Task: Minimum positive multiple in base 10 using only 0 and 1


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

__int128 imax(__int128 a, __int128 b) {
    if (a > b) {
        return a;
    }
    return b;
}

__int128 ipow(__int128 b, __int128 n) {
    if (n == 0) {
        return 1;
    }
    if (n == 1) {
        return b;
    }

    __int128 res = b;
    while (n > 1) {
        res *= b;
        n--;
    }
    return res;
}

__int128 imod(__int128 m, __int128 n) {
    __int128 result = m % n;
    if (result < 0) {
        result += n;
    }
    return result;
}

bool valid(__int128 n) {
    if (n < 0) {
        return false;
    }
    while (n > 0) {
        int r = n % 10;
        if (r > 1) {
            return false;
        }
        n /= 10;
    }
    return true;
}

__int128 mpm(const __int128 n) {
    if (n == 1) {
        return 1;
    }

    std::vector<__int128> L(n * n, 0);
    L[0] = 1;
    L[1] = 1;

    __int128 m, k, r, j;
    m = 0;
    while (true) {
        m++;
        if (L[(m - 1) * n + imod(-ipow(10, m), n)] == 1) {
            break;
        }
        L[m * n + 0] = 1;
        for (k = 1; k < n; k++) {
            L[m * n + k] = imax(L[(m - 1) * n + k], L[(m - 1) * n + imod(k - ipow(10, m), n)]);
        }
    }

    r = ipow(10, m);
    k = imod(-r, n);

    for (j = m - 1; j >= 1; j--) {
        if (L[(j - 1) * n + k] == 0) {
            r = r + ipow(10, j);
            k = imod(k - ipow(10, j), n);
        }
    }

    if (k == 1) {
        r++;
    }
    return r / n;
}

std::ostream& operator<<(std::ostream& os, __int128 n) {
    char buffer[64]; 
    int pos = (sizeof(buffer) / sizeof(char)) - 1;
    bool negative = false;

    if (n < 0) {
        negative = true;
        n = -n;
    }

    buffer[pos] = 0;
    while (n > 0) {
        int rem = n % 10;
        buffer[--pos] = rem + '0';
        n /= 10;
    }
    if (negative) {
        buffer[--pos] = '-';
    }
    return os << &buffer[pos];
}

void test(__int128 n) {
    __int128 mult = mpm(n);
    if (mult > 0) {
        std::cout << n << " * " << mult << " = " << (n * mult) << '\n';
    } else {
        std::cout << n << "(no solution)\n";
    }
}

int main() {
    int i;

    
    for (i = 1; i <= 10; i++) {
        test(i);
    }
    
    for (i = 95; i <= 105; i++) {
        test(i);
    }
    test(297);
    test(576);
    test(594); 
    test(891);
    test(909);
    test(999); 

    
    test(1998);
    test(2079);
    test(2251);
    test(2277);

    
    test(2439);
    test(2997);
    test(4878);

    return 0;
}







VB: Imports System, System.Linq, System.Collections.Generic, System.Console

Module Module1

    Dim fmt As String = "{0,4} * {1,31:n0} = {2,-28}" & vbLf

    Sub B10(ByVal n As Integer)
        If n <= 1 Then Return
        Dim pow As Integer() = New Integer(n) {},
            val As Integer() = New Integer(n) {},
            count As Integer = 0, ten As Integer = 1, x As Integer = 1
        While x <= n : val(x) = ten : For j As Integer = 0 To n
                If pow(j) <> 0 AndAlso pow((j + ten) Mod n) = 0 AndAlso _
                   pow(j) <> x Then pow((j + ten) Mod n) = x
            Next : If pow(ten) = 0 Then pow(ten) = x
            ten = (10 * ten) Mod n : If pow(0) <> 0 Then
                x = n : Dim s As String = "" : While x <> 0
                    Dim p As Integer = pow(x Mod n)
                    If count > p Then s += New String("0"c, count - p)
                    count = p - 1 : s += "1"
                    x = (n + x - val(p)) Mod n : End While
                If count > 0 Then s += New String("0"c, count)
                Write(fmt, n, Decimal.Parse(s) / n, s) : Return
            End If : x += 1 : End While : Write("Can
    End Sub

    Sub Main(ByVal args As String())
        Dim st As DateTime = DateTime.Now
        Dim m As List(Of Integer) = New List(Of Integer) From _
            {297,576,594,891,909,999,1998,2079,2251,2277,2439,2997,4878}
        Write(fmt, "n", "multiplier", "B10")
        WriteLine(New String("-"c, 69)) : Write(fmt, 1, 1, 1)
        For n As Integer = 1 To m.Last()
            If n <= 10 OrElse n >= 95 AndAlso n <= 105 OrElse m.Contains(n) Then B10(n)
        Next : WriteLine(vbLf & "Took {0}ms", (DateTime.Now - st).TotalMilliseconds)
    End Sub
End Module