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;
}




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;
    }

}