Package g2801_2900.s2867_count_valid_paths_in_a_tree

Class Solution

java.lang.Object
g2801_2900.s2867_count_valid_paths_in_a_tree.Solution
public class Solution extends java.lang.Object
2867 - Count Valid Paths in a Tree.

Hard

There is an undirected tree with n nodes labeled from 1 to n. You are given the integer n and a 2D integer array edges of length n - 1, where edges[i] = [ui, vi] indicates that there is an edge between nodes ui and vi in the tree.

Return the number of valid paths in the tree.

A path (a, b) is valid if there exists exactly one prime number among the node labels in the path from a to b.

Note that:

  • The path (a, b) is a sequence of distinct nodes starting with node a and ending with node b such that every two adjacent nodes in the sequence share an edge in the tree.
  • Path (a, b) and path (b, a) are considered the same and counted only once.

Example 1:

Input: n = 5, edges = [[1,2],[1,3],[2,4],[2,5]]

Output: 4

Explanation: The pairs with exactly one prime number on the path between them are:

  • (1, 2) since the path from 1 to 2 contains prime number 2.
  • (1, 3) since the path from 1 to 3 contains prime number 3.
  • (1, 4) since the path from 1 to 4 contains prime number 2.
  • (2, 4) since the path from 2 to 4 contains prime number 2.

It can be shown that there are only 4 valid paths.

Example 2:

Input: n = 6, edges = [[1,2],[1,3],[2,4],[3,5],[3,6]]

Output: 6

Explanation: The pairs with exactly one prime number on the path between them are:

  • (1, 2) since the path from 1 to 2 contains prime number 2.
  • (1, 3) since the path from 1 to 3 contains prime number 3.
  • (1, 4) since the path from 1 to 4 contains prime number 2.
  • (1, 6) since the path from 1 to 6 contains prime number 3.
  • (2, 4) since the path from 2 to 4 contains prime number 2.
  • (3, 6) since the path from 3 to 6 contains prime number 3.

It can be shown that there are only 6 valid paths.

Constraints:

  • 1 <= n <= 105
  • edges.length == n - 1
  • edges[i].length == 2
  • 1 <= ui, vi <= n
  • The input is generated such that edges represent a valid tree.

  • Constructor Summary

    Constructors
    Constructor
    Description
    Solution()
     

  • Method Summary

    Modifier and Type
    Method
    Description
    long
    countPaths(int n, int[][] edges)
     

    Methods inherited from class java.lang.Object

    clone, equals, finalize, getClass, hashCode, notify, notifyAll, toString, wait, wait, wait

  • Constructor Details

    • Solution

      public Solution()

  • Method Details

    • countPaths

      public long countPaths(int n, int[][] edges)