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English Version

题目描述

房间中的某个位置上有一个机器人,你需要控制它清扫房间。房间被建模为一个 m x n 的二进制网格,其中 0 表示单元格中有障碍物,1 表示空单元格。

机器人从一个未知的空单元格开始出发,并且你无法访问网格,但你可以使用给定的 API Robot 控制机器人。

你的任务是使用机器人清扫整个房间(即清理房间中的每个空单元格)。机器人具有四个给定的API,可以前进、向左转或向右转。每次转弯 90 度。

当机器人试图移动到一个存在障碍物的单元格时,它的碰撞传感器会检测到障碍物,并停留在当前单元格。

设计一个算法,使用下述 API 清扫整个房间:

interface Robot {
  // 若下一个单元格为空,则返回 true ,并移动至该单元格。
  // 若下一个单元格为障碍物,则返回 false ,并停留在当前单元格。
  boolean move();

  // 在调用 turnLeft/turnRight 后机器人会停留在当前单元格。
  // 每次转弯 90 度。
  void turnLeft();
  void turnRight();

  // 清理当前单元格。
  void clean();
}

注意 扫地机器人的初始方向向上。你可以假定网格的四周都被墙包围。

 

自定义测试:

输入只用于初始化房间和机器人的位置。你需要「盲解」这个问题。换而言之,你必须在对房间和机器人位置一无所知的情况下,只使用 4 个给出的 API 解决问题。 

 

示例 1:

输入:room = [[1,1,1,1,1,0,1,1],[1,1,1,1,1,0,1,1],[1,0,1,1,1,1,1,1],[0,0,0,1,0,0,0,0],[1,1,1,1,1,1,1,1]], row = 1, col = 3
输出:Robot cleaned all rooms.
解释:
房间内的所有单元格用 0 或 1 填充。
0 表示障碍物,1 表示可以通过。 
机器人从 row=1, col=3 的初始位置出发。
在左上角的一行以下,三列以右。

示例 2:

输入:room = [[1]], row = 0, col = 0
输出:Robot cleaned all rooms.

 

提示:

  • m == room.length
  • n == room[i].length
  • 1 <= m <= 100
  • 1 <= n <= 200
  • room[i][j]01.
  • 0 <= row < m
  • 0 <= col < n
  • room[row][col] == 1
  • 所有空单元格都可以从起始位置出发访问到。

解法

方法一:DFS

我们不妨假设机器人的初始位置为 $(0, 0)$,方向为 $d=0$。我们将初始位置进行打扫,并标记为已访问。然后,我们依次选择上、右、下、左四个方向进行探索,每次探索前都先判断是否已经访问过,如果没有访问过,我们就朝着该方向前进一步,然后递归探索。如果已经访问过,我们就顺时针旋转 $90^\circ$,然后继续探索下一个方向。当我们探索完所有的方向后,我们需要回到上一个位置,这时我们只需要顺时针旋转 $180^\circ$,然后前进一步,再顺时针旋转 $180^\circ$ 即可。

时间复杂度 $O(4^{n-m})$,空间复杂度 $O(n-m)$。其中 $n$$m$ 分别是房间的数量以及障碍物的数量。

# """
# This is the robot's control interface.
# You should not implement it, or speculate about its implementation
# """
# class Robot:
#    def move(self):
#        """
#        Returns true if the cell in front is open and robot moves into the cell.
#        Returns false if the cell in front is blocked and robot stays in the current cell.
#        :rtype bool
#        """
#
#    def turnLeft(self):
#        """
#        Robot will stay in the same cell after calling turnLeft/turnRight.
#        Each turn will be 90 degrees.
#        :rtype void
#        """
#
#    def turnRight(self):
#        """
#        Robot will stay in the same cell after calling turnLeft/turnRight.
#        Each turn will be 90 degrees.
#        :rtype void
#        """
#
#    def clean(self):
#        """
#        Clean the current cell.
#        :rtype void
#        """


class Solution:
    def cleanRoom(self, robot):
        """
        :type robot: Robot
        :rtype: None
        """

        def dfs(i, j, d):
            vis.add((i, j))
            robot.clean()
            for k in range(4):
                nd = (d + k) % 4
                x, y = i + dirs[nd], j + dirs[nd + 1]
                if (x, y) not in vis and robot.move():
                    dfs(x, y, nd)
                    robot.turnRight()
                    robot.turnRight()
                    robot.move()
                    robot.turnRight()
                    robot.turnRight()
                robot.turnRight()

        dirs = (-1, 0, 1, 0, -1)
        vis = set()
        dfs(0, 0, 0)
/**
 * // This is the robot's control interface.
 * // You should not implement it, or speculate about its implementation
 * interface Robot {
 *     // Returns true if the cell in front is open and robot moves into the cell.
 *     // Returns false if the cell in front is blocked and robot stays in the current cell.
 *     public boolean move();
 *
 *     // Robot will stay in the same cell after calling turnLeft/turnRight.
 *     // Each turn will be 90 degrees.
 *     public void turnLeft();
 *     public void turnRight();
 *
 *     // Clean the current cell.
 *     public void clean();
 * }
 */

class Solution {
    private int[] dirs = {-1, 0, 1, 0, -1};
    private Set<List<Integer>> vis = new HashSet<>();
    private Robot robot;

    public void cleanRoom(Robot robot) {
        this.robot = robot;
        dfs(0, 0, 0);
    }

    private void dfs(int i, int j, int d) {
        robot.clean();
        vis.add(List.of(i, j));
        for (int k = 0; k < 4; ++k) {
            int nd = (d + k) % 4;
            int x = i + dirs[nd], y = j + dirs[nd + 1];
            if (!vis.contains(List.of(x, y)) && robot.move()) {
                dfs(x, y, nd);
                robot.turnRight();
                robot.turnRight();
                robot.move();
                robot.turnRight();
                robot.turnRight();
            }
            robot.turnRight();
        }
    }
}
/**
 * // This is the robot's control interface.
 * // You should not implement it, or speculate about its implementation
 * class Robot {
 *   public:
 *     // Returns true if the cell in front is open and robot moves into the cell.
 *     // Returns false if the cell in front is blocked and robot stays in the current cell.
 *     bool move();
 *
 *     // Robot will stay in the same cell after calling turnLeft/turnRight.
 *     // Each turn will be 90 degrees.
 *     void turnLeft();
 *     void turnRight();
 *
 *     // Clean the current cell.
 *     void clean();
 * };
 */

class Solution {
public:
    void cleanRoom(Robot& robot) {
        int dirs[5] = {-1, 0, 1, 0, -1};
        set<pair<int, int>> vis;
        function<void(int, int, int)> dfs = [&](int i, int j, int d) {
            robot.clean();
            vis.insert({i, j});
            for (int k = 0; k < 4; ++k) {
                int nd = (d + k) % 4;
                int x = i + dirs[nd], y = j + dirs[nd + 1];
                if (!vis.count({x, y}) && robot.move()) {
                    dfs(x, y, nd);
                    robot.turnRight();
                    robot.turnRight();
                    robot.move();
                    robot.turnRight();
                    robot.turnRight();
                }
                robot.turnRight();
            }
        };
        dfs(0, 0, 0);
    }
};
/**
 * // This is the robot's control interface.
 * // You should not implement it, or speculate about its implementation
 * type Robot struct {
 * }
 *
 * // Returns true if the cell in front is open and robot moves into the cell.
 * // Returns false if the cell in front is blocked and robot stays in the current cell.
 * func (robot *Robot) Move() bool {}
 *
 * // Robot will stay in the same cell after calling TurnLeft/TurnRight.
 * // Each turn will be 90 degrees.
 * func (robot *Robot) TurnLeft() {}
 * func (robot *Robot) TurnRight() {}
 *
 * // Clean the current cell.
 * func (robot *Robot) Clean() {}
 */

func cleanRoom(robot *Robot) {
	vis := map[[2]int]bool{}
	dirs := [5]int{-1, 0, 1, 0, -1}
	var dfs func(int, int, int)
	dfs = func(i, j, d int) {
		vis[[2]int{i, j}] = true
		robot.Clean()
		for k := 0; k < 4; k++ {
			nd := (d + k) % 4
			x, y := i+dirs[nd], j+dirs[nd+1]
			if !vis[[2]int{x, y}] && robot.Move() {
				dfs(x, y, nd)
				robot.TurnRight()
				robot.TurnRight()
				robot.Move()
				robot.TurnRight()
				robot.TurnRight()
			}
			robot.TurnRight()
		}
	}
	dfs(0, 0, 0)
}
/**
 * class Robot {
 *      // Returns true if the cell in front is open and robot moves into the cell.
 *      // Returns false if the cell in front is blocked and robot stays in the current cell.
 * 		move(): boolean {}
 *
 *      // Robot will stay in the same cell after calling turnLeft/turnRight.
 *      // Each turn will be 90 degrees.
 * 		turnRight() {}
 *
 *      // Robot will stay in the same cell after calling turnLeft/turnRight.
 *      // Each turn will be 90 degrees.
 * 		turnLeft() {}
 *
 * 		// Clean the current cell.
 * 		clean(): {}
 * }
 */

function cleanRoom(robot: Robot) {
    const dirs = [-1, 0, 1, 0, -1];
    const vis = new Set<string>();
    const dfs = (i: number, j: number, d: number) => {
        vis.add(`${i}-${j}`);
        robot.clean();
        for (let k = 0; k < 4; ++k) {
            const nd = (d + k) % 4;
            const [x, y] = [i + dirs[nd], j + dirs[nd + 1]];
            if (!vis.has(`${x}-${y}`) && robot.move()) {
                dfs(x, y, nd);
                robot.turnRight();
                robot.turnRight();
                robot.move();
                robot.turnRight();
                robot.turnRight();
            }
            robot.turnRight();
        }
    };
    dfs(0, 0, 0);
}