You have a 2-D grid of size m x n representing a box, and you have n balls. The box is open on the top and bottom sides.

Each cell in the box has a diagonal board spanning two corners of the cell that can redirect a ball to the right or to the left.

• A board that redirects the ball to the right spans the top-left corner to the bottom-right corner and is represented in the grid as 1.
• A board that redirects the ball to the left spans the top-right corner to the bottom-left corner and is represented in the grid as -1.

We drop one ball at the top of each column of the box. Each ball can get stuck in the box or fall out of the bottom. A ball gets stuck if it hits a "V" shaped pattern between two boards or if a board redirects the ball into either wall of the box.

Return an array answer of size n where answer[i] is the column that the ball falls out of at the bottom after dropping the ball from the ith column at the top, or -1 if the ball gets stuck in the box.

Example 1:

Input: grid = [[1,1,1,-1,-1],[1,1,1,-1,-1],[-1,-1,-1,1,1],[1,1,1,1,-1],[-1,-1,-1,-1,-1]]
Output: [1,-1,-1,-1,-1]
Explanation: This example is shown in the photo.
Ball b0 is dropped at column 0 and falls out of the box at column 1.
Ball b1 is dropped at column 1 and will get stuck in the box between column 2 and 3 and row 1.
Ball b2 is dropped at column 2 and will get stuck on the box between column 2 and 3 and row 0.
Ball b3 is dropped at column 3 and will get stuck on the box between column 2 and 3 and row 0.
Ball b4 is dropped at column 4 and will get stuck on the box between column 2 and 3 and row 1.

Example 2:

Input: grid = [[-1]]
Output: [-1]
Explanation: The ball gets stuck against the left wall.

Example 3:

Input: grid = [[1,1,1,1,1,1],[-1,-1,-1,-1,-1,-1],[1,1,1,1,1,1],[-1,-1,-1,-1,-1,-1]]
Output: [0,1,2,3,4,-1] 

Constraints:

• m == grid.length
• n == grid[i].length
• 1 <= m, n <= 100
• grid[i][j] is 1 or -1.

球会落何处。

用一个大小为 m x n 的二维网格 grid 表示一个箱子。你有 n 颗球。箱子的顶部和底部都是开着的。

箱子中的每个单元格都有一个对角线挡板，跨过单元格的两个角，可以将球导向左侧或者右侧。

将球导向右侧的挡板跨过左上角和右下角，在网格中用 1 表示。
将球导向左侧的挡板跨过右上角和左下角，在网格中用 -1 表示。
在箱子每一列的顶端各放一颗球。每颗球都可能卡在箱子里或从底部掉出来。如果球恰好卡在两块挡板之间的 "V" 形图案，或者被一块挡导向到箱子的任意一侧边上，就会卡住。

返回一个大小为 n 的数组 answer ，其中 answer[i] 是球放在顶部的第 i 列后从底部掉出来的那一列对应的下标，如果球卡在盒子里，则返回 -1 。

来源：力扣（LeetCode）
链接：https://leetcode-cn.com/problems/where-will-the-ball-fall
著作权归领扣网络所有。商业转载请联系官方授权，非商业转载请注明出处。

这是一道模拟题。题意说的很明白了，input 给的是一个 mxn 的矩阵，在矩阵顶部的每个位置上都有一个球，现在让球落下，根据矩阵里每个位置的挡板的情况，输出最后球的位置信息。

注意一开始球的位置是在矩阵外的，所以球落入第一排 matrix[0][y] 也需要判断。因为球只会根据挡板的位置而改变行进方向，而且挡板位置左上 - 右下用 1 表示，右上 - 左下用 -1 表示。这个表示方法正好对应了球下一个位置的方向，因为如果是左上 - 右下，正好是往右下走；如果是右上 - 左下，正好是往左下走。所以这道题我按照题目模拟出来即可。

时间O(mn) - 有 N 个球，每个球最坏情况都会从箱子底部调出来

空间O(n)

Java实现

 1 class Solution {
 2     int rows, cols;
 3 
 4     public int[] findBall(int[][] grid) {
 5         rows = grid.length;
 6         cols = grid[0].length;
 7         int[] res = new int[cols];
 8         for (int i = 0; i < cols; i++) {
 9             res[i] = helper(i, grid);
10         }
11         return res;
12     }
13 
14     private int helper(int n, int[][] grid) {
15         int r = 0;
16         int c = n;
17         while (r < rows) {
18             int nextC = c + grid[r][c];
19             if (nextC < 0 || nextC > cols - 1 || grid[r][c] != grid[r][nextC]) {
20                 return -1;
21             }
22             r++;
23             c = nextC;
24         }
25         return c;
26     }
27 }

 

LeetCode 题目总结