Task: Sum to 100



C#: using System;
using System.Collections.Generic;
using System.Linq;

class Program
{
    static void Main(string[] args)
    {
        
        var expressionsPlus = Enumerable.Range(0, (int)Math.Pow(3, 8)).AsParallel().Select(i => new Expression(i, 1));
        
        var expressionsMinus = Enumerable.Range(0, (int)Math.Pow(3, 8)).AsParallel().Select(i => new Expression(i, -1));
        var expressions = expressionsPlus.Concat(expressionsMinus);
        var results = new Dictionary<int, List<Expression>>();
        foreach (var e in expressions)
        {
            if (results.Keys.Contains(e.Value))
                results[e.Value].Add(e);
            else
                results[e.Value] = new List<Expression>() { e };
        }
        Console.WriteLine("Show all solutions that sum to 100");
        foreach (Expression e in results[100])
            Console.WriteLine("  " + e);
        Console.WriteLine("Show the sum that has the maximum number of solutions (from zero to infinity)");
        var summary = results.Keys.Select(k => new Tuple<int, int>(k, results[k].Count));
        var maxSols = summary.Aggregate((a, b) => a.Item2 > b.Item2 ? a : b);
        Console.WriteLine("  The sum " + maxSols.Item1 + " has " + maxSols.Item2 + " solutions.");
        Console.WriteLine("Show the lowest positive sum that can't be expressed (has no solutions), using the rules for this task");
        var lowestPositive = Enumerable.Range(1, int.MaxValue).First(x => !results.Keys.Contains(x));
        Console.WriteLine("  " + lowestPositive);
        Console.WriteLine("Show the ten highest numbers that can be expressed using the rules for this task (extra credit)");
        var highest = from k in results.Keys
                      orderby k descending
                      select k;
        foreach (var x in highest.Take(10))
            Console.WriteLine("  " + x);
    }
}
public enum Operations { Plus, Minus, Join };
public class Expression
{
    protected Operations[] Gaps;
    
    
    public int Value; 
    protected int _one;
    
    public Expression(int serial, int one)
    {
        _one = one;
        Gaps = new Operations[8];
        
        int divisor = 2187; 
        int times;
        for (int i = 0; i < 8; i++)
        {
            times = Math.DivRem(serial, divisor, out serial);
            divisor /= 3;
            if (times == 0)
                Gaps[i] = Operations.Join;
            else if (times == 1)
                Gaps[i] = Operations.Minus;
            else
                Gaps[i] = Operations.Plus;
        }
        
        
        Value = Evaluate();
    }
    public override string ToString()
    {
        string ret = _one.ToString();
        for (int i = 0; i < 8; i++)
        {
            switch (Gaps[i])
            {
                case Operations.Plus:
                    ret += "+";
                    break;
                case Operations.Minus:
                    ret += "-";
                    break;
            }
            ret += (i + 2);
        }
        return ret;
    }
    private int Evaluate()
        
    {
        var numbers = new int[9];
        int nc = 0;
        var operations = new List<Operations>();
        int a = 1;
        for (int i = 0; i < 8; i++)
        {
            if (Gaps[i] == Operations.Join)
                a = a * 10 + (i + 2);
            else
            {
                if (a > 0)
                {
                    if (nc == 0)
                        a *= _one;
                    numbers[nc++] = a;
                    a = i + 2;
                }
                operations.Add(Gaps[i]);
            }
        }
        if (nc == 0)
            a *= _one;
        numbers[nc++] = a;
        int ni = 0;
        int left = numbers[ni++];
        foreach (var operation in operations)
        {
            int right = numbers[ni++];
            if (operation == Operations.Plus)
                left = left + right;
            else
                left = left - right;
        }
        return left;
    }
}








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