Task: Partition an integer x into n primes


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;
}







VB: 
    dim p(),a(32),b(32),v,g: redim p(64)
    what="99809 1  18 2  19 3  20 4  2017 24  22699 1-4  40355 3"
    t1=split(what,"  ")
    for j=0 to ubound(t1)
        t2=split(t1(j)): x=t2(0): n=t2(1)
        t3=split(x,"-"): x=clng(t3(0))
        if ubound(t3)=1 then y=clng(t3(1)) else y=x
        t3=split(n,"-"): n=clng(t3(0))
        if ubound(t3)=1 then m=clng(t3(1)) else m=n
        genp y 
        for g=x to y
            for q=n to m: part: next 
        next 
    next 

sub genp(high)
    p(1)=2: p(2)=3: c=2: i=p(c)+2
    do 
        k=2: bk=false
        do while k*k<=i and not bk 
            if i mod p(k)=0 then bk=true
            k=k+1
        loop 
        if not bk then
            c=c+1: if c>ubound(p) then redim preserve p(ubound(p)+8)
            p(c)=i
        end if
        i=i+2
    loop until p(c)>high 
end sub 

sub getp(z)
    if a(z)=0 then w=z-1: a(z)=a(w)
    a(z)=a(z)+1: w=a(z): b(z)=p(w)
end sub 

function list()
    w=b(1)
    if v=g then for i=2 to q: w=w&"+"&b(i): next else w="(not possible)"
    list="primes: "&w
end function 

sub part()
    for i=lbound(a) to ubound(a): a(i)=0: next 
    for i=1 to q: call getp(i): next 
    do while true: v=0: bu=false
        for s=1 to q
            v=v+b(s)
            if v>g then
                if s=1 then exit do
                for k=s to q: a(k)=0: next 
                for r=s-1 to q: call getp(r): next 
                bu=true: exit for
            end if
        next 
        if not bu then
            if v=g then exit do
            if v<g then call getp(q)
        end if    
    loop
    wscript.echo "partition "&g&" into "&q&" "&list
end sub