Package g1701_1800.s1766_tree_of_coprimes

Class Solution

java.lang.Object
g1701_1800.s1766_tree_of_coprimes.Solution
public class Solution extends Object
1766 - Tree of Coprimes.<p>Hard</p> <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> <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&rsquo;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> <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> <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> <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> <p><strong>Example 1:</strong></p> <p><strong><img src="https://assets.leetcode.com/uploads/2021/01/06/untitled-diagram.png" alt="" /></strong></p> <p><strong>Input:</strong> nums = [2,3,3,2], edges = [[0,1],[1,2],[1,3]]</p> <p><strong>Output:</strong> [-1,0,0,1]</p> <p><strong>Explanation:</strong> In the above figure, each node&rsquo;s value is in parentheses.</p> <ul> <li> <p>Node 0 has no coprime ancestors.</p> </li> <li> <p>Node 1 has only one ancestor, node 0. Their values are coprime (gcd(2,3) == 1). - Node 2 has two ancestors, nodes 1 and 0. Node 1&rsquo;s value is not coprime (gcd(3,3) == 3), but node 0&rsquo;s value is (gcd(2,3) == 1), so node 0 is the closest valid ancestor.</p> </li> <li> <p>Node 3 has two ancestors, nodes 1 and 0. It is coprime with node 1 (gcd(3,2) == 1), so node 1 is its closest valid ancestor.</p> </li> </ul> <p><strong>Example 2:</strong></p> <p><img src="https://assets.leetcode.com/uploads/2021/01/06/untitled-diagram1.png" alt="" /></p> <p><strong>Input:</strong> nums = [5,6,10,2,3,6,15], edges = [[0,1],[0,2],[1,3],[1,4],[2,5],[2,6]]</p> <p><strong>Output:</strong> [-1,0,-1,0,0,0,-1]</p> <p><strong>Constraints:</strong></p> <ul> <li><code>nums.length == n</code></li> <li><code>1 <= nums[i] <= 50</code></li> <li><code>1 <= n <= 10<sup>5</sup></code></li> <li><code>edges.length == n - 1</code></li> <li><code>edges[j].length == 2</code></li> <li><code>0 <= u<sub>j</sub>, v<sub>j</sub> < n</code></li> <li><code>u<sub>j</sub> != v<sub>j</sub></code></li> </ul>

  • Constructor Details

    • Solution

      public Solution()

  • Method Details

    • getCoprimes

      public int[] getCoprimes(int[] nums, int[][] edges)