mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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189 lines
29 KiB
JSON
189 lines
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"title": "Number of Valid Move Combinations On Chessboard",
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"content": "<p>There is an <code>8 x 8</code> chessboard containing <code>n</code> pieces (rooks, queens, or bishops). You are given a string array <code>pieces</code> of length <code>n</code>, where <code>pieces[i]</code> describes the type (rook, queen, or bishop) of the <code>i<sup>th</sup></code> piece. In addition, you are given a 2D integer array <code>positions</code> also of length <code>n</code>, where <code>positions[i] = [r<sub>i</sub>, c<sub>i</sub>]</code> indicates that the <code>i<sup>th</sup></code> piece is currently at the <strong>1-based</strong> coordinate <code>(r<sub>i</sub>, c<sub>i</sub>)</code> on the chessboard.</p>\n\n<p>When making a <strong>move</strong> for a piece, you choose a <strong>destination</strong> square that the piece will travel toward and stop on.</p>\n\n<ul>\n\t<li>A rook can only travel <strong>horizontally or vertically</strong> from <code>(r, c)</code> to the direction of <code>(r+1, c)</code>, <code>(r-1, c)</code>, <code>(r, c+1)</code>, or <code>(r, c-1)</code>.</li>\n\t<li>A queen can only travel <strong>horizontally, vertically, or diagonally</strong> from <code>(r, c)</code> to the direction of <code>(r+1, c)</code>, <code>(r-1, c)</code>, <code>(r, c+1)</code>, <code>(r, c-1)</code>, <code>(r+1, c+1)</code>, <code>(r+1, c-1)</code>, <code>(r-1, c+1)</code>, <code>(r-1, c-1)</code>.</li>\n\t<li>A bishop can only travel <strong>diagonally</strong> from <code>(r, c)</code> to the direction of <code>(r+1, c+1)</code>, <code>(r+1, c-1)</code>, <code>(r-1, c+1)</code>, <code>(r-1, c-1)</code>.</li>\n</ul>\n\n<p>You must make a <strong>move</strong> for every piece on the board simultaneously. A <strong>move combination</strong> consists of all the <strong>moves</strong> performed on all the given pieces. Every second, each piece will instantaneously travel <strong>one square</strong> towards their destination if they are not already at it. All pieces start traveling at the <code>0<sup>th</sup></code> second. A move combination is <strong>invalid</strong> if, at a given time, <strong>two or more</strong> pieces occupy the same square.</p>\n\n<p>Return <em>the number of <strong>valid</strong> move combinations</em>.</p>\n\n<p><strong>Notes:</strong></p>\n\n<ul>\n\t<li><strong>No two pieces</strong> will start in the<strong> same</strong> square.</li>\n\t<li>You may choose the square a piece is already on as its <strong>destination</strong>.</li>\n\t<li>If two pieces are <strong>directly adjacent</strong> to each other, it is valid for them to <strong>move past each other</strong> and swap positions in one second.</li>\n</ul>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/09/23/a1.png\" style=\"width: 215px; height: 215px;\" />\n<pre>\n<strong>Input:</strong> pieces = ["rook"], positions = [[1,1]]\n<strong>Output:</strong> 15\n<strong>Explanation:</strong> The image above shows the possible squares the piece can move to.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/09/23/a2.png\" style=\"width: 215px; height: 215px;\" />\n<pre>\n<strong>Input:</strong> pieces = ["queen"], positions = [[1,1]]\n<strong>Output:</strong> 22\n<strong>Explanation:</strong> The image above shows the possible squares the piece can move to.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/09/23/a3.png\" style=\"width: 214px; height: 215px;\" />\n<pre>\n<strong>Input:</strong> pieces = ["bishop"], positions = [[4,3]]\n<strong>Output:</strong> 12\n<strong>Explanation:</strong> The image above shows the possible squares the piece can move to.\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>n == pieces.length </code></li>\n\t<li><code>n == positions.length</code></li>\n\t<li><code>1 <= n <= 4</code></li>\n\t<li><code>pieces</code> only contains the strings <code>"rook"</code>, <code>"queen"</code>, and <code>"bishop"</code>.</li>\n\t<li>There will be at most one queen on the chessboard.</li>\n\t<li><code>1 <= x<sub>i</sub>, y<sub>i</sub> <= 8</code></li>\n\t<li>Each <code>positions[i]</code> is distinct.</li>\n</ul>\n",
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"translatedTitle": "棋盘上有效移动组合的数目",
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"translatedContent": "<p>有一个 <code>8 x 8</code> 的棋盘，它包含 <code>n</code> 个棋子（棋子包括车，后和象三种）。给你一个长度为 <code>n</code> 的字符串数组 <code>pieces</code> ，其中 <code>pieces[i]</code> 表示第 <code>i</code> 个棋子的类型（车，后或象）。除此以外，还给你一个长度为 <code>n</code> 的二维整数数组 <code>positions</code> ，其中 <code>positions[i] = [r<sub>i</sub>, c<sub>i</sub>]</code> 表示第 <code>i</code> 个棋子现在在棋盘上的位置为 <code>(r<sub>i</sub>, c<sub>i</sub>)</code> ，棋盘下标从 <strong>1</strong> 开始。</p>\n\n<p>棋盘上每个棋子都可以移动 <b>至多一次</b> 。每个棋子的移动中，首先选择移动的 <strong>方向</strong> ，然后选择 <strong>移动的步数</strong> ，同时你要确保移动过程中棋子不能移到棋盘以外的地方。棋子需按照以下规则移动：</p>\n\n<ul>\n\t<li>车可以 <strong>水平或者竖直</strong> 从 <code>(r, c)</code> 沿着方向 <code>(r+1, c)</code>，<code>(r-1, c)</code>，<code>(r, c+1)</code> 或者 <code>(r, c-1)</code> 移动。</li>\n\t<li>后可以 <strong>水平竖直或者斜对角</strong> 从 <code>(r, c)</code> 沿着方向 <code>(r+1, c)</code>，<code>(r-1, c)</code>，<code>(r, c+1)</code>，<code>(r, c-1)</code>，<code>(r+1, c+1)</code>，<code>(r+1, c-1)</code>，<code>(r-1, c+1)</code>，<code>(r-1, c-1)</code> 移动。</li>\n\t<li>象可以 <strong>斜对角</strong> 从 <code>(r, c)</code> 沿着方向 <code>(r+1, c+1)</code>，<code>(r+1, c-1)</code>，<code>(r-1, c+1)</code>，<code>(r-1, c-1)</code> 移动。</li>\n</ul>\n\n<p><strong>移动组合</strong> 包含所有棋子的 <strong>移动</strong> 。每一秒，每个棋子都沿着它们选择的方向往前移动 <strong>一步</strong> ，直到它们到达目标位置。所有棋子从时刻 <code>0</code> 开始移动。如果在某个时刻，两个或者更多棋子占据了同一个格子，那么这个移动组合 <strong>不有效</strong> 。</p>\n\n<p>请你返回 <strong>有效</strong> 移动组合的数目。</p>\n\n<p><strong>注意：</strong></p>\n\n<ul>\n\t<li>初始时，<strong>不会有两个棋子</strong> 在 <strong>同一个位置 。</strong></li>\n\t<li>有可能在一个移动组合中，有棋子不移动。</li>\n\t<li>如果两个棋子 <strong>直接相邻</strong> 且两个棋子下一秒要互相占据对方的位置，可以将它们在同一秒内 <strong>交换位置</strong> 。</li>\n</ul>\n\n<p> </p>\n\n<p><strong>示例 1:</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/09/23/a1.png\" style=\"width: 215px; height: 215px;\" /></p>\n\n<pre>\n<b>输入：</b>pieces = [\"rook\"], positions = [[1,1]]\n<b>输出：</b>15\n<b>解释：</b>上图展示了棋子所有可能的移动。\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/09/23/a2.png\" style=\"width: 215px; height: 215px;\" /></p>\n\n<pre>\n<b>输入：</b>pieces = [\"queen\"], positions = [[1,1]]\n<b>输出：</b>22\n<b>解释：</b>上图展示了棋子所有可能的移动。\n</pre>\n\n<p><strong>示例 3:</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/09/23/a3.png\" style=\"width: 214px; height: 215px;\" /></p>\n\n<pre>\n<b>输入：</b>pieces = [\"bishop\"], positions = [[4,3]]\n<b>输出：</b>12\n<b>解释：</b>上图展示了棋子所有可能的移动。\n</pre>\n\n<p><strong>示例 4:</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/09/23/a4.png\" style=\"width: 216px; height: 219px;\" /></p>\n\n<pre>\n<b>输入：</b>pieces = [\"rook\",\"rook\"], positions = [[1,1],[8,8]]\n<b>输出：</b>223\n<b>解释：</b>每个车有 15 种移动，所以总共有 15 * 15 = 225 种移动组合。\n但是，有两个是不有效的移动组合：\n- 将两个车都移动到 (8, 1) ，会导致它们在同一个格子相遇。\n- 将两个车都移动到 (1, 8) ，会导致它们在同一个格子相遇。\n所以，总共有 225 - 2 = 223 种有效移动组合。\n注意，有两种有效的移动组合，分别是一个车在 (1, 8) ，另一个车在 (8, 1) 。\n即使棋盘状态是相同的，这两个移动组合被视为不同的，因为每个棋子移动操作是不相同的。\n</pre>\n\n<p><strong>示例 5：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2021/09/23/a5.png\" style=\"width: 214px; height: 213px;\" /></p>\n\n<pre>\n<b>输入：</b>pieces = [\"queen\",\"bishop\"], positions = [[5,7],[3,4]]\n<b>输出：</b>281\n<b>解释：</b>总共有 12 * 24 = 288 种移动组合。\n但是，有一些不有效的移动组合：\n- 如果后停在 (6, 7) ，它会阻挡象到达 (6, 7) 或者 (7, 8) 。\n- 如果后停在 (5, 6) ，它会阻挡象到达 (5, 6) ，(6, 7) 或者 (7, 8) 。\n- 如果象停在 (5, 2) ，它会阻挡后到达 (5, 2) 或者 (5, 1) 。\n在 288 个移动组合当中，281 个是有效的。\n</pre>\n\n<p> </p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>n == pieces.length </code></li>\n\t<li><code>n == positions.length</code></li>\n\t<li><code>1 <= n <= 4</code></li>\n\t<li><code>pieces</code> 只包含字符串 <code>\"rook\"</code> ，<code>\"queen\"</code> 和 <code>\"bishop\"</code> 。</li>\n\t<li>棋盘上总共最多只有一个后。</li>\n\t<li><code>1 <= x<sub>i</sub>, y<sub>i</sub> <= 8</code></li>\n\t<li>每一个 <code>positions[i]</code> 互不相同。</li>\n</ul>\n",
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