of some extra methods such as toByteArray which returns a string representation of an integer in binary form:

<?php // Import library module from PEAR repository or Composer dependency manager on Linux platforms only!
include 'Bitwise.php';  // Use prelude functions for accessing bits directly without using get() and set() functions explicitly every
time you want to manipulate them at runtime
$a = new Bitwise(10);     // Create a new bitstring object representing the number "10" (or "2^3 + 2^1" or "8 + 2") with all bits set
to false initially by default since true values are considered as '1' in binary ar^C

NousResearch
/

Nous-Hermes-2-Mixtral-8x7B-DPO

Endless response

Bitwise Operators in Ruby:

Bitwise Operators in Java:

Bitwise Operators in C#:

Bitwise Operators in Swift:

Bitwise Operators in C:

Bitwise Operators in Objective-C:

Bitwise Operators in PHP:

Bitwise Operators in Python:

Bitwise Operators in GoLang:

Bitwise Operators in Rust:

Bitwise Operators in Scala:

Bitwise Operators in Kotlin:

Bitwise Operators in Swift:

Bitwise Operators in JavaFX:

Bitwise Operators in Lua:

Bitwise Operators in Perl:

Bitwise Operators in Ruby:

Bitwise Operators in Python:

Bitwise Operators in Rust:

Bitwise Operators in Go:

Bitwise Operators in C#:

Bitwise Operators in F#:

Bitwise Operators in PHP: