Task: Fraction reduction





Java: import java.util.ArrayList;
import java.util.Collections;
import java.util.HashMap;
import java.util.List;
import java.util.Map;

public class FractionReduction {

    public static void main(String[] args) {
        for ( int size = 2 ; size <= 5 ; size++ ) {
            reduce(size);
        }
    }
    
    private static void reduce(int numDigits) {
        System.out.printf("Fractions with digits of length %d where cancellation is valid.  Examples:%n", numDigits);
        
        
        int min = (int) Math.pow(10, numDigits-1);
        int max = (int) Math.pow(10, numDigits) - 1;
        List<Integer> values = new ArrayList<>();
        for ( int number = min ; number <= max ; number++ ) {
            if ( isValid(number) ) {
                values.add(number);
            }
        }
        
        Map<Integer,Integer> cancelCount = new HashMap<>(); 
        int size = values.size();
        int solutions = 0;
        for ( int nIndex = 0 ; nIndex < size - 1 ; nIndex++ ) {
            int numerator = values.get(nIndex);
            
            for ( int dIndex = nIndex + 1 ; dIndex < size ; dIndex++ ) {
                int denominator = values.get(dIndex);
                for ( int commonDigit : digitsInCommon(numerator, denominator) ) {
                    int numRemoved = removeDigit(numerator, commonDigit);
                    int denRemoved = removeDigit(denominator, commonDigit);
                    if ( numerator * denRemoved == denominator * numRemoved ) {
                        solutions++;
                        cancelCount.merge(commonDigit, 1, (v1, v2) -> v1 + v2);
                        if ( solutions <= 12 ) {
                            System.out.printf("    When %d is removed, %d/%d = %d/%d%n", commonDigit, numerator, denominator, numRemoved, denRemoved);
                        }
                    }
                }
            }
        }
        System.out.printf("Number of fractions where cancellation is valid = %d.%n", solutions);
        List<Integer> sorted = new ArrayList<>(cancelCount.keySet());
        Collections.sort(sorted);
        for ( int removed : sorted ) {
            System.out.printf("    The digit %d was removed %d times.%n", removed, cancelCount.get(removed));
        }
        System.out.println();
    }
    
    private static int[] powers = new int[] {1, 10, 100, 1000, 10000, 100000};
    
    
    private static int removeDigit(int n, int removed) {
        int m = 0;
        int pow = 0;
        while ( n > 0 ) {
            int r = n % 10;
            if ( r != removed ) {
                m = m + r*powers[pow];
                pow++;
            }
            n /= 10;
        }
        return m;
    }
        
    
    private static List<Integer> digitsInCommon(int n1, int n2) {
        int[] count = new int[10];
        List<Integer> common = new ArrayList<>();
        while ( n1 > 0 ) {
            int r = n1 % 10;
            count[r] += 1;
            n1 /= 10;
        }
        while ( n2 > 0 ) {
            int r = n2 % 10;
            if ( count[r] > 0 ) {
                common.add(r);
            }
            n2 /= 10;
        }
        return common;
    }
    
    
    private static boolean isValid(int num) {
        int[] count = new int[10];
        while ( num > 0 ) {
            int r = num % 10;
            if ( r == 0 || count[r] == 1 ) {
                return false;
            }
            count[r] = 1;
            num /= 10;
        }
        return true;
    }

}




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