Task: Partition an integer x into n primes

C: #include <assert.h>
#include <stdbool.h>
#include <stdint.h>
#include <stdio.h>
#include <stdlib.h>

typedef struct bit_array_tag {
    uint32_t size;
    uint32_t* array;
} bit_array;

bool bit_array_create(bit_array* b, uint32_t size) {
    uint32_t* array = calloc((size + 31)/32, sizeof(uint32_t));
    if (array == NULL)
        return false;
    b->size = size;
    b->array = array;
    return true;
}

void bit_array_destroy(bit_array* b) {
    free(b->array);
    b->array = NULL;
}

void bit_array_set(bit_array* b, uint32_t index, bool value) {
    assert(index < b->size);
    uint32_t* p = &b->array[index >> 5];
    uint32_t bit = 1 << (index & 31);
    if (value)
        *p |= bit;
    else
        *p &= ~bit;
}

bool bit_array_get(const bit_array* b, uint32_t index) {
    assert(index < b->size);
    uint32_t bit = 1 << (index & 31);
    return (b->array[index >> 5] & bit) != 0;
}

typedef struct sieve_tag {
    uint32_t limit;
    bit_array not_prime;
} sieve;

bool sieve_create(sieve* s, uint32_t limit) {
    if (!bit_array_create(&s->not_prime, limit + 1))
        return false;
    bit_array_set(&s->not_prime, 0, true);
    bit_array_set(&s->not_prime, 1, true);
    for (uint32_t p = 2; p * p <= limit; ++p) {
        if (bit_array_get(&s->not_prime, p) == false) {
            for (uint32_t q = p * p; q <= limit; q += p)
                bit_array_set(&s->not_prime, q, true);
        }
    }
    s->limit = limit;
    return true;
}

void sieve_destroy(sieve* s) {
    bit_array_destroy(&s->not_prime);
}

bool is_prime(const sieve* s, uint32_t n) {
    assert(n <= s->limit);
    return bit_array_get(&s->not_prime, n) == false;
}

bool find_prime_partition(const sieve* s, uint32_t number, uint32_t count,
                          uint32_t min_prime, uint32_t* p) {
    if (count == 1) {
        if (number >= min_prime && is_prime(s, number)) {
            *p = number;
            return true;
        }
        return false;
    }
    for (uint32_t prime = min_prime; prime < number; ++prime) {
        if (!is_prime(s, prime))
            continue;
        if (find_prime_partition(s, number - prime, count - 1,
                                 prime + 1, p + 1)) {
            *p = prime;
            return true;
        }
    }
    return false;
}

void print_prime_partition(const sieve* s, uint32_t number, uint32_t count) {
    assert(count > 0);
    uint32_t* primes = malloc(count * sizeof(uint32_t));
    if (primes == NULL) {
        fprintf(stderr, "Out of memory\n");
        return;
    }
    if (!find_prime_partition(s, number, count, 2, primes)) {
        printf("%u cannot be partitioned into %u primes.\n", number, count);
    } else {
        printf("%u = %u", number, primes[0]);
        for (uint32_t i = 1; i < count; ++i)
            printf(" + %u", primes[i]);
        printf("\n");
    }
    free(primes);
}

int main() {
    const uint32_t limit = 100000;
    sieve s = { 0 };
    if (!sieve_create(&s, limit)) {
        fprintf(stderr, "Out of memory\n");
        return 1;
    }
    print_prime_partition(&s, 99809, 1);
    print_prime_partition(&s, 18, 2);
    print_prime_partition(&s, 19, 3);
    print_prime_partition(&s, 20, 4);
    print_prime_partition(&s, 2017, 24);
    print_prime_partition(&s, 22699, 1);
    print_prime_partition(&s, 22699, 2);
    print_prime_partition(&s, 22699, 3);
    print_prime_partition(&s, 22699, 4);
    print_prime_partition(&s, 40355, 3);
    sieve_destroy(&s);
    return 0;
}


C++: #include <algorithm>
#include <functional>
#include <iostream>
#include <vector>

std::vector<int> primes;

struct Seq {
public:
    bool empty() {
        return p < 0;
    }

    int front() {
        return p;
    }

    void popFront() {
        if (p == 2) {
            p++;
        } else {
            p += 2;
            while (!empty() && !isPrime(p)) {
                p += 2;
            }
        }
    }

private:
    int p = 2;

    bool isPrime(int n) {
        if (n < 2) return false;
        if (n % 2 == 0) return n == 2;
        if (n % 3 == 0) return n == 3;

        int d = 5;
        while (d * d <= n) {
            if (n % d == 0) return false;
            d += 2;
            if (n % d == 0) return false;
            d += 4;
        }
        return true;
    }
};


void init() {
    Seq seq;

    while (!seq.empty() && primes.size() < 50000) {
        primes.push_back(seq.front());
        seq.popFront();
    }
}

bool findCombo(int k, int x, int m, int n, std::vector<int>& combo) {
    if (k >= m) {
        int sum = 0;
        for (int idx : combo) {
            sum += primes[idx];
        }

        if (sum == x) {
            auto word = (m > 1) ? "primes" : "prime";
            printf("Partitioned %5d with %2d %s ", x, m, word);
            for (int idx = 0; idx < m; ++idx) {
                std::cout << primes[combo[idx]];
                if (idx < m - 1) {
                    std::cout << '+';
                } else {
                    std::cout << '\n';
                }
            }
            return true;
        }
    } else {
        for (int j = 0; j < n; j++) {
            if (k == 0 || j > combo[k - 1]) {
                combo[k] = j;
                bool foundCombo = findCombo(k + 1, x, m, n, combo);
                if (foundCombo) {
                    return true;
                }
            }
        }
    }

    return false;
}

void partition(int x, int m) {
    if (x < 2 || m < 1 || m >= x) {
        throw std::runtime_error("Invalid parameters");
    }

    std::vector<int> filteredPrimes;
    std::copy_if(
        primes.cbegin(), primes.cend(),
        std::back_inserter(filteredPrimes),
        [x](int a) { return a <= x; }
    );

    int n = filteredPrimes.size();
    if (n < m) {
        throw std::runtime_error("Not enough primes");
    }

    std::vector<int> combo;
    combo.resize(m);
    if (!findCombo(0, x, m, n, combo)) {
        auto word = (m > 1) ? "primes" : "prime";
        printf("Partitioned %5d with %2d %s: (not possible)\n", x, m, word);
    }
}

int main() {
    init();

    std::vector<std::pair<int, int>> a{
        {99809,  1},
        {   18,  2},
        {   19,  3},
        {   20,  4},
        { 2017, 24},
        {22699,  1},
        {22699,  2},
        {22699,  3},
        {22699,  4},
        {40355,  3}
    };

    for (auto& p : a) {
        partition(p.first, p.second);
    }

    return 0;
}