思路：用0/1代表所处位置，农夫、狼、羊、菜过河就是0000->1111,一共是16种状态，去掉其中的不可能的状态如0011(羊和菜单独一起)是10种。

可以用图的方式表示：

或者用树的方式表示

简单代码实现如下：

package algorithm;

import java.util.ArrayList;

import java.util.List;

import java.util.stream.IntStream;

public class CrossRiver {

static int farmer = 0, wolf = 1, sheep = 2, cabbage = 3;

static int start = 0, end = 15;

static List listResult = new ArrayList();

static boolean cross(int[] conds) {

for (int curr : conds) {

// 跳过已发生的状态

if (listResult.contains("" + curr)) continue;

listResult.add("" + curr);

// 如已找到解，则返回

if (curr == end) return true;

// 找到可以转化的状态

int[] nexts = IntStream.range(0, 16).filter(item -> isValid(curr, item)).toArray();

// 如所有状态都无解，则移除当前步骤

if (!cross(nexts)) listResult.remove("" + curr);

// 如已找到解，则直接返回

if(listResult.contains("" + end)) return true;

}

return false;

}

// 是否满足条件

static boolean isValid(int curr, int next) {

if (position(curr, farmer) == position(next, farmer)) {

return false;

} // 农夫没过河

if (position(next, wolf) == position(next, sheep) & position(next, farmer) != position(next, wolf)) {

return false;

} // 狼羊单独

if (position(next, sheep) == position(next, cabbage) & position(next, farmer) != position(next, sheep)) {

return false;

} // 羊菜单独

if (position(curr, farmer) != position(curr, wolf) & position(curr, wolf) != position(next, wolf)) {

return false;

} // 狼不在身边不能带着过河

if (position(curr, farmer) != position(curr, sheep) & position(curr, sheep) != position(next, sheep)) {

return false;

} // 羊不在身边不能带着过河

if (position(curr, farmer) != position(curr, cabbage) & position(curr, cabbage) != position(next, cabbage)) {

return false;

} // 菜不在身边不能带着过河

if (Math.abs(curr - next) != 8 & Math.abs(curr - next) != 9 & Math.abs(curr - next) != 10

& Math.abs(curr - next) != 12) {

return false;

} // 超载或其他情况

return true;

}

// 获取位置

static char position(int i, int pos) {

String tmp = Integer.toBinaryString(i);

tmp = ("0000" + tmp).substring(tmp.length());

return tmp.charAt(pos);

}

static void print() {

String out = "";

String east = "东岸：";

String west = "西岸：";

if (position(15, farmer) == 0) {

east += "农夫 ";

} else {

west += "农夫 ";

}

if (position(15, wolf) == 0) {

east += "狼 ";

} else {

west += "狼 ";

}

if (position(15, sheep) == 0) {

east += "羊 ";

} else {

west += "羊 ";

}

if (position(15, cabbage) == 0) {

east += "菜 ";

} else {

west += "菜 ";

}

out += east + "\n" + west + "\n";

System.out.println(out);

}

public static void main(String[] args) {

//把农夫、狼、羊、菜过河看作从0000 -> 1111的变化

int[] conditions = { start };

cross(conditions);

listResult.stream().forEach(item -> {

String tmp = Integer.toBinaryString(Integer.valueOf(item));

tmp = ("0000" + tmp).substring(tmp.length());

System.out.print(tmp + " ");

});

}

}