Leetcode Problem 2867. Count Valid Paths in a Tree

2867. Count Valid Paths in a Tree

Leetcode Solutions

DFS/Tree-DP Approach

  1. Use a sieve algorithm to precompute all prime numbers up to n.
  2. Initialize a global variable to store the total number of valid paths.
  3. Perform a DFS traversal starting from the root node.
  4. At each node, calculate two values:
    • The number of paths in the subtree that contain no prime numbers (A).
    • The number of paths in the subtree that contain exactly one prime number (B).
  5. For each child node, combine its A and B with those of other children to update the global count of valid paths.
  6. If the current node is a prime, set its A to 0 and B to the sum of A's from all children.
  7. If the current node is not a prime, update its A and B by adding the A's and B's from all children respectively.
  8. Return the global count of valid paths after the DFS traversal is complete.
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