mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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208 lines
31 KiB
JSON
208 lines
31 KiB
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"title": "Maximum Number of Moves to Kill All Pawns",
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"content": "<p>There is a <code>50 x 50</code> chessboard with <strong>one</strong> knight and some pawns on it. You are given two integers <code>kx</code> and <code>ky</code> where <code>(kx, ky)</code> denotes the position of the knight, and a 2D array <code>positions</code> where <code>positions[i] = [x<sub>i</sub>, y<sub>i</sub>]</code> denotes the position of the pawns on the chessboard.</p>\n\n<p>Alice and Bob play a <em>turn-based</em> game, where Alice goes first. In each player's turn:</p>\n\n<ul>\n\t<li>The player <em>selects </em>a pawn that still exists on the board and captures it with the knight in the <strong>fewest</strong> possible <strong>moves</strong>. <strong>Note</strong> that the player can select <strong>any</strong> pawn, it <strong>might not</strong> be one that can be captured in the <strong>least</strong> number of moves.</li>\n\t<li><span>In the process of capturing the <em>selected</em> pawn, the knight <strong>may</strong> pass other pawns <strong>without</strong> capturing them</span>. <strong>Only</strong> the <em>selected</em> pawn can be captured in <em>this</em> turn.</li>\n</ul>\n\n<p>Alice is trying to <strong>maximize</strong> the <strong>sum</strong> of the number of moves made by <em>both</em> players until there are no more pawns on the board, whereas Bob tries to <strong>minimize</strong> them.</p>\n\n<p>Return the <strong>maximum</strong> <em>total</em> number of moves made during the game that Alice can achieve, assuming both players play <strong>optimally</strong>.</p>\n\n<p>Note that in one <strong>move, </strong>a chess knight has eight possible positions it can move to, as illustrated below. Each move is two cells in a cardinal direction, then one cell in an orthogonal direction.</p>\n\n<p><img src=\"https://assets.leetcode.com/uploads/2024/08/01/chess_knight.jpg\" style=\"width: 275px; height: 273px;\" /></p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">kx = 1, ky = 1, positions = [[0,0]]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">4</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/08/16/gif3.gif\" style=\"width: 275px; height: 275px;\" /></p>\n\n<p>The knight takes 4 moves to reach the pawn at <code>(0, 0)</code>.</p>\n</div>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">kx = 0, ky = 2, positions = [[1,1],[2,2],[3,3]]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">8</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p><strong><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/08/16/gif4.gif\" style=\"width: 320px; height: 320px;\" /></strong></p>\n\n<ul>\n\t<li>Alice picks the pawn at <code>(2, 2)</code> and captures it in two moves: <code>(0, 2) -> (1, 4) -> (2, 2)</code>.</li>\n\t<li>Bob picks the pawn at <code>(3, 3)</code> and captures it in two moves: <code>(2, 2) -> (4, 1) -> (3, 3)</code>.</li>\n\t<li>Alice picks the pawn at <code>(1, 1)</code> and captures it in four moves: <code>(3, 3) -> (4, 1) -> (2, 2) -> (0, 3) -> (1, 1)</code>.</li>\n</ul>\n</div>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">kx = 0, ky = 0, positions = [[1,2],[2,4]]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">3</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<ul>\n\t<li>Alice picks the pawn at <code>(2, 4)</code> and captures it in two moves: <code>(0, 0) -> (1, 2) -> (2, 4)</code>. Note that the pawn at <code>(1, 2)</code> is not captured.</li>\n\t<li>Bob picks the pawn at <code>(1, 2)</code> and captures it in one move: <code>(2, 4) -> (1, 2)</code>.</li>\n</ul>\n</div>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>0 <= kx, ky <= 49</code></li>\n\t<li><code>1 <= positions.length <= 15</code></li>\n\t<li><code>positions[i].length == 2</code></li>\n\t<li><code>0 <= positions[i][0], positions[i][1] <= 49</code></li>\n\t<li>All <code>positions[i]</code> are unique.</li>\n\t<li>The input is generated such that <code>positions[i] != [kx, ky]</code> for all <code>0 <= i < positions.length</code>.</li>\n</ul>\n",
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"translatedTitle": "吃掉所有兵需要的最多移动次数",
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"translatedContent": "<p>给你一个 <code>50 x 50</code> 的国际象棋棋盘，棋盘上有 <strong>一个</strong> 马和一些兵。给你两个整数 <code>kx</code> 和 <code>ky</code> ，其中 <code>(kx, ky)</code> 表示马所在的位置，同时还有一个二维数组 <code>positions</code> ，其中 <code>positions[i] = [x<sub>i</sub>, y<sub>i</sub>]</code> 表示第 <code>i</code> 个兵在棋盘上的位置。</p>\n\n<p>Alice 和 Bob 玩一个回合制游戏，Alice 先手。玩家的一次操作中，可以执行以下操作：</p>\n\n<ul>\n\t<li>玩家选择一个仍然在棋盘上的兵，然后移动马，通过 <strong>最少</strong> 的 <strong>步数</strong> 吃掉这个兵。<strong>注意</strong> ，玩家可以选择 <strong>任意</strong> 一个兵，<strong>不一定</strong> 要选择从马的位置出发 <strong>最少</strong> 移动步数的兵。</li>\n\t<li><span>在马吃兵的过程中，马 <strong>可能</strong> 会经过一些其他兵的位置，但这些兵 <strong>不会</strong> 被吃掉。<strong>只有</strong> 选中的兵在这个回合中被吃掉。</span></li>\n</ul>\n\n<p>Alice 的目标是 <strong>最大化</strong> 两名玩家的 <strong>总</strong> 移动次数，直到棋盘上不再存在兵，而 Bob 的目标是 <strong>最小化</strong> 总移动次数。</p>\n\n<p>假设两名玩家都采用 <strong>最优</strong> 策略，请你返回可以达到的 <strong>最大</strong> 总移动次数。</p>\n\n<p>在一次 <strong>移动</strong> 中，如下图所示，马有 8 个可以移动到的位置，每个移动位置都是沿着坐标轴的一个方向前进 2 格，然后沿着垂直的方向前进 1 格。</p>\n\n<p><img src=\"https://assets.leetcode.com/uploads/2024/08/01/chess_knight.jpg\" style=\"width: 275px; height: 273px;\" /></p>\n\n<p> </p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<div class=\"example-block\">\n<p><span class=\"example-io\"><b>输入：</b>kx = 1, ky = 1, positions = [[0,0]]</span></p>\n\n<p><span class=\"example-io\"><b>输出：</b>4</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/08/16/gif3.gif\" style=\"width: 275px; height: 275px;\" /></p>\n\n<p>马需要移动 4 步吃掉 <code>(0, 0)</code> 处的兵。</p>\n</div>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<div class=\"example-block\">\n<p><span class=\"example-io\"><b>输入：</b>kx = 0, ky = 2, positions = [[1,1],[2,2],[3,3]]</span></p>\n\n<p><span class=\"example-io\"><b>输出：</b>8</span></p>\n\n<p><strong>解释：</strong></p>\n\n<p><strong><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2024/08/16/gif4.gif\" style=\"width: 320px; height: 320px;\" /></strong></p>\n\n<ul>\n\t<li>Alice 选择 <code>(2, 2)</code> 处的兵，移动马吃掉它需要 2 步：<code>(0, 2) -> (1, 4) -> (2, 2)</code> 。</li>\n\t<li>Bob 选择 <code>(3, 3)</code> 处的兵，移动马吃掉它需要 2 步：<code>(2, 2) -> (4, 1) -> (3, 3)</code> 。</li>\n\t<li>Alice 选择 <code>(1, 1)</code> 处的兵，移动马吃掉它需要 4 步：<code>(3, 3) -> (4, 1) -> (2, 2) -> (0, 3) -> (1, 1)</code> 。</li>\n</ul>\n</div>\n\n<p><strong class=\"example\">示例 3：</strong></p>\n\n<div class=\"example-block\">\n<p><span class=\"example-io\"><b>输入：</b>kx = 0, ky = 0, positions = [[1,2],[2,4]]</span></p>\n\n<p><span class=\"example-io\"><b>输出：</b>3</span></p>\n\n<p><strong>解释：</strong></p>\n\n<ul>\n\t<li>Alice 选择 <code>(2, 4)</code> 处的兵，移动马吃掉它需要 2 步：<code>(0, 0) -> (1, 2) -> (2, 4)</code> 。注意，<code>(1, 2)</code> 处的兵不会被吃掉。</li>\n\t<li>Bob 选择 <code>(1, 2)</code> 处的兵，移动马吃掉它需要 1 步：<code>(2, 4) -> (1, 2)</code> 。</li>\n</ul>\n</div>\n\n<p> </p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>0 <= kx, ky <= 49</code></li>\n\t<li><code>1 <= positions.length <= 15</code></li>\n\t<li><code>positions[i].length == 2</code></li>\n\t<li><code>0 <= positions[i][0], positions[i][1] <= 49</code></li>\n\t<li><code>positions[i]</code> 两两互不相同。</li>\n\t<li>输入保证对于所有 <code>0 <= i < positions.length</code> ，都有 <code>positions[i] != [kx, ky]</code> 。</li>\n</ul>\n",
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