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Utilize a Depth-First Search (DFS) strategy and serialize each subtree. Treat the serialization as a key in a hashmap to track occurrences of identical subtrees. Duplicate entries are detected when a serialized key is encountered more than once.
Time Complexity: O(N), where N is the number of nodes since we visit each node once.
Space Complexity: O(N), accounting for the hashmap to store serialized trees and recursion stack space.
1using System;
2using System.Collections.Generic;
3
4public class TreeNode {
5 public int val;
6 public TreeNode left;
7 public TreeNode right;
8 public TreeNode(int x) { val = x; }
9}
10
11public class Solution {
12 public IList<TreeNode> FindDuplicateSubtrees(TreeNode root) {
13 var map = new Dictionary<string, List<TreeNode>>();
14 Serialize(root, map);
15 var result = new List<TreeNode>();
16 foreach (var pair in map) {
17 if (pair.Value.Count > 1) {
18 result.Add(pair.Value[0]);
19 }
20 }
21 return result;
22 }
23
24 private string Serialize(TreeNode node, Dictionary<string, List<TreeNode>> map) {
25 if (node == null) {
26 return "#";
27 }
28 string serial = node.val + "," + Serialize(node.left, map) + "," + Serialize(node.right, map);
29 if (!map.ContainsKey(serial)) {
30 map[serial] = new List<TreeNode>();
31 }
32 map[serial].Add(node);
33 return serial;
34 }
35}This C# implementation performs a tree serialization similarly to prior examples, storing serialized representations in a dictionary. Duplicate subtrees are identified through dictionary entries with multiple nodes.
Rather than using direct serialization strings, assign each unique subtree encountered a unique ID using a hash map. If a subtree's ID is seen again, it's a duplicate.
Time Complexity: O(N), as we traverse each node.
Space Complexity: O(N), necessary for dictionaries and recursive processing space.
1#include <unordered_map>
2#include <vector>
3
struct TreeNode {
int val;
TreeNode *left;
TreeNode *right;
TreeNode(int x) : val(x), left(NULL), right(NULL) {}
};
class Solution {
unordered_map<string, int> ids;
unordered_map<string, int> count;
vector<TreeNode*> result;
int idCounter = 1;
public:
vector<TreeNode*> findDuplicateSubtrees(TreeNode* root) {
serialize(root);
return result;
}
private:
int serialize(TreeNode* node) {
if (!node) return 0;
string serial = to_string(node->val) + ',' + to_string(serialize(node->left)) + ',' + to_string(serialize(node->right));
if (!ids.count(serial)) {
ids[serial] = idCounter++;
}
int id = ids[serial];
if (++count[serial] == 2) {
result.push_back(node);
}
return id;
}
};This C++ implementation stands by using unique identifiers to serialize subtree structures uniquely. Duplicate subtrees' roots are identified through the repeated presence of the generated IDs.