迷宫求解算法一直是算法学习的经典,实现自然也是多种多样,包括动态规划,递归等实现,这里我们使用穷举求解,加深对栈的理解和应用
定义Position类用于存储坐标点
起点坐标为(1,1),终点坐标为(8,8)
地图打印在最下面
class Position { private int px; private int py; public Position(int px, int py) { this.px = px; this.py = py; } public int getPx() { return px; } public void setPx(int px) { this.px = px; } public int getPy() { return py; } public void setPy(int py) { this.py = py; }}
这里我们简单介绍下move()
函数
move函数分别向四个方向移动,然后将可行的path入栈.
注意,这里栈元素中每个栈元素Position都是new出来的,栈中存的是reference,
注意看下面这种写法: currentPosition.setPy(currentPosition.getPy()+1);stacks.push(currentPosition);
这种写法一度让我陷入困惑,因为pop出来的Position都是一样的,原因大家可能应该明白了。。。
public void move() { if (moveRight()) { Position temp = new Position(currentPosition.getPx() + 1, currentPosition.getPy()); test.add(temp); stacks.push(temp); } else if (moveBottom()) { Position temp = new Position(currentPosition.getPx(), currentPosition.getPy() + 1); test.add(temp); stacks.push(temp); } else if (moveTop()) { Position temp = new Position(currentPosition.getPx(), currentPosition.getPy() - 1); test.add(temp); stacks.push(temp); } else if (moveLeft()) { Position temp = new Position(currentPosition.getPx() - 1, currentPosition.getPy()); test.add(temp); stacks.push(temp); } else { currentPosition = stacks.pop();//若当前位置四个方向都走不通,则将当前位置出栈,继续遍历上一节点 } }
整体代码
class Position { private int px; private int py; public Position(int px, int py) { this.px = px; this.py = py; } public int getPx() { return px; } public void setPx(int px) { this.px = px; } public int getPy() { return py; } public void setPy(int py) { this.py = py; }}public class Maze { private final Position start;//迷宫的起点final private final Position end;//迷宫的终点final private ArrayListfootPrint;//足迹 private ArrayList test; private MyStack stacks;//自定义栈(也可以用java.util中的Stack栈)若想了解MyStack的实现,可以参考我的另一篇博客 private Position currentPosition;//定义当前位置 public Maze() {//集合,栈的初始化工作 start = new Position(1, 1); end = new Position(8, 8); currentPosition = start; stacks = new MyStack<>(); test = new ArrayList<>(); } public static final int map[][] = //定义地图10*10的方格 { {1, 1, 1, 1, 1, 1, 1, 1, 1, 1}, {1, 0, 0, 1, 0, 0, 0, 1, 0, 1}, {1, 0, 0, 1, 0, 0, 0, 1, 0, 1}, {1, 0, 0, 0, 0, 1, 1, 0, 0, 1}, {1, 0, 1, 1, 1, 0, 0, 0, 0, 1}, {1, 0, 0, 0, 1, 0, 0, 0, 0, 1}, {1, 0, 1, 0, 0, 0, 1, 0, 0, 1}, {1, 0, 1, 1, 1, 0, 1, 1, 0, 1}, {1, 1, 0, 0, 0, 0, 0, 0, 0, 1}, {1, 1, 1, 1, 1, 1, 1, 1, 1, 1}}; public static void printMap() {//打印地图 for (int i = 0; i < 10; i++) { for (int j = 0; j < 10; j++) { if (map[i][j] == 1) System.out.print(" ■"); else System.out.print(" "); } System.out.println(); } } public boolean moveTop() {//上移 String s = currentPosition.getPx() + "" + (currentPosition.getPy() - 1); if ((map[currentPosition.getPx()][currentPosition.getPy() - 1] != 1) & !isArrived(s)) { footPrint.add(s); return true; } return false; } public boolean moveRight() {//右移 String s = (currentPosition.getPx() + 1) + "" + currentPosition.getPy(); if (map[currentPosition.getPx() + 1][currentPosition.getPy()] != 1 & !isArrived(s)) { footPrint.add(s); return true; } return false; } public boolean moveBottom() {//下移 String s = currentPosition.getPx() + "" + (currentPosition.getPy() + 1); if ((map[currentPosition.getPx()][currentPosition.getPy() + 1] != 1) & !isArrived(s)) { footPrint.add(s); return true; } return false; } public boolean moveLeft() {//左移 String s = (currentPosition.getPx() - 1) + "" + currentPosition.getPy(); if ((map[currentPosition.getPx() - 1][currentPosition.getPy()] != 1) & !isArrived(s)) { footPrint.add(s); return true; } return false; } public boolean isArrived(String position) {//判断当前位置是否已经到打过 return footPrint.contains(position); } public void move() {//move函数分别向四个方向移动,然后将可行的path入栈 if (moveRight()) { Position temp = new Position(currentPosition.getPx() + 1, currentPosition.getPy()); test.add(temp); stacks.push(temp); } else if (moveBottom()) { Position temp = new Position(currentPosition.getPx(), currentPosition.getPy() + 1); test.add(temp); stacks.push(temp); } else if (moveTop()) { Position temp = new Position(currentPosition.getPx(), currentPosition.getPy() - 1); test.add(temp); stacks.push(temp); } else if (moveLeft()) { Position temp = new Position(currentPosition.getPx() - 1, currentPosition.getPy()); test.add(temp); stacks.push(temp); } else { currentPosition = stacks.pop();//若当前位置四个方向都走不通,则将当前位置出栈,继续遍历上一节点 } } public static void main(String[] args) { Maze m = new Maze(); m.footPrint = new ArrayList<>(); m.footPrint.add("11"); m.stacks.push(m.start); while (m.currentPosition.getPx() != 8 || m.currentPosition.getPy() != 8) { m.move(); } printMap(); System.out.println("下面是足迹,长度是:" + m.footPrint.size()); m.printFootPrint(); } public void printFootPrint() { for (int i = 0; i < footPrint.size(); i++) { System.out.print(footPrint.get(i) + ","); } System.out.println(); }}
大家可能会疑惑,为什么足迹是不连续的(例如:21,12)两个位置是走不通的,是因为在path遍历过程中存在跳栈,既当前位置走不通便会将当前位置的Position出栈(stacks.pop),然后继续上一节点遍历。
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