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62 lines
2.5 KiB
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62 lines
2.5 KiB
HTML
<p>You are given an array <code>pairs</code>, where <code>pairs[i] = [x<sub>i</sub>, y<sub>i</sub>]</code>, and:</p>
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<ul>
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<li>There are no duplicates.</li>
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<li><code>x<sub>i</sub> < y<sub>i</sub></code></li>
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</ul>
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<p>Let <code>ways</code> be the number of rooted trees that satisfy the following conditions:</p>
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<ul>
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<li>The tree consists of nodes whose values appeared in <code>pairs</code>.</li>
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<li>A pair <code>[x<sub>i</sub>, y<sub>i</sub>]</code> exists in <code>pairs</code> <strong>if and only if</strong> <code>x<sub>i</sub></code> is an ancestor of <code>y<sub>i</sub></code> or <code>y<sub>i</sub></code> is an ancestor of <code>x<sub>i</sub></code>.</li>
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<li><strong>Note:</strong> the tree does not have to be a binary tree.</li>
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</ul>
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<p>Two ways are considered to be different if there is at least one node that has different parents in both ways.</p>
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<p>Return:</p>
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<ul>
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<li><code>0</code> if <code>ways == 0</code></li>
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<li><code>1</code> if <code>ways == 1</code></li>
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<li><code>2</code> if <code>ways > 1</code></li>
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</ul>
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<p>A <strong>rooted tree</strong> is a tree that has a single root node, and all edges are oriented to be outgoing from the root.</p>
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<p>An <strong>ancestor</strong> of a node is any node on the path from the root to that node (excluding the node itself). The root has no ancestors.</p>
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<p> </p>
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<p><strong>Example 1:</strong></p>
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<img src="https://assets.leetcode.com/uploads/2020/12/03/trees2.png" style="width: 208px; height: 221px;" />
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<pre>
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<strong>Input:</strong> pairs = [[1,2],[2,3]]
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<strong>Output:</strong> 1
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<strong>Explanation:</strong> There is exactly one valid rooted tree, which is shown in the above figure.
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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/2020/12/03/tree.png" style="width: 234px; height: 241px;" />
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<pre>
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<strong>Input:</strong> pairs = [[1,2],[2,3],[1,3]]
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<strong>Output:</strong> 2
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<strong>Explanation:</strong> There are multiple valid rooted trees. Three of them are shown in the above figures.
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</pre>
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<p><strong>Example 3:</strong></p>
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<pre>
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<strong>Input:</strong> pairs = [[1,2],[2,3],[2,4],[1,5]]
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<strong>Output:</strong> 0
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<strong>Explanation:</strong> There are no valid rooted trees.</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>1 <= pairs.length <= 10<sup>5</sup></code></li>
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<li><code>1 <= x<sub>i </sub>< y<sub>i</sub> <= 500</code></li>
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<li>The elements in <code>pairs</code> are unique.</li>
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</ul>
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