where-will-the-ball-fall

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Algorithms

You have a 2-D <code>grid</code> of size <code>m x n</code> representing a box, and you have <code>n</code> 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.

<ul>
	<li>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 <code>1</code>.</li>
	<li>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 <code>-1</code>.</li>
</ul>

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 &quot;V&quot; shaped pattern between two boards or if a board redirects the ball into either wall of the box.

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

&nbsp;
Example 1:

<img alt="" src="https://assets.leetcode.com/uploads/2019/09/26/ball.jpg" style="width: 500px; height: 385px;" />

<pre>
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.
</pre>

Example 2:

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

Example 3:

<pre>
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]
</pre>

&nbsp;
Constraints:

<ul>
	<li><code>m == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 100</code></li>
	<li><code>grid[i][j]</code> is <code>1</code> or <code>-1</code>.</li>
</ul>

findBall

Where Will the Ball Fall

Array

Matrix

Simulation

用一个大小为 <code>m x n</code> 的二维网格 <code>grid</code> 表示一个箱子。你有 <code>n</code> 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。

<ul>
	<li>将球导向右侧的挡板跨过左上角和右下角，在网格中用 <code>1</code> 表示。</li>
	<li>将球导向左侧的挡板跨过右上角和左下角，在网格中用 <code>-1</code> 表示。</li>
</ul>

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 <code>n</code> 的数组 <code>answer</code> ，其中 <code>answer[i]</code> 是球放在顶部的第 <code>i</code> 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 <code>-1</code> 。

 

示例 1：

<img alt="" src="https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2020/12/26/ball.jpg" style="width: 500px; height: 385px;" />

<pre>
输入：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]]
输出：[1,-1,-1,-1,-1]
解释：示例如图：
b0 球开始放在第 0 列上，最终从箱子底部第 1 列掉出。
b1 球开始放在第 1 列上，会卡在第 2、3 列和第 1 行之间的 "V" 形里。
b2 球开始放在第 2 列上，会卡在第 2、3 列和第 0 行之间的 "V" 形里。
b3 球开始放在第 3 列上，会卡在第 2、3 列和第 0 行之间的 "V" 形里。
b4 球开始放在第 4 列上，会卡在第 2、3 列和第 1 行之间的 "V" 形里。
</pre>

示例 2：

<pre>
输入：grid = [[-1]]
输出：[-1]
解释：球被卡在箱子左侧边上。
</pre>

示例 3：

<pre>
输入：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]]
输出：[0,1,2,3,4,-1]
</pre>

 

提示：

<ul>
	<li><code>m == grid.length</code></li>
	<li><code>n == grid[i].length</code></li>
	<li><code>1 <= m, n <= 100</code></li>
	<li><code>grid[i][j]</code> 为 <code>1</code> 或 <code>-1</code></li>
</ul>