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LeetCode 3425: Longest Special Path Solution

Master LeetCode problem 3425 (Longest Special Path), a hard challenge, with our optimized solutions in Java, C++, and Python. Explore detailed explanations, test your code in our interactive editor, and prepare for coding interviews.

Problem Explanation

Explanation:

To solve this problem, we can perform a Depth First Search (DFS) starting from each node in the tree. During the DFS traversal, we keep track of the current path length and the number of unique nodes visited so far. We update the longest special path found and the minimum number of nodes in all possible longest special paths.

Here are the main steps of the algorithm:

  1. Build an adjacency list from the given edges.
  2. Perform a DFS starting from each node in the tree.
  3. During DFS traversal, keep track of the current path length and the number of unique nodes visited.
  4. Update the longest special path found and the minimum number of nodes in all possible longest special paths.
  5. Return the result array containing the length of the longest special path and the minimum number of nodes in all longest special paths.
  • Time complexity: O(n), where n is the number of nodes in the tree.
  • Space complexity: O(n) for the adjacency list and recursive stack space.

:

Solution Code

class Solution {
    private int longestPath;
    private int minNodes;

    public int[] longestSpecialPath(int n, int[][] edges, int[] nums) {
        List<List<Integer>> adjList = new ArrayList<>();
        for (int i = 0; i < n; i++) {
            adjList.add(new ArrayList<>());
        }
        for (int[] edge : edges) {
            adjList.get(edge[0]).add(edge[1]);
            adjList.get(edge[1]).add(edge[0]);
        }

        longestPath = 0;
        minNodes = Integer.MAX_VALUE;

        for (int i = 0; i < n; i++) {
            boolean[] visited = new boolean[n];
            dfs(adjList, i, nums, visited, new HashSet<>(), 0, 0);
        }

        return new int[]{longestPath, minNodes};
    }

    private void dfs(List<List<Integer>> adjList, int node, int[] nums, boolean[] visited, Set<Integer> pathSet, int pathLength, int uniqueNodes) {
        visited[node] = true;
        pathSet.add(nums[node]);
        pathLength++;
        uniqueNodes++;

        longestPath = Math.max(longestPath, pathLength);
        if (pathLength == longestPath) {
            minNodes = Math.min(minNodes, uniqueNodes);
        }

        for (int neighbor : adjList.get(node)) {
            if (!visited[neighbor] && !pathSet.contains(nums[neighbor])) {
                dfs(adjList, neighbor, nums, visited, new HashSet<>(pathSet), pathLength, uniqueNodes);
            }
        }
    }
}

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