I have a simple grid-based map composed of rooms, like this (A=entrance, B=exit):

   0 1 2 3
  #########
0 #B# #####
  #########
1 #   ### #
  #########
2 # #     #
  # #     #
3 # #     #
  #########
4 # ###   #
  #########
5 ###A    #
  ###     #
6 ###     #
  #########

And I'm stuck trying to make a suitable algorithm to create a path of doors between the rooms, in such a way that the player has to explore most of the map before finding the exit.

In other words, I'm trying to find the longest possible path from A to B.

(I'm aware that this problem can be solved for acyclic graphs; however, in this case there can be cycles.)

EDIT: Another example where rooms are connected using floodfill, and the exit is chosen as the farthest room from the entrance:

   0 1 2 3
  #########
0 #B#     #
  # #-#####
1 # | #   #
  ### #   #
2 ### #   #
  ###-#-###
3 #   | ###
  #-#######
4 #A|     #
  # #     #
5 # #     #
  # #     #
6 # #     #
  #########

I have a simple grid-based map composed of rooms, like this (A=entrance, B=exit):

   0 1 2 3
  #########
0 #B# #####
  #########
1 #   ### #
  #########
2 # #     #
  # #     #
3 # #     #
  #########
4 # ###   #
  #########
5 ###A    #
  ###     #
6 ###     #
  #########

And I'm stuck trying to make a suitable algorithm to create a path of doors between the rooms, in such a way that the player has to explore most of the map before finding the exit.

In other words, I'm trying to find the longest possible path from A to B.

(I'm aware that this problem can be solved for acyclic graphs; however, in this case there can be cycles.)

EDIT: Another example where rooms are connected using floodfill, and the exit is chosen as the farthest room from the entrance:

   0 1 2 3
  #########
0 #B#     #
  # #-#####
1 # | #   #
  ### #   #
2 ### #   #
  ###-#-###
3 #   | ###
  #-#######
4 #A|     #
  # #     #
5 # #     #
  # #     #
6 # #     #
  #########

Note that the path to the exit is not the longest possible path at all.

I have a simple grid-based map composed of rooms, like this (A=entry, B=exit):

   0 1 2 3
  #########
0 #B# #####
  #########
1 #   ### #
  #########
2 # #     #
  # #     #
3 # #     #
  #########
4 # ###   #
  #########
5 ###A    #
  ###     #
6 ###     #
  #########

And I'm stuck trying to make a suitable algorithm to create a path of doors between the rooms, in such a way that the player has to explore most of the map before finding the exit.

In other words, I'm trying to find the longest possible path from A to B.

(I'm aware that this problem can be solved for acyclic graphs; however, in this case there can be cycles.)

I have a simple grid-based map composed of rooms, like this (A=entrance, B=exit):

   0 1 2 3
  #########
0 #B# #####
  #########
1 #   ### #
  #########
2 # #     #
  # #     #
3 # #     #
  #########
4 # ###   #
  #########
5 ###A    #
  ###     #
6 ###     #
  #########

And I'm stuck trying to make a suitable algorithm to create a path of doors between the rooms, in such a way that the player has to explore most of the map before finding the exit.

In other words, I'm trying to find the longest possible path from A to B.

(I'm aware that this problem can be solved for acyclic graphs; however, in this case there can be cycles.)

EDIT: Another example where rooms are connected using floodfill, and the exit is chosen as the farthest room from the entrance:

   0 1 2 3
  #########
0 #B#     #
  # #-#####
1 # | #   #
  ### #   #
2 ### #   #
  ###-#-###
3 #   | ###
  #-#######
4 #A|     #
  # #     #
5 # #     #
  # #     #
6 # #     #
  #########