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49 lines
3.0 KiB
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<p>There is a tree (i.e., a connected, undirected graph that has no cycles) consisting of <code>n</code> nodes numbered from <code>0</code> to <code>n - 1</code> and exactly <code>n - 1</code> edges. Each node has a value associated with it, and the <strong>root</strong> of the tree is node <code>0</code>.</p>
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<p>To represent this tree, you are given an integer array <code>nums</code> and a 2D array <code>edges</code>. Each <code>nums[i]</code> represents the <code>i<sup>th</sup></code> node's value, and each <code>edges[j] = [u<sub>j</sub>, v<sub>j</sub>]</code> represents an edge between nodes <code>u<sub>j</sub></code> and <code>v<sub>j</sub></code> in the tree.</p>
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<p>Two values <code>x</code> and <code>y</code> are <strong>coprime</strong> if <code>gcd(x, y) == 1</code> where <code>gcd(x, y)</code> is the <strong>greatest common divisor</strong> of <code>x</code> and <code>y</code>.</p>
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<p>An ancestor of a node <code>i</code> is any other node on the shortest path from node <code>i</code> to the <strong>root</strong>. A node is <strong>not </strong>considered an ancestor of itself.</p>
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<p>Return <em>an array </em><code>ans</code><em> of size </em><code>n</code>, <em>where </em><code>ans[i]</code><em> is the closest ancestor to node </em><code>i</code><em> such that </em><code>nums[i]</code> <em>and </em><code>nums[ans[i]]</code> are <strong>coprime</strong>, or <code>-1</code><em> if there is no such ancestor</em>.</p>
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<p> </p>
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<p><strong>Example 1:</strong></p>
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<p><strong><img alt="" src="https://assets.leetcode.com/uploads/2021/01/06/untitled-diagram.png" style="width: 191px; height: 281px;" /></strong></p>
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<pre>
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<strong>Input:</strong> nums = [2,3,3,2], edges = [[0,1],[1,2],[1,3]]
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<strong>Output:</strong> [-1,0,0,1]
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<strong>Explanation:</strong> In the above figure, each node's value is in parentheses.
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- Node 0 has no coprime ancestors.
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- Node 1 has only one ancestor, node 0. Their values are coprime (gcd(2,3) == 1).
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- Node 2 has two ancestors, nodes 1 and 0. Node 1's value is not coprime (gcd(3,3) == 3), but node 0's
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value is (gcd(2,3) == 1), so node 0 is the closest valid ancestor.
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- Node 3 has two ancestors, nodes 1 and 0. It is coprime with node 1 (gcd(3,2) == 1), so node 1 is its
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closest valid ancestor.
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</pre>
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<p><strong>Example 2:</strong></p>
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<p><img alt="" src="https://assets.leetcode.com/uploads/2021/01/06/untitled-diagram1.png" style="width: 441px; height: 291px;" /></p>
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<pre>
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<strong>Input:</strong> nums = [5,6,10,2,3,6,15], edges = [[0,1],[0,2],[1,3],[1,4],[2,5],[2,6]]
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<strong>Output:</strong> [-1,0,-1,0,0,0,-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>nums.length == n</code></li>
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<li><code>1 <= nums[i] <= 50</code></li>
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<li><code>1 <= n <= 10<sup>5</sup></code></li>
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<li><code>edges.length == n - 1</code></li>
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<li><code>edges[j].length == 2</code></li>
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<li><code>0 <= u<sub>j</sub>, v<sub>j</sub> < n</code></li>
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<li><code>u<sub>j</sub> != v<sub>j</sub></code></li>
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</ul>
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