Java代码回溯法解决狼羊菜过河问题

狼羊菜过河问题是一个经典的人工智能问题，也是回溯算法的一个典型应用。下面是Java代码实现：

import java.util.*;

public class WolfGoatCabbage {
    // 定义狼、羊、菜、人的编号
    private static final int WOLF = 0;
    private static final int GOAT = 1;
    private static final int CABBAGE = 2;
    private static final int PERSON = 3;

    // 定义船只状态
    private static final int LEFT = 0;
    private static final int RIGHT = 1;

    // 定义状态类
    private static class State {
        private int[] items = new int[4];
        private int boat;

        public State(int wolf, int goat, int cabbage, int person, int boat) {
            items[WOLF] = wolf;
            items[GOAT] = goat;
            items[CABBAGE] = cabbage;
            items[PERSON] = person;
            this.boat = boat;
        }

        public boolean isValid() {
            if (items[WOLF] == items[GOAT] && items[WOLF] != items[PERSON]) {
                return false;
            }
            if (items[GOAT] == items[CABBAGE] && items[GOAT] != items[PERSON]) {
                return false;
            }
            return true;
        }

        public boolean isGoal() {
            return items[WOLF] == RIGHT && items[GOAT] == RIGHT
                && items[CABBAGE] == RIGHT && items[PERSON] == RIGHT;
        }

        public List<State> getNextStates() {
            List<State> nextStates = new ArrayList<State>();
            int nextBoat = 1 - boat;
            for (int i = 0; i < 4; i++) {
                if (items[i] == boat) {
                    State nextState = new State(items[WOLF], items[GOAT], items[CABBAGE], items[PERSON], nextBoat);
                    nextState.items[i] = nextBoat;
                    if (nextState.isValid()) {
                        nextStates.add(nextState);
                    }
                }
            }
            return nextStates;
        }

        public String toString() {
            String s = "";
            s += items[WOLF] == LEFT ? "W" : "-";
            s += items[GOAT] == LEFT ? "G" : "-";
            s += items[CABBAGE] == LEFT ? "C" : "-";
            s += items[PERSON] == LEFT ? "P" : "-";
            s += boat == LEFT ? "  |---|  " : "  |---|  ";
            s += items[WOLF] == RIGHT ? "W" : "-";
            s += items[GOAT] == RIGHT ? "G" : "-";
            s += items[CABBAGE] == RIGHT ? "C" : "-";
            s += items[PERSON] == RIGHT ? "P" : "-";
            return s;
        }
    }

    // 定义搜索函数
    private static boolean search(State state, Set<State> visited, Stack<State> path) {
        visited.add(state);
        path.push(state);
        if (state.isGoal()) {
            return true;
        }
        for (State nextState : state.getNextStates()) {
            if (!visited.contains(nextState)) {
                if (search(nextState, visited, path)) {
                    return true;
                }
            }
        }
        path.pop();
        return false;
    }

    // 定义主函数
    public static void main(String[] args) {
        State startState = new State(LEFT, LEFT, LEFT, LEFT, LEFT);
        Set<State> visited = new HashSet<State>();
        Stack<State> path = new Stack<State>();
        if (search(startState, visited, path)) {
            System.out.println("Solution found!");
            for (State state : path) {
                System.out.println(state);
            }
        } else {
            System.out.println("Solution not found!");
        }
    }
}

该代码使用了一个状态类来表示问题状态，包括狼、羊、菜、人的位置和船只状态。使用回溯算法搜索状态空间，直到找到符合条件的状态，即所有物品和人都在对岸。在搜索过程中，使用一个集合来记录已经访问过的状态，避免重复搜索。搜索过程中，使用一个栈来记录路径，找到目标状态后输出路径即可。