Task: Greedy algorithm for Egyptian fractions
C: #include <stdbool.h>
#include <stdint.h>
#include <stdio.h>

typedef int64_t integer;

struct Pair {
    integer md;
    int tc;
};

integer mod(integer x, integer y) {
    return ((x % y) + y) % y;
}

integer gcd(integer a, integer b) {
    if (0 == a) return b;
    if (0 == b) return a;
    if (a == b) return a;
    if (a > b) return gcd(a - b, b);
    return gcd(a, b - a);
}

void write0(bool show, char *str) {
    if (show) {
        printf(str);
    }
}

void write1(bool show, char *format, integer a) {
    if (show) {
        printf(format, a);
    }
}

void write2(bool show, char *format, integer a, integer b) {
    if (show) {
        printf(format, a, b);
    }
}

struct Pair egyptian(integer x, integer y, bool show) {
    struct Pair ret;
    integer acc = 0;
    bool first = true;

    ret.tc = 0;
    ret.md = 0;

    write2(show, "Egyptian fraction for %lld/%lld: ", x, y);
    while (x > 0) {
        integer z = (y + x - 1) / x;
        if (z == 1) {
            acc++;
        } else {
            if (acc > 0) {
                write1(show, "%lld + ", acc);
                first = false;
                acc = 0;
                ret.tc++;
            } else if (first) {
                first = false;
            } else {
                write0(show, " + ");
            }
            if (z > ret.md) {
                ret.md = z;
            }
            write1(show, "1/%lld", z);
            ret.tc++;
        }
        x = mod(-y, x);
        y = y * z;
    }
    if (acc > 0) {
        write1(show, "%lld", acc);
        ret.tc++;
    }
    write0(show, "\n");

    return ret;
}

int main() {
    struct Pair p;
    integer nm = 0, dm = 0, dmn = 0, dmd = 0, den = 0;;
    int tm, i, j;

    egyptian(43, 48, true);
    egyptian(5, 121, true); 
    egyptian(2014, 59, true);

    tm = 0;
    for (i = 1; i < 100; i++) {
        for (j = 1; j < 100; j++) {
            p = egyptian(i, j, false);
            if (p.tc > tm) {
                tm = p.tc;
                nm = i;
                dm = j;
            }
            if (p.md > den) {
                den = p.md;
                dmn = i;
                dmd = j;
            }
        }
    }
    printf("Term max is %lld/%lld with %d terms.\n", nm, dm, tm); 
    printf("Denominator max is %lld/%lld\n", dmn, dmd);           
    egyptian(dmn, dmd, true);                                     

    return 0;
}

Go: package main

import (
    "fmt"
    "math/big"
    "strings"
)

var zero = new(big.Int)
var one = big.NewInt(1)

func toEgyptianRecursive(br *big.Rat, fracs []*big.Rat) []*big.Rat {
    if br.Num().Cmp(zero) == 0 {
        return fracs
    }
    iquo := new(big.Int)
    irem := new(big.Int)
    iquo.QuoRem(br.Denom(), br.Num(), irem)
    if irem.Cmp(zero) > 0 {
        iquo.Add(iquo, one)
    }
    rquo := new(big.Rat).SetFrac(one, iquo)
    fracs = append(fracs, rquo)
    num2 := new(big.Int).Neg(br.Denom())
    num2.Rem(num2, br.Num())
    if num2.Cmp(zero) < 0 {
        num2.Add(num2, br.Num())
    }
    denom2 := new(big.Int)
    denom2.Mul(br.Denom(), iquo)
    f := new(big.Rat).SetFrac(num2, denom2)
    if f.Num().Cmp(one) == 0 {
        fracs = append(fracs, f)
        return fracs
    }
    fracs = toEgyptianRecursive(f, fracs)
    return fracs
}

func toEgyptian(rat *big.Rat) []*big.Rat {
    if rat.Num().Cmp(zero) == 0 {
        return []*big.Rat{rat}
    }
    var fracs []*big.Rat
    if rat.Num().CmpAbs(rat.Denom()) >= 0 {
        iquo := new(big.Int)
        iquo.Quo(rat.Num(), rat.Denom())
        rquo := new(big.Rat).SetFrac(iquo, one)
        rrem := new(big.Rat)
        rrem.Sub(rat, rquo)
        fracs = append(fracs, rquo)
        fracs = toEgyptianRecursive(rrem, fracs)
    } else {
        fracs = toEgyptianRecursive(rat, fracs)
    }
    return fracs
}

func main() {
    fracs := []*big.Rat{big.NewRat(43, 48), big.NewRat(5, 121), big.NewRat(2014, 59)}
    for _, frac := range fracs {
        list := toEgyptian(frac)
        if list[0].Denom().Cmp(one) == 0 {
            first := fmt.Sprintf("[%v]", list[0].Num())
            temp := make([]string, len(list)-1)
            for i := 1; i < len(list); i++ {
                temp[i-1] = list[i].String()
            }
            rest := strings.Join(temp, " + ")
            fmt.Printf("%v -> %v + %s\n", frac, first, rest)
        } else {
            temp := make([]string, len(list))
            for i := 0; i < len(list); i++ {
                temp[i] = list[i].String()
            }
            all := strings.Join(temp, " + ")
            fmt.Printf("%v -> %s\n", frac, all)
        }
    }

    for _, r := range [2]int{98, 998} {
        if r == 98 {
            fmt.Println("\nFor proper fractions with 1 or 2 digits:")
        } else {
            fmt.Println("\nFor proper fractions with 1, 2 or 3 digits:")
        }
        maxSize := 0
        var maxSizeFracs []*big.Rat
        maxDen := zero
        var maxDenFracs []*big.Rat
        var sieve = make([][]bool, r+1) 
        for i := 0; i <= r; i++ {
            sieve[i] = make([]bool, r+2)
        }
        for i := 1; i <= r; i++ {
            for j := i + 1; j <= r+1; j++ {
                if sieve[i][j] {
                    continue
                }
                f := big.NewRat(int64(i), int64(j))
                list := toEgyptian(f)
                listSize := len(list)
                if listSize > maxSize {
                    maxSize = listSize
                    maxSizeFracs = maxSizeFracs[0:0]
                    maxSizeFracs = append(maxSizeFracs, f)
                } else if listSize == maxSize {
                    maxSizeFracs = append(maxSizeFracs, f)
                }
                listDen := list[len(list)-1].Denom()
                if listDen.Cmp(maxDen) > 0 {
                    maxDen = listDen
                    maxDenFracs = maxDenFracs[0:0]
                    maxDenFracs = append(maxDenFracs, f)
                } else if listDen.Cmp(maxDen) == 0 {
                    maxDenFracs = append(maxDenFracs, f)
                }
                if i < r/2 {
                    k := 2
                    for {
                        if j*k > r+1 {
                            break
                        }
                        sieve[i*k][j*k] = true
                        k++
                    }
                }
            }
        }
        fmt.Println("  largest number of items =", maxSize)
        fmt.Println("  fraction(s) with this number :", maxSizeFracs)
        md := maxDen.String()
        fmt.Print("  largest denominator = ", len(md), " digits, ")
        fmt.Print(md[0:20], "...", md[len(md)-20:], "\b\n")
        fmt.Println("  fraction(s) with this denominator :", maxDenFracs)
    }
}