task

Write a program that takes four digits, either from user input or by random generation, and computes arithmetic expressions following the rules of the 24 game.

Show examples of solutions generated by the program.



Related task

   Arithmetic Evaluator


program solve_24
  use helpers
  implicit none
  real                 :: vector(4), reals(4), p, q, r, s
  integer              :: numbers(4), n, i, j, k, a, b, c, d
  character, parameter :: ops(4) = (/ '+', '-', '*', '/' /)
  logical              :: last
  real,parameter       :: eps = epsilon(1.0)
 
  do n=1,12
    call random_number(vector)
    reals   = 9 * vector + 1
    numbers = int(reals)
    call Insertion_Sort(numbers)
 
    permutations: do
      a = numbers(1); b = numbers(2); c = numbers(3); d = numbers(4)
      reals = real(numbers)
      p = reals(1);   q = reals(2);   r = reals(3);   s = reals(4)
      ! combinations of operators:
      do i=1,4
        do j=1,4
          do k=1,4
            if      ( abs(op(op(op(p,i,q),j,r),k,s)-24.0) < eps ) then
              write (*,*) numbers, ' : ', '((',a,ops(i),b,')',ops(j),c,')',ops(k),d
              exit permutations
            else if ( abs(op(op(p,i,op(q,j,r)),k,s)-24.0) < eps ) then
              write (*,*) numbers, ' : ', '(',a,ops(i),'(',b,ops(j),c,'))',ops(k),d
              exit permutations
            else if ( abs(op(p,i,op(op(q,j,r),k,s))-24.0) < eps ) then
              write (*,*) numbers, ' : ', a,ops(i),'((',b,ops(j),c,')',ops(k),d,')'
              exit permutations
            else if ( abs(op(p,i,op(q,j,op(r,k,s)))-24.0) < eps ) then
              write (*,*) numbers, ' : ', a,ops(i),'(',b,ops(j),'(',c,ops(k),d,'))'
              exit permutations
            else if ( abs(op(op(p,i,q),j,op(r,k,s))-24.0) < eps ) then
              write (*,*) numbers, ' : ', '(',a,ops(i),b,')',ops(j),'(',c,ops(k),d,')'
              exit permutations
            end if
          end do
        end do
      end do
      call nextpermutation(numbers,last)  
      if ( last ) then
        write (*,*) numbers, ' : no solution.'
        exit permutations
      end if
    end do permutations
 
  end do
 
contains
 
  pure real function op(x,c,y)
    integer, intent(in) :: c
    real, intent(in)    :: x,y
    select case ( ops(c) )
      case ('+')
        op = x+y
      case ('-')
        op = x-y
      case ('*')
        op = x*y
      case ('/')
        op = x/y
    end select
  end function op
 
end program solve_24