Task: Fraction reduction


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

int indexOf(const std::vector<int> &haystack, int needle) {
    auto it = haystack.cbegin();
    auto end = haystack.cend();
    int idx = 0;
    for (; it != end; it = std::next(it)) {
        if (*it == needle) {
            return idx;
        }
        idx++;
    }
    return -1;
}

bool getDigits(int n, int le, std::vector<int> &digits) {
    while (n > 0) {
        auto r = n % 10;
        if (r == 0 || indexOf(digits, r) >= 0) {
            return false;
        }
        le--;
        digits[le] = r;
        n /= 10;
    }
    return true;
}

int removeDigit(const std::vector<int> &digits, int le, int idx) {
    static std::array<int, 5> pows = { 1, 10, 100, 1000, 10000 };

    int sum = 0;
    auto pow = pows[le - 2];
    for (int i = 0; i < le; i++) {
        if (i == idx) continue;
        sum += digits[i] * pow;
        pow /= 10;
    }
    return sum;
}

int main() {
    std::vector<std::pair<int, int>> lims = { {12, 97}, {123, 986}, {1234, 9875}, {12345, 98764} };
    std::array<int, 5> count;
    std::array<std::array<int, 10>, 5> omitted;

    std::fill(count.begin(), count.end(), 0);
    std::for_each(omitted.begin(), omitted.end(),
        [](auto &a) {
            std::fill(a.begin(), a.end(), 0);
        }
    );

    for (size_t i = 0; i < lims.size(); i++) {
        std::vector<int> nDigits(i + 2);
        std::vector<int> dDigits(i + 2);

        for (int n = lims[i].first; n <= lims[i].second; n++) {
            std::fill(nDigits.begin(), nDigits.end(), 0);
            bool nOk = getDigits(n, i + 2, nDigits);
            if (!nOk) {
                continue;
            }
            for (int d = n + 1; d <= lims[i].second + 1; d++) {
                std::fill(dDigits.begin(), dDigits.end(), 0);
                bool dOk = getDigits(d, i + 2, dDigits);
                if (!dOk) {
                    continue;
                }
                for (size_t nix = 0; nix < nDigits.size(); nix++) {
                    auto digit = nDigits[nix];
                    auto dix = indexOf(dDigits, digit);
                    if (dix >= 0) {
                        auto rn = removeDigit(nDigits, i + 2, nix);
                        auto rd = removeDigit(dDigits, i + 2, dix);
                        if ((double)n / d == (double)rn / rd) {
                            count[i]++;
                            omitted[i][digit]++;
                            if (count[i] <= 12) {
                                std::cout << n << '/' << d << " = " << rn << '/' << rd << " by omitting " << digit << "'s\n";
                            }
                        }
                    }
                }
            }
        }

        std::cout << '\n';
    }

    for (int i = 2; i <= 5; i++) {
        std::cout << "There are " << count[i - 2] << ' ' << i << "-digit fractions of which:\n";
        for (int j = 1; j <= 9; j++) {
            if (omitted[i - 2][j] == 0) {
                continue;
            }
            std::cout << std::setw(6) << omitted[i - 2][j] << " have " << j << "'s omitted\n";
        }
        std::cout << '\n';
    }

    return 0;
}







VB: Module Module1

    Function IndexOf(n As Integer, s As Integer()) As Integer
        For ii = 1 To s.Length
            Dim i = ii - 1
            If s(i) = n Then
                Return i
            End If
        Next
        Return -1
    End Function

    Function GetDigits(n As Integer, le As Integer, digits As Integer()) As Boolean
        While n > 0
            Dim r = n Mod 10
            If r = 0 OrElse IndexOf(r, digits) >= 0 Then
                Return False
            End If
            le -= 1
            digits(le) = r
            n \= 10
        End While
        Return True
    End Function

    Function RemoveDigit(digits As Integer(), le As Integer, idx As Integer) As Integer
        Dim pows = {1, 10, 100, 1000, 10000}
        Dim sum = 0
        Dim pow = pows(le - 2)
        For ii = 1 To le
            Dim i = ii - 1
            If i = idx Then
                Continue For
            End If
            sum += digits(i) * pow
            pow \= 10
        Next
        Return sum
    End Function

    Sub Main()
        Dim lims = {{12, 97}, {123, 986}, {1234, 9875}, {12345, 98764}}
        Dim count(5) As Integer
        Dim omitted(5, 10) As Integer
        Dim upperBound = lims.GetLength(0)
        For ii = 1 To upperBound
            Dim i = ii - 1
            Dim nDigits(i + 2 - 1) As Integer
            Dim dDigits(i + 2 - 1) As Integer
            Dim blank(i + 2 - 1) As Integer
            For n = lims(i, 0) To lims(i, 1)
                blank.CopyTo(nDigits, 0)
                Dim nOk = GetDigits(n, i + 2, nDigits)
                If Not nOk Then
                    Continue For
                End If
                For d = n + 1 To lims(i, 1) + 1
                    blank.CopyTo(dDigits, 0)
                    Dim dOk = GetDigits(d, i + 2, dDigits)
                    If Not dOk Then
                        Continue For
                    End If
                    For nixt = 1 To nDigits.Length
                        Dim nix = nixt - 1
                        Dim digit = nDigits(nix)
                        Dim dix = IndexOf(digit, dDigits)
                        If dix >= 0 Then
                            Dim rn = RemoveDigit(nDigits, i + 2, nix)
                            Dim rd = RemoveDigit(dDigits, i + 2, dix)
                            If (n / d) = (rn / rd) Then
                                count(i) += 1
                                omitted(i, digit) += 1
                                If count(i) <= 12 Then
                                    Console.WriteLine("{0}/{1} = {2}/{3} by omitting {4}
                                End If
                            End If
                        End If
                    Next
                Next
            Next
            Console.WriteLine()
        Next

        For i = 2 To 5
            Console.WriteLine("There are {0} {1}-digit fractions of which:", count(i - 2), i)
            For j = 1 To 9
                If omitted(i - 2, j) = 0 Then
                    Continue For
                End If
                Console.WriteLine("{0,6} have {1}
            Next
            Console.WriteLine()
        Next
    End Sub

End Module