490. The Maze

There is a ball in a maze with empty spaces and walls. The ball can go through empty spaces by rolling up , down , left or right , but it won't stop rolling until hitting a wall. When the ball stops, it could choose the next direction.

Given the ball's start position , the destination and the maze , determine whether the ball could stop at the destination.

The maze is represented by a binary 2D array. 1 means the wall and 0 means the empty space. You may assume that the borders of the maze are all walls. The start and destination coordinates are represented by row and column indexes.

Example 1:

Input 1:

 a maze represented by a 2D array
0 0 1 0 0
0 0 0 0 0
0 0 0 1 0
1 1 0 1 1
0 0 0 0 0
Input 2:

 start coordinate (rowStart, colStart) = (0, 4)
Input 3:

 destination coordinate (rowDest, colDest) = (4, 4)
Output:

 true
Explanation:

 One possible way is : left -> down -> left -> down -> right -> down -> right.

Example 2:

Input 1:

 a maze represented by a 2D array
0 0 1 0 0
0 0 0 0 0
0 0 0 1 0
1 1 0 1 1
0 0 0 0 0
Input 2:

 start coordinate (rowStart, colStart) = (0, 4)
Input 3:

 destination coordinate (rowDest, colDest) = (3, 2)
Output:

 false
Explanation:

 There is no way for the ball to stop at the destination.

Note:

1. There is only one ball and one destination in the maze.
2. Both the ball and the destination exist on an empty space, and they will not be at the same position initially.
3. The given maze does not contain border (like the red rectangle in the example pictures), but you could assume the border of the maze are all walls.
4. The maze contains at least 2 empty spaces, and both the width and height of the maze won't exceed 100.

1、题目描述¶

由空地和墙组成的迷宫中有一个**球**。球可以向**上下左右**四个方向滚动，但在遇到墙壁前不会停止滚动。当球停下时，可以选择下一个方向。

给定球的**起始位置**，目的地**和**迷宫，判断球能否在目的地停下。

迷宫由一个**0**和**1**的二维数组表示。 **1**表示墙壁，**0**表示空地。你可以假定迷宫的边缘都是墙壁。起始位置和目的地的坐标通过行号和列号给出。

示例 1:

输入 1: 迷宫由以下二维数组表示

0 0 1 0 0
0 0 0 0 0
0 0 0 1 0
1 1 0 1 1
0 0 0 0 0

输入 2: 起始位置坐标 (rowStart, colStart) = (0, 4)
输入 3: 目的地坐标 (rowDest, colDest) = (4, 4)

输出: true

解析: 一个可能的路径是 : 左 -> 下 -> 左 -> 下 -> 右 -> 下 -> 右。

示例 2:

输入 1: 迷宫由以下二维数组表示

0 0 1 0 0
0 0 0 0 0
0 0 0 1 0
1 1 0 1 1
0 0 0 0 0

输入 2: 起始位置坐标 (rowStart, colStart) = (0, 4)
输入 3: 目的地坐标 (rowDest, colDest) = (3, 2)

输出: false

解析: 没有能够使球停在目的地的路径。

注意:

• 迷宫中只有一个球和一个目的地。
• 球和目的地都在空地上，且初始时它们不在同一位置。
• 给定的迷宫不包括边界 (如图中的红色矩形), 但你可以假设迷宫的边缘都是墙壁。
• 迷宫至少包括2块空地，行数和列数均不超过100。