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"questionFrontendId": "1706",
"categoryTitle": "Algorithms",
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"title": "Where Will the Ball Fall",
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"content": "<p>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.</p>\n\n<p>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.</p>\n\n<ul>\n\t<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>\n\t<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>\n</ul>\n\n<p>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.</p>\n\n<p>Return <em>an array </em><code>answer</code><em> of size </em><code>n</code><em> where </em><code>answer[i]</code><em> is the column that the ball falls out of at the bottom after dropping the ball from the </em><code>i<sup>th</sup></code><em> column at the top, or <code>-1</code><em> if the ball gets stuck in the box</em>.</em></p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<p><strong><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2019/09/26/ball.jpg\" style=\"width: 500px; height: 385px;\" /></strong></p>\n\n<pre>\n<strong>Input:</strong> 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]]\n<strong>Output:</strong> [1,-1,-1,-1,-1]\n<strong>Explanation:</strong> This example is shown in the photo.\nBall b0 is dropped at column 0 and falls out of the box at column 1.\nBall b1 is dropped at column 1 and will get stuck in the box between column 2 and 3 and row 1.\nBall b2 is dropped at column 2 and will get stuck on the box between column 2 and 3 and row 0.\nBall b3 is dropped at column 3 and will get stuck on the box between column 2 and 3 and row 0.\nBall b4 is dropped at column 4 and will get stuck on the box between column 2 and 3 and row 1.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> grid = [[-1]]\n<strong>Output:</strong> [-1]\n<strong>Explanation:</strong> The ball gets stuck against the left wall.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> 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]]\n<strong>Output:</strong> [0,1,2,3,4,-1]\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>m == grid.length</code></li>\n\t<li><code>n == grid[i].length</code></li>\n\t<li><code>1 &lt;= m, n &lt;= 100</code></li>\n\t<li><code>grid[i][j]</code> is <code>1</code> or <code>-1</code>.</li>\n</ul>\n",
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"translatedTitle": "球会落何处",
"translatedContent": "<p>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。</p>\n\n<p>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。</p>\n\n<ul>\n\t<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>\n\t<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>\n</ul>\n\n<p>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。</p>\n\n<p>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> 。</p>\n\n<p> </p>\n\n<p><strong>示例 1</strong></p>\n\n<p><strong><img alt=\"\" src=\"https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2020/12/26/ball.jpg\" style=\"width: 500px; height: 385px;\" /></strong></p>\n\n<pre>\n<strong>输入:</strong>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]]\n<strong>输出:</strong>[1,-1,-1,-1,-1]\n<strong>解释:</strong>示例如图:\nb0 球开始放在第 0 列上,最终从箱子底部第 1 列掉出。\nb1 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。\nb2 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。\nb3 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。\nb4 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。\n</pre>\n\n<p><strong>示例 2</strong></p>\n\n<pre>\n<strong>输入:</strong>grid = [[-1]]\n<strong>输出:</strong>[-1]\n<strong>解释:</strong>球被卡在箱子左侧边上。\n</pre>\n\n<p><strong>示例 3</strong></p>\n\n<pre>\n<strong>输入:</strong>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]]\n<strong>输出:</strong>[0,1,2,3,4,-1]\n</pre>\n\n<p> </p>\n\n<p><strong>提示:</strong></p>\n\n<ul>\n\t<li><code>m == grid.length</code></li>\n\t<li><code>n == grid[i].length</code></li>\n\t<li><code>1 <= m, n <= 100</code></li>\n\t<li><code>grid[i][j]</code> 为 <code>1</code> 或 <code>-1</code></li>\n</ul>\n",
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