Yong Ouyang: Solving Farmer-Wolf-Goat-Cabbage riddle with Groovy/Java

Yong Ouyang: Solving Farmer-Wolf-Goat-Cabbage riddle with Groovy/Java

A farmer is on the west bank of a river with a wolf, a goat and a cabbage in his care. Without his presence the wolf would eat the goat or the goat would eat the cabbage. The wolf is not interested in the cabbage. The farmer wishes to bring his three charges across the river. However the boat available to him can only carry one of the wolf, goat and cabbage besides himself. The puzzle is: is there a sequence of river crossings so that the farmer can transfer himself and the other three all intact to the east bank?

The Solution

It is a task that given an initial state, a final state, and a set of rules, one will start from the initial state and try to reach to the final state by passing through some intermediate states. Each move will transform from one state to the other, and there might be multiple valid moves from a given state. Such a collection of interconnected states can be represented by State Space Graph.
Let's use 'f', 'c', 'g', 'w' to denote the farmer, the cabbage, the goat, and the wolf, and use '|' to separate the river where left of the '|' denotes west bank and right of the '|' denotes east bank. Initially, they are all at the west bank of the river, which is represented as 'fcgw |' as shown below. We can solve the riddle by figuring out what the possible and valid moves are, using either Breadth-First Search or Depth-First Search, on a state space graph shown below

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