Task: Sum to 100




Go: package main

import (
	"fmt"
	"sort"
)

const pow3_8 = 3 * 3 * 3 * 3 * 3 * 3 * 3 * 3 
const pow3_9 = 3 * pow3_8                    
const maxExprs = 2 * pow3_8                  

type op uint8

const (
	Add  op = iota 
	Sub            
	Join           
)




type code uint16


func (c code) evaluate() (sum int) {
	num, pow := 0, 1
	for k := 9; k >= 1; k-- {
		num += pow * k
		switch op(c % 3) {
		case Add:
			sum += num
			num, pow = 0, 1
		case Sub:
			sum -= num
			num, pow = 0, 1
		case Join:
			pow *= 10
		}
		c /= 3
	}
	return sum
}

func (c code) String() string {
	buf := make([]byte, 0, 18)
	a, b := code(pow3_9), code(pow3_8)
	for k := 1; k <= 9; k++ {
		switch op((c % a) / b) {
		case Add:
			if k > 1 {
				buf = append(buf, '+')
			}
		case Sub:
			buf = append(buf, '-')
		}
		buf = append(buf, '0'+byte(k))
		a, b = b, b/3
	}
	return string(buf)
}

type sumCode struct {
	sum  int
	code code
}
type sumCodes []sumCode

type sumCount struct {
	sum   int
	count int
}
type sumCounts []sumCount


func (p sumCodes) Len() int            { return len(p) }
func (p sumCodes) Swap(i, j int)       { p[i], p[j] = p[j], p[i] }
func (p sumCodes) Less(i, j int) bool  { return p[i].sum < p[j].sum }
func (p sumCounts) Len() int           { return len(p) }
func (p sumCounts) Swap(i, j int)      { p[i], p[j] = p[j], p[i] }
func (p sumCounts) Less(i, j int) bool { return p[i].count > p[j].count }


func (sc sumCode) String() string {
	return fmt.Sprintf("% 10d = %v", sc.sum, sc.code)
}
func (sc sumCount) String() string {
	return fmt.Sprintf("% 10d has %d solutions", sc.sum, sc.count)
}

func main() {
	
	expressions := make(sumCodes, 0, maxExprs/2)
	counts := make(sumCounts, 0, 1715)
	for c := code(0); c < maxExprs; c++ {
		
		
		
		sum := c.evaluate()
		if sum >= 0 {
			expressions = append(expressions, sumCode{sum, c})
		}
	}
	sort.Sort(expressions)

	
	sc := sumCount{expressions[0].sum, 1}
	for _, e := range expressions[1:] {
		if e.sum == sc.sum {
			sc.count++
		} else {
			counts = append(counts, sc)
			sc = sumCount{e.sum, 1}
		}
	}
	counts = append(counts, sc)
	sort.Sort(counts)

	

	fmt.Println("All solutions that sum to 100:")
	i := sort.Search(len(expressions), func(i int) bool {
		return expressions[i].sum >= 100
	})
	for _, e := range expressions[i:] {
		if e.sum != 100 {
			break
		}
		fmt.Println(e)
	}

	fmt.Println("\nThe positive sum with maximum number of solutions:")
	fmt.Println(counts[0])

	fmt.Println("\nThe lowest positive number that can't be expressed:")
	s := 1
	for _, e := range expressions {
		if e.sum == s {
			s++
		} else if e.sum > s {
			fmt.Printf("% 10d\n", s)
			break
		}
	}

	fmt.Println("\nThe ten highest numbers that can be expressed:")
	for _, e := range expressions[len(expressions)-10:] {
		fmt.Println(e)
	}
}







Fortran: 









program sumto100
    
    parameter (nexpr = 13122)

    print *
    print *, 'Show all solutions that sum to 100'
    print *
    do i = 0, nexpr-1
        if ( ievaluate(i) .eq. 100 ) then
            call printexpr(i)
        endif    
    enddo
    
    print *
    print *, 'Show the sum that has the maximum number of solutions'
    print *    
    ibest = -1
    nbest = -1
    do i = 0, nexpr-1
        itest = ievaluate(i)
        if ( itest .ge. 0 ) then
            ntest = 0
            do j = 0, nexpr-1
                if ( ievaluate(j) .eq. itest ) then
                    ntest = ntest + 1
                endif
            enddo
            if ( (ntest .gt. nbest) ) then
                ibest = itest
                nbest = ntest
            endif
        endif
    enddo
    print *, ibest, ' has ', nbest, ' solutions'
    print *






    print *
    print *, 'Show the lowest positive number that can''t be expressed'
    print *
    loop: do i = 0,123456789
        do j = 0,nexpr-1
            if ( i .eq. ievaluate(j) ) then
                cycle loop
            endif
        enddo
        exit
    enddo loop
    print *, i
 
    print *
    print *, 'Show the ten highest numbers that can be expressed'
    print *
    ilimit = 123456789
    do i = 1,10
        ibest = 0
        do j = 0, nexpr-1
            itest = ievaluate(j)
            if ( (itest .le. ilimit) .and. (itest .gt. ibest ) ) then
                ibest = itest
            endif
        enddo
        do j = 0, nexpr-1    
            if ( ievaluate(j) .eq. ibest ) then
                call printexpr(j)
            endif    
        enddo
        ilimit = ibest - 1;
    enddo
       
end 

function ievaluate(icode)
    ic = icode
    ievaluate = 0
    n = 0
    ip = 1
    do k = 9,1,-1
        n = ip*k + n
        select case(mod(ic,3))
            case ( 0 )
                ievaluate = ievaluate + n
                n = 0
                ip = 1
            case ( 1 )
                ievaluate = ievaluate - n
                n = 0
                ip = 1
            case ( 2 )
                ip = ip * 10
        end select
        ic = ic / 3                
    enddo
end 

subroutine printexpr(icode)
    character(len=32) s
    ia = 19683
    ib =  6561
    s = ""
    do k = 1,9
        ic = mod(icode,ia) / ib
        ia = ib
        ib = ib / 3
        select case(mod(ic,3))
            case ( 0 )
                if ( k .gt. 1 ) then
                    s = trim(s) // '+'
                endif
            case ( 1 )
                s = trim(s) // '-'
        end select
        s = trim(s) // char(ichar('0')+k)
    end do
    ivalue = ievaluate(icode)
    print *, ivalue, ' = ', s
end