1617. Count Subtrees With Max Distance Between Cities: RETRY, credit: https://leetcode.com/problems/count-subtrees-with-max-distance-between-cities/solutions/3181795/just-a-runnable-solution/

Author: tan-wei

src/solution/mod.rs

@@ -1219,3 +1219,4 @@ mod s1611_minimum_one_bit_operations_to_make_integers_zero;
 mod s1614_maximum_nesting_depth_of_the_parentheses;
 mod s1615_maximal_network_rank;
 mod s1616_split_two_strings_to_make_palindrome;
+mod s1617_count_subtrees_with_max_distance_between_cities;

src/solution/s1617_count_subtrees_with_max_distance_between_cities.rs

@@ -0,0 +1,113 @@
+/**
+ * [1617] Count Subtrees With Max Distance Between Cities
+ *
+ * There are n cities numbered from 1 to n. You are given an array edges of size n-1, where edges[i] = [ui, vi] represents a bidirectional edge between cities ui and vi. There exists a unique path between each pair of cities. In other words, the cities form a tree.
+ *
+ * A subtree is a subset of cities where every city is reachable from every other city in the subset, where the path between each pair passes through only the cities from the subset. Two subtrees are different if there is a city in one subtree that is not present in the other.
+ *
+ * For each d from 1 to n-1, find the number of subtrees in which the maximum distance between any two cities in the subtree is equal to d.
+ *
+ * Return an array of size n-1 where the d^th element (1-indexed) is the number of subtrees in which the maximum distance between any two cities is equal to d.
+ *
+ * Notice that the distance between the two cities is the number of edges in the path between them.
+ *
+ *  
+ * Example 1:
+ *
+ * <img alt="" src="https://assets.leetcode.com/uploads/2020/09/21/p1.png" style="width: 161px; height: 181px;" />
+ *
+ *
+ * Input: n = 4, edges = [[1,2],[2,3],[2,4]]
+ * Output: [3,4,0]
+ * Explanation:
+ * The subtrees with subsets {1,2}, {2,3} and {2,4} have a max distance of 1.
+ * The subtrees with subsets {1,2,3}, {1,2,4}, {2,3,4} and {1,2,3,4} have a max distance of 2.
+ * No subtree has two nodes where the max distance between them is 3.
+ *
+ *
+ * Example 2:
+ *
+ *
+ * Input: n = 2, edges = [[1,2]]
+ * Output: [1]
+ *
+ *
+ * Example 3:
+ *
+ *
+ * Input: n = 3, edges = [[1,2],[2,3]]
+ * Output: [2,1]
+ *
+ *
+ *  
+ * Constraints:
+ *
+ *
+ * 	2 <= n <= 15
+ * 	edges.length == n-1
+ * 	edges[i].length == 2
+ * 	1 <= ui, vi <= n
+ * 	All pairs (ui, vi) are distinct.
+ *
+ */
+pub struct Solution {}
+
+// problem: https://leetcode.com/problems/count-subtrees-with-max-distance-between-cities/
+// discuss: https://leetcode.com/problems/count-subtrees-with-max-distance-between-cities/discuss/?currentPage=1&orderBy=most_votes&query=
+
+// submission codes start here
+
+impl Solution {
+    // Credit: https://leetcode.com/problems/count-subtrees-with-max-distance-between-cities/solutions/3181795/just-a-runnable-solution/
+    pub fn count_subgraphs_for_each_diameter(n: i32, edges: Vec<Vec<i32>>) -> Vec<i32> {
+        let mut g = vec![vec![999; n as usize]; n as usize];
+
+        for e in edges.iter() {
+            let i = (e[0] - 1) as usize;
+            let j = (e[1] - 1) as usize;
+            g[i][j] = 1;
+            g[j][i] = 1;
+        }
+
+        for k in 0..n as usize {
+            for i in 0..n as usize {
+                for j in 0..n as usize {
+                    g[i][j] = g[i][j].min(g[i][k] + g[k][j]);
+                }
+            }
+        }
+
+        let mut result = vec![0; n as usize - 1];
+
+        for s in 0_i32..(1 << n) {
+            let k = s.count_ones() as i32;
+            let (mut e, mut d) = (0_i32, 0_i32);
+            for (i, item) in g.iter().enumerate().take(n as usize) {
+                if s & (1 << i) != 0 {
+                    for (j, &item_j) in item.iter().enumerate().take(n as usize).skip(i + 1) {
+                        if s & (1 << j) != 0 {
+                            e += i32::from(g[i][j] == 1);
+                            d = d.max(item_j);
+                        }
+                    }
+                }
+            }
+
+            if e == k - 1 && d > 0 {
+                result[(d - 1) as usize] += 1;
+            }
+        }
+
+        result
+    }
+}
+
+// submission codes end
+
+#[cfg(test)]
+mod tests {
+    use super::*;
+
+    #[test]
+    fn test_1617_example_1() {}
+}