From 2c7a678406f03dcc697e1aedf21f2602c5c9941c Mon Sep 17 00:00:00 2001
From: jackfiled <xcrenchangjun@outlook.com>
Date: Tue, 27 Feb 2024 09:21:05 +0800
Subject: [PATCH] 20240227 Finished

---
 src/problem/mod.rs                            |  3 +-
 .../p2867_count_valid_paths_in_a_tree.rs      | 93 +++++++++++++++++++
 2 files changed, 95 insertions(+), 1 deletion(-)
 create mode 100644 src/problem/p2867_count_valid_paths_in_a_tree.rs

diff --git a/src/problem/mod.rs b/src/problem/mod.rs
index bdcf592..c81c3f4 100644
--- a/src/problem/mod.rs
+++ b/src/problem/mod.rs
@@ -56,4 +56,5 @@ mod p235_lowest_common_ancestor_of_a_binary_search_tree;
 mod p2583_kth_largest_sum_in_a_binary_tree;
 mod p2476_closest_nodes_queries_in_a_binary_search_tree;
 mod p938_range_sum_of_bst;
-mod p889_construct_binary_tree_from_preorder_and_postorder_traversal;
\ No newline at end of file
+mod p889_construct_binary_tree_from_preorder_and_postorder_traversal;
+mod p2867_count_valid_paths_in_a_tree;
\ No newline at end of file
diff --git a/src/problem/p2867_count_valid_paths_in_a_tree.rs b/src/problem/p2867_count_valid_paths_in_a_tree.rs
new file mode 100644
index 0000000..a4b51be
--- /dev/null
+++ b/src/problem/p2867_count_valid_paths_in_a_tree.rs
@@ -0,0 +1,93 @@
+/**
+ * [2867] Count Valid Paths in a Tree
+ */
+pub struct Solution {}
+
+
+// submission codes start here
+
+impl Solution {
+    fn dfs(graph: &Vec<Vec<usize>>, primes: &Vec<bool>, seen: &mut Vec<usize>, 
+        i: usize, pre: usize) {
+        seen.push(i);
+
+        for next in &graph[i] {
+            let next = *next;
+            if next != pre && !primes[next] {
+                Solution::dfs(graph, primes, seen, next, i);
+            } 
+        }
+    }
+
+    pub fn count_paths(n: i32, edges: Vec<Vec<i32>>) -> i64 {
+        let n = n as usize;
+        let mut primes = vec![true;n + 1];
+        primes[1] = false;
+        for i in 2..=n {
+            if primes[i] {
+                if i * i > n {
+                    continue;
+                }
+    
+                for j in (i * i..=n).step_by(i) {
+                    primes[j] = false;
+                }
+            }
+        }
+        primes = dbg!(primes);
+
+        let mut graph = vec![vec![];n + 1];
+        for edge in edges {
+            let x = edge[0] as usize;
+            let y = edge[1] as usize;
+
+            graph[x].push(y);
+            graph[y].push(x);
+        }
+
+        let mut count = vec![0; n + 1];
+        let mut result = 0;
+
+        for root in 1..=n {
+            if !primes[root] {
+                continue;
+            }
+            
+            let mut current = 0;
+            for i in &graph[root] {
+                let i = *i;
+                if (primes[i]) {
+                    continue;
+                }
+                
+                if count[i] == 0 {
+                    let mut seen = Vec::new();
+                    Solution::dfs(&graph, &primes, &mut seen, i, 0);
+                    for k in &seen {
+                        count[*k] = seen.len() as i64; 
+                    }
+                }
+
+                result += count[i] * current;
+                current += count[i];
+            }
+
+            result += current;
+        }
+
+        result
+    }
+}
+
+// submission codes end
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_2867() {
+        assert_eq!(6, Solution::count_paths(6, 
+            vec![vec![1,2],vec![1,3],vec![2,4],vec![3,5],vec![3,6]]));
+    }
+}