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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.
1function TreeNode(val) {
2 this.val = val;
3 this.left = this.right = null;
4}
5
6var findDuplicateSubtrees = function(root) {
7 const map = new Map();
8 function serialize(node) {
9 if (!node) return '#';
10 const serial = `${node.val},${serialize(node.left)},${serialize(node.right)}`;
11 if (!map.has(serial)) {
12 map.set(serial, []);
13 }
14 map.get(serial).push(node);
15 return serial;
16 }
17 serialize(root);
18 const result = [];
19 for (const nodes of map.values()) {
20 if (nodes.length > 1) {
21 result.push(nodes[0]);
22 }
23 }
24 return result;
25};
This JavaScript solution serializes subtrees into strings via DFS, storing those strings in a map. Duplicate strings imply duplicate subtrees, and such occurrences are returned.
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.