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53 lines
2.3 KiB
HTML
53 lines
2.3 KiB
HTML
<p>A game on an <strong>undirected</strong> graph is played by two players, Mouse and Cat, who alternate turns.</p>
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<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>
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<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>
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<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>
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<p>Additionally, it is not allowed for the Cat to travel to the Hole (node 0.)</p>
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<p>Then, the game can end in three ways:</p>
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<ul>
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<li>If ever the Cat occupies the same node as the Mouse, the Cat wins.</li>
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<li>If ever the Mouse reaches the Hole, the Mouse wins.</li>
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<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>
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</ul>
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<p>Given a <code>graph</code>, and assuming both players play optimally, return</p>
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<ul>
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<li><code>1</code> if the mouse wins the game,</li>
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<li><code>2</code> if the cat wins the game, or</li>
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<li><code>0</code> if the game is a draw.</li>
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</ul>
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<p> </p>
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<p><strong>Example 1:</strong></p>
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<img alt="" src="https://assets.leetcode.com/uploads/2020/11/17/cat1.jpg" style="width: 300px; height: 300px;" />
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<pre>
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<strong>Input:</strong> graph = [[2,5],[3],[0,4,5],[1,4,5],[2,3],[0,2,3]]
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<strong>Output:</strong> 0
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</pre>
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<p><strong>Example 2:</strong></p>
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<img alt="" src="https://assets.leetcode.com/uploads/2020/11/17/cat2.jpg" style="width: 200px; height: 200px;" />
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<pre>
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<strong>Input:</strong> graph = [[1,3],[0],[3],[0,2]]
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<strong>Output:</strong> 1
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</pre>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>3 <= graph.length <= 50</code></li>
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<li><code>1 <= graph[i].length < graph.length</code></li>
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<li><code>0 <= graph[i][j] < graph.length</code></li>
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<li><code>graph[i][j] != i</code></li>
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<li><code>graph[i]</code> is unique.</li>
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<li>The mouse and the cat can always move. </li>
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</ul>
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