迷宮小車演算法
我的思路：
按照人類走迷宮的方法，貼著左邊走，左邊有路就向左走，左邊沒路向前走，左邊前面都沒路向右走
機器人的應該是：1.判斷左邊是否有牆，無牆：機器人左轉，前進一步，繼續判斷左。。
2.左邊有牆，則判斷前方是否有牆，無則向前一步，跳回第一步
3.前方有牆（此時狀態是左有牆，前有牆），則向機器人右轉，跳回第一步
另外有個前提條件，機器人轉彎需要原地轉，有轉彎半徑的肯定不行。
還有個問題，就是機器人自己不知道自己已經從迷宮出來了，會一直走。。
B. 求走迷宮問題的演算法，要求用java寫的
public class Maze { private int[][] maze = null;
private int[] xx = { 1, 0, -1, 0 };
private int[] yy = { 0, 1, 0, -1 };
private Queue queue = null; public Maze(int[][] maze) {
this.maze = maze;
queue = new Queue(maze.length * maze.length);
} public void go() {
Point outPt = new Point(maze.length - 1, maze[0].length - 1);
Point curPt = new Point(0, 0);
Node curNode = new Node(curPt, null);
maze[curPt.x][curPt.y] = 2;
queue.entryQ(curNode); while (!queue.isEmpty()) {
curNode = queue.outQ();
for (int i = 0; i < xx.length; ++i) {
Point nextPt = new Point();
nextPt.x = (curNode.point).x + xx[i];
nextPt.y = (curNode.point).y + yy[i];
if (check(nextPt)) {
Node nextNode = new Node(nextPt, curNode);
queue.entryQ(nextNode);
maze[nextPt.x][nextPt.y] = 2;
if (nextPt.equals(outPt)) {
java.util.Stack<Node> stack = new java.util.Stack<Node>();
stack.push(nextNode);
while ((curNode = nextNode.previous) != null) {
nextNode = curNode;
stack.push(curNode);
}
System.out.println("A Path is:");
while (!stack.isEmpty()) {
curNode = stack.pop();
System.out.println(curNode.point);
}
return;
}
}
}
}
System.out.println("Non solution!");
} private boolean check(Point p) {
if (p.x < 0 || p.x >= maze.length || p.y < 0 || p.y >= maze[0].length) {
return false;
}
if (maze[p.x][p.y] != 0) {
return false;
}
return true;
} public static void main(String[] args) {
int[][] maze = {
{ 0, 0, 1, 0, 1, 0, 1, 0, 1, 0 },
{ 0, 0, 1, 1, 1, 0, 0, 0, 1, 0 },
{ 0, 1, 0, 0, 1, 0, 0, 0, 0, 1 },
{ 0, 0, 0, 0, 1, 0, 0, 0, 1, 1 },
{ 0, 0, 1, 0, 0, 0, 0, 0, 0, 1 },
{ 1, 0, 1, 0, 1, 0, 0, 1, 0, 0 },
{ 0, 1, 0, 0, 1, 0, 0, 1, 0, 1 },
{ 1, 0, 1, 0, 1, 1, 0, 1, 0, 0 }
};
new Maze(maze).go();
} private class Queue { Node[] array = null;
int size = 0;
int len = 0;
int head = 0;
int tail = 0; public Queue(int n) {
array = new Node[n + 1];
size = n + 1;
} public boolean entryQ(Node node) {
if (isFull()) {
return false;
}
tail = (tail + 1) % size;
array[tail] = node;
len++;
return true;
} public Node outQ() {
if (isEmpty()) {
return null;
}
head = (head + 1) % size;
len--;
return array[head];
} public boolean isEmpty() {
return (len == 0 || head == tail) ? true : false;
} public boolean isFull() {
return ((tail + 1) % size == head) ? true : false;
}
} private class Node { Point point = null;
Node previous = null; public Node() {
this(null,null);
} public Node(Point point, Node node) {
this.point = point;
this.previous = node;
}
} private class Point { int x = 0;
int y = 0; public Point() {
this(0, 0);
} public Point(int x, int y) {
this.x = x;
this.y = y;
} public boolean equals(Point p) {
return (x == p.x) && (y == p.y);
} @Override
public String toString() {
return "(" + x + "," + y + ")";
}
}
}
C. 簡單的迷宮演算法
用python遞歸求解
dirs=[(0,1),(1,0),(0,-1),(-1,0)] #當前位置四個方向的偏移量
path=[] #存找到的路徑
def mark(maze,pos): #給迷宮maze的位置pos標"2"表示「倒過了」
maze[pos[0]][pos[1]]=2
def passable(maze,pos): #檢查迷宮maze的位置pos是否可通行
return maze[pos[0]][pos[1]]==0
def find_path(maze,pos,end):
mark(maze,pos)
if pos==end:
print(pos,end=" ") #已到達出口，輸出這個位置。成功結束
path.append(pos)
return True
for i in range(4): #否則按四個方向順序檢查
nextp=pos[0]+dirs[i][0],pos[1]+dirs[i][1]
#考慮下一個可能方向
if passable(maze,nextp): #不可行的相鄰位置不管
if find_path(maze,nextp,end):#如果從nextp可達出口，輸出這個位置，成功結束
print(pos,end=" ")
path.append(pos)
return True
return False
def see_path(maze,path): #使尋找到的路徑可視化
for i,p in enumerate(path):
if i==0:
maze[p[0]][p[1]] ="E"
elif i==len(path)-1:
maze[p[0]][p[1]]="S"
else:
maze[p[0]][p[1]] =3
print("\n")
for r in maze:
for c in r:
if c==3:
print('\033[0;31m'+"*"+" "+'\033[0m',end="")
elif c=="S" or c=="E":
print('\033[0;34m'+c+" " + '\033[0m', end="")
elif c==2:
print('\033[0;32m'+"#"+" "+'\033[0m',end="")
elif c==1:
print('\033[0;;40m'+" "*2+'\033[0m',end="")
else:
print(" "*2,end="")
print()
if __name__ == '__main__':
maze=[[1,1,1,1,1,1,1,1,1,1,1,1,1,1],\
[1,0,0,0,1,1,0,0,0,1,0,0,0,1],\
[1,0,1,0,0,0,0,1,0,1,0,1,0,1],\
[1,0,1,0,1,1,1,1,0,1,0,1,0,1],\
[1,0,1,0,0,0,0,0,0,1,1,1,0,1],\
[1,0,1,1,1,1,1,1,1,1,0,0,0,1],\
[1,0,1,0,0,0,0,0,0,0,0,1,0,1],\
[1,0,0,0,1,1,1,0,1,0,1,1,0,1],\
[1,0,1,0,1,0,1,0,1,0,1,0,0,1],\
[1,0,1,0,1,0,1,0,1,1,1,1,0,1],\
[1,0,1,0,0,0,1,0,0,1,0,0,0,1],\
[1,1,1,1,1,1,1,1,1,1,1,1,1,1]]
start=(1,1)
end=(10,12)
find_path(maze,start,end)
see_path(maze,path)
D. 迷宮演算法復雜度如何計算
迷宮生成可以O(n*m)完成。走迷宮的話可以O(n*m*2)左右。
只要記錄走到每一格的最優解就可以了。
最好不要用深度優先搜索。用廣度優先的實現方便。