The game

Given an   N×N   square array of zeroes or ones in an initial configuration,   and a target configuration of zeroes and ones.



The game is to transform one to the other in as few moves as possible by inverting whole numbered rows or whole lettered
columns at once   (as one move).

In an inversion.   any  1  becomes  0,   and any  0  becomes  1  for that whole row or column.



Task

Create a program to score for the Flipping bits game.

 The game should create an original random target configuration and a starting configuration.
 Ensure that the starting position is never the target position.
 The target position must be guaranteed as reachable from the starting position.   (One possible way to do this is to generate the start position by legal flips from a random target position.   The flips will always be reversible back to the target from the given start position).
 The number of moves taken so far should be shown.


Show an example of a short game here, on this page, for a   3×3   array of bits.




 
!Implemented by Anant Dixit (October 2014)
program flipping_bits
implicit none
character(len=*), parameter :: cfmt = "(A3)", ifmt = "(I3)"
integer :: N, i, j, io, seed(8), moves, input
logical, allocatable :: Brd(:,:), Trgt(:,:)
logical :: solved
double precision :: r
 
do
  write(*,*) 'Enter the number of squares (between 1 and 10) you would like: '
  read(*,*,iostat=io) N
  if(N.gt.0 .and. N.le.10 .and. io.eq.0) exit
  write(*,*) 'Please, an integer between 1 and 10'
end do
 
allocate(Brd(N,N),Trgt(N,N))
call date_and_time(values=seed)
call srand(1000*seed(7)+seed(8)+60000*seed(6))
do i = 1,N
  do j = 1,N
    r = rand()
    if(r.gt.0.5D0) then
      Brd(i,j) = .TRUE.
      Trgt(i,j) = .TRUE.
    else
      Brd(i,j) = .FALSE.
      Trgt(i,j) = .FALSE.
    end if
  end do
end do
! Random moves taken by the program to `create' a target
moves = N
do i = 1,moves
  r = 1+2.0D0*dble(N)*rand() - 1.0D-17 !Only to make sure that the number is between 1 and 2N (less than 2N-1)
  if(floor(r).le.N) then
    do j = 1,N
      Trgt(floor(r),j) = .NOT.Trgt(floor(r),j)
    end do
  else
    r = r-N
    do j = 1,N
      Trgt(j,floor(r)) = .NOT.Trgt(j,floor(r))
    end do
  end if
end do
 
!This part checks if the target and the starting configurations are same or not.
do
  input = N
  call next_move(Brd,Trgt,N,input,solved)
  call next_move(Brd,Trgt,N,input,solved)
  if(solved) then
    r = 1+2.0D0*dble(N)*rand() - 1.0D-17
    if(floor(r).le.N) then
      do j = 1,N
        Trgt(floor(r),j) = .NOT.Trgt(floor(r),j)
      end do
    else
      r = r-N
      do j = 1,N
        Trgt(j,floor(r)) = .NOT.Trgt(j,floor(r))
      end do
    end if
  else
    exit
  end if
end do
 
write(*,*) 'Welcome to the Flipping Bits game!'
write(*,*) 'You have the current position'
 
moves = 0
call display(Brd,Trgt,N)
input = N
do
  write(*,*) 'Number of moves so far:', moves
  write(*,*) 'Select the column or row you wish to flip: '
  read(*,*,iostat=io) input
  if(io.eq.0 .and. input.gt.0 .and. input.le.(2*N)) then
    moves = moves+1
    write(*,*) 'Flipping ', input
    call next_move(Brd,Trgt,N,input,solved)
    call display(Brd,Trgt,N)
    if(solved) exit
  else
    write(*,*) 'Please enter a valid column or row number. To quit, press Ctrl+C!'
  end if
end do
 
write(*,*) 'Congratulations! You finished the game!'
write(*,ifmt,advance='no') moves
write(*,*) ' moves were taken by you!!'
deallocate(Brd,Trgt)
end program
 
subroutine display(Brd,Trgt,N)
implicit none
!arguments
integer :: N
logical :: Brd(N,N), Trgt(N,N)
!local
character(len=*), parameter :: cfmt = "(A3)", ifmt = "(I3)"
integer :: i, j
write(*,*) 'Current Configuration: '
do i = 0,N
  if(i.eq.0) then
    write(*,cfmt,advance='no') 'R/C'
    write(*,cfmt,advance='no') ' | '
  else
    write(*,ifmt,advance='no') i
  end if
end do
write(*,*) 
do i = 0,N
  if(i.eq.0) then
    do j = 0,N+2
      write(*,cfmt,advance='no') '---'
    end do
  else
    write(*,ifmt,advance='no') i+N
    write(*,cfmt,advance='no') ' | '
    do j = 1,N
      if(Brd(i,j)) then
        write(*,ifmt,advance='no') 1
      else
        write(*,ifmt,advance='no') 0
      end if
    end do
  end if
  write(*,*)
end do
 
write(*,*)
write(*,*)
 
write(*,*) 'Target Configuration'
do i = 0,N
  if(i.eq.0) then
    write(*,cfmt,advance='no') 'R/C'
    write(*,cfmt,advance='no') ' | '
  else
    write(*,ifmt,advance='no') i
  end if
end do
write(*,*) 
do i = 0,N
  if(i.eq.0) then
    do j = 0,N+2
      write(*,cfmt,advance='no') '---'
    end do
  else
    write(*,ifmt,advance='no') i+N
    write(*,cfmt,advance='no') ' | '
    do j = 1,N
      if(Trgt(i,j)) then
        write(*,ifmt,advance='no') 1
      else
        write(*,ifmt,advance='no') 0
      end if
    end do
  end if
  write(*,*)
end do
write(*,*)
write(*,*)
end subroutine
 
subroutine next_move(Brd,Trgt,N,input,solved)
implicit none
!arguments
integer :: N, input
logical :: Brd(N,N), Trgt(N,N), solved
!others
integer :: i,j
 
if(input.gt.N) then
  input = input-N
  do i = 1,N
    Brd(input,i) = .not.Brd(input,i)
  end do
else
  do i = 1,N
    Brd(i,input) = .not.Brd(i,input)
  end do
end if
solved = .TRUE.
do i = 1,N
  do j = 1,N
    if( (.not.Brd(i,j).and.Trgt(i,j)) .or. (Brd(i,j).and..not.Trgt(i,j)) ) then
      solved = .FALSE.
      exit
    end if
  end do
  if(.not.solved) exit
end do
end subroutine
 