mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
synced 2025-01-11 02:58:13 +08:00
198 lines
24 KiB
JSON
198 lines
24 KiB
JSON
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"title": "Cat and Mouse",
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"content": "<p>A game on an <strong>undirected</strong> graph is played by two players, Mouse and Cat, who alternate turns.</p>\n\n<p>The graph is given as follows: <code>graph[a]</code> is a list of all nodes <code>b</code> such that <code>ab</code> is an edge of the graph.</p>\n\n<p>The mouse starts at node <code>1</code> and goes first, the cat starts at node <code>2</code> and goes second, and there is a hole at node <code>0</code>.</p>\n\n<p>During each player's turn, they <strong>must</strong> travel along one edge of the graph that meets where they are. For example, if the Mouse is at node 1, it <strong>must</strong> travel to any node in <code>graph[1]</code>.</p>\n\n<p>Additionally, it is not allowed for the Cat to travel to the Hole (node 0.)</p>\n\n<p>Then, the game can end in three ways:</p>\n\n<ul>\n\t<li>If ever the Cat occupies the same node as the Mouse, the Cat wins.</li>\n\t<li>If ever the Mouse reaches the Hole, the Mouse wins.</li>\n\t<li>If ever a position is repeated (i.e., the players are in the same position as a previous turn, and it is the same player's turn to move), the game is a draw.</li>\n</ul>\n\n<p>Given a <code>graph</code>, and assuming both players play optimally, return</p>\n\n<ul>\n\t<li><code>1</code> if the mouse wins the game,</li>\n\t<li><code>2</code> if the cat wins the game, or</li>\n\t<li><code>0</code> if the game is a draw.</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/2020/11/17/cat1.jpg\" style=\"width: 300px; height: 300px;\" />\n<pre>\n<strong>Input:</strong> graph = [[2,5],[3],[0,4,5],[1,4,5],[2,3],[0,2,3]]\n<strong>Output:</strong> 0\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/11/17/cat2.jpg\" style=\"width: 200px; height: 200px;\" />\n<pre>\n<strong>Input:</strong> graph = [[1,3],[0],[3],[0,2]]\n<strong>Output:</strong> 1\n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>3 <= graph.length <= 50</code></li>\n\t<li><code>1 <= graph[i].length < graph.length</code></li>\n\t<li><code>0 <= graph[i][j] < graph.length</code></li>\n\t<li><code>graph[i][j] != i</code></li>\n\t<li><code>graph[i]</code> is unique.</li>\n\t<li>The mouse and the cat can always move. </li>\n</ul>\n",
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"translatedTitle": "猫和老鼠",
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"translatedContent": "<p>两位玩家分别扮演猫和老鼠,在一张 <strong>无向</strong> 图上进行游戏,两人轮流行动。</p>\n\n<p>图的形式是:<code>graph[a]</code> 是一个列表,由满足 <code>ab</code> 是图中的一条边的所有节点 <code>b</code> 组成。</p>\n\n<p>老鼠从节点 <code>1</code> 开始,第一个出发;猫从节点 <code>2</code> 开始,第二个出发。在节点 <code>0</code> 处有一个洞。</p>\n\n<p>在每个玩家的行动中,他们 <strong>必须</strong> 沿着图中与所在当前位置连通的一条边移动。例如,如果老鼠在节点 <code>1</code> ,那么它必须移动到 <code>graph[1]</code> 中的任一节点。</p>\n\n<p>此外,猫无法移动到洞中(节点 <code>0</code>)。</p>\n\n<p>然后,游戏在出现以下三种情形之一时结束:</p>\n\n<ul>\n\t<li>如果猫和老鼠出现在同一个节点,猫获胜。</li>\n\t<li>如果老鼠到达洞中,老鼠获胜。</li>\n\t<li>如果某一位置重复出现(即,玩家的位置和移动顺序都与上一次行动相同),游戏平局。</li>\n</ul>\n\n<p>给你一张图 <code>graph</code> ,并假设两位玩家都都以最佳状态参与游戏:</p>\n\n<ul>\n\t<li>如果老鼠获胜,则返回 <code>1</code>;</li>\n\t<li>如果猫获胜,则返回 <code>2</code>;</li>\n\t<li>如果平局,则返回 <code>0</code> 。</li>\n</ul>\n \n\n<p><strong>示例 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/11/17/cat1.jpg\" style=\"width: 300px; height: 300px;\" />\n<pre>\n<strong>输入:</strong>graph = [[2,5],[3],[0,4,5],[1,4,5],[2,3],[0,2,3]]\n<strong>输出:</strong>0\n</pre>\n\n<p><strong>示例 2:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/11/17/cat2.jpg\" style=\"width: 200px; height: 200px;\" />\n<pre>\n<strong>输入:</strong>graph = [[1,3],[0],[3],[0,2]]\n<strong>输出:</strong>1\n</pre>\n\n<p> </p>\n\n<p><strong>提示:</strong></p>\n\n<ul>\n\t<li><code>3 <= graph.length <= 50</code></li>\n\t<li><code>1 <= graph[i].length < graph.length</code></li>\n\t<li><code>0 <= graph[i][j] < graph.length</code></li>\n\t<li><code>graph[i][j] != i</code></li>\n\t<li><code>graph[i]</code> 互不相同</li>\n\t<li>猫和老鼠在游戏中总是可以移动</li>\n</ul>\n",
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