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River Crossing

Task

A farmer has five animals on one side. He needs to get all animals to the other side of the river. Unfortunately, he only has two spaces available on his boat and some animals cannot be left on their own. Find a series of boat crossings to get all animals to the other side.

Animals

  • 2 Wolves
  • 1 Fox
  • 1 Chicken
  • 1 Worm

Constraints

  • Wolves eat foxes.
  • Wolves eat chickens.
  • Foxes eat chickens.
  • Chickens eat worms.

Solution

The problem is solved using Answer Set Planning in DLV with the planning frontend. The planning frontend can be invoked with the -FP switch.

The command to run the solver is

dlv -FP -n=1 -stats -planlength=7 -planminactions=1 -planmaxactions=1 crossing.plan crossing.bk

STATE 0: boat_here, here(wolf1), here(wolf2), here(fox), here(chicken), here(worm)
ACTIONS: crossTogether(chicken,fox)
STATE 1: here(wolf1), here(wolf2), -here(fox), -here(chicken), here(worm), -boat_here
ACTIONS: cross(fox)
STATE 2: here(wolf1), here(wolf2), here(fox), -here(chicken), here(worm), boat_here
ACTIONS: crossTogether(fox,worm)
STATE 3: here(wolf1), here(wolf2), -here(fox), -here(chicken), -here(worm), -boat_here
ACTIONS: cross(chicken)
STATE 4: here(wolf1), here(wolf2), -here(fox), here(chicken), -here(worm), boat_here
ACTIONS: crossTogether(wolf1,wolf2)
STATE 5: -here(wolf1), -here(wolf2), -here(fox), here(chicken), -here(worm), -boat_here
ACTIONS: cross(fox)
STATE 6: -here(wolf1), -here(wolf2), here(fox), here(chicken), -here(worm), boat_here
ACTIONS: crossTogether(chicken,fox)
STATE 7: -here(wolf1), -here(wolf2), -here(fox), -here(chicken), -here(worm), -boat_here
PLAN: crossTogether(chicken,fox); cross(fox); crossTogether(fox,worm); cross(chicken); crossTogether(wolf1,wolf2); cross(fox); crossTogether(chicken,fox)