Task: AKS test for primes


C++: #include <iomanip>
#include <iostream>
using namespace std;

const int pasTriMax = 61;

uint64_t pasTri[pasTriMax + 1];

void pascalTriangle(unsigned long n)

{
    unsigned long j, k;

    pasTri[0] = 1;
    j = 1;
    while (j <= n)
    {
        j++;
        k = j / 2;
        pasTri[k] = pasTri[k - 1];
        for ( ;k >= 1; k--)
            pasTri[k] += pasTri[k - 1];
    }
}

bool isPrime(unsigned long n)
{
    if (n > pasTriMax)
    {
        cout << n << " is out of range" << endl;
        exit(1);
    }
    
    pascalTriangle(n);
    bool res = true;
    int i = n / 2;
    while (res && (i > 1))
    {
        res = res && (pasTri[i] % n == 0);
        i--;
    }
    return res;
}

void expandPoly(unsigned long n)
{
    const char vz[] = {'+', '-'};    
    
    if (n > pasTriMax)
    {
        cout << n << " is out of range" << endl;
        exit(1);
    }
    
    switch (n)
    {
        case 0:
            cout << "(x-1)^0 = 1" << endl;
            break;
        case 1:
            cout << "(x-1)^1 = x-1" << endl;
            break;
        default:
            pascalTriangle(n);
            cout << "(x-1)^" << n << " = ";
            cout << "x^" << n;
            bool bVz = true;
            int nDiv2 = n / 2;
            for (unsigned long j = n - 1; j > nDiv2; j--, bVz = !bVz)
                cout << vz[bVz] << pasTri[n - j] << "*x^" << j;
            for (unsigned long j = nDiv2; j > 1; j--, bVz = !bVz)
                cout << vz[bVz] << pasTri[j] << "*x^" << j;
            cout << vz[bVz] << pasTri[1] << "*x";
            bVz = !bVz;
            cout << vz[bVz] << pasTri[0] << endl;
            break;
    }
}

int main()
{
    for (unsigned long n = 0; n <= 9; n++)
        expandPoly(n);      
    for (unsigned long n = 2; n <= pasTriMax; n++)
        if (isPrime(n))
            cout << setw(3) << n;
    cout << endl;        
}







VB: 



Const MAX = 99
Dim c(MAX + 1) As Variant
Private Sub coef(n As Integer)

    c(n) = CDec(1) 
    For i = n - 1 To 2 Step -1
        c(i) = c(i) + c(i - 1)
    Next i
End Sub
Private Function is_prime(fn As Variant) As Boolean
    fn = CDec(fn)
    Call coef(fn + 1)   
    For i = 2 To fn - 1 
        If c(i) - fn * Int(c(i) / fn) <> 0 Then 
            is_prime = False: Exit Function
        End If
    Next i
    is_prime = True
End Function
Private Sub show(n As Integer)

    Dim ci As Variant
    For i = n To 1 Step -1
        ci = c(i)
        If ci = 1 Then
            If (n - i) Mod 2 = 0 Then
                If i = 1 Then
                    If n = 1 Then
                        ci = "1"
                    Else
                        ci = "+1"
                    End If
                Else
                    ci = ""
                End If
            Else
                ci = "-1"
            End If
        Else
            If (n - i) Mod 2 = 0 Then
                ci = "+" & ci
            Else
                ci = "-" & ci
            End If
        End If
        If i = 1 Then 
            Debug.Print ci
        Else
            If i = 2 Then 
                Debug.Print ci & "x";
            Else
                Debug.Print ci & "x^" & i - 1;
            End If
        End If
    Next i
End Sub
Public Sub AKS_test_for_primes()
    Dim n As Integer
    For n = 1 To 10 
        coef n
        Debug.Print "(x-1)^" & n - 1 & " = ";
        show n
    Next n
    Debug.Print "primes (<="; MAX; "):"
    coef 2 
    For n = 2 To MAX
        If is_prime(n) Then
            Debug.Print n;
        End If
    Next n
End Sub