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This approach involves using a queue to perform a level order traversal of the tree. At each level of the tree, we'll connect the 'next' pointers of all nodes at that level. Since it is a perfect binary tree, each node at a level is directly followed by its sibling or by NULL if it is the last node at that level.
Time Complexity: O(N), where N is the number of nodes, since each node is processed once.
Space Complexity: O(1), as no extra space other than pointers is used—the perfect use of a constant space solution.
1public class Node {
2 public int val;
3 public Node left;
4 public Node right;
5 public Node next;
6 public Node() { }
7 public Node(int _val) { val = _val; }
8}
9
10public class Solution {
11 public Node Connect(Node root) {
12 if (root == null) return null;
13 Node current = root;
14 while (current.left != null) {
15 Node head = current;
16 while (head != null) {
17 head.left.next = head.right;
18 if (head.next != null) {
19 head.right.next = head.next.left;
20 }
21 head = head.next;
22 }
23 current = current.left;
24 }
25 return root;
26 }
27}In this C# implementation, each level is processed with connections established between each node's left and right children, and across to the next node's left child.
The recursive method explores the tree depth-first and connects nodes level-wise. This approach effectively utilizes the call stack for traversal, aligning with the tree's inherent properties.
Time Complexity: O(N), which implies visiting each node once.
Space Complexity: O(logN) for recursion stack, since depth is proportional to the logarithm of node count.
1public:
int val;
Node* left;
Node* right;
Node* next;
Node() : val(0), left(NULL), right(NULL), next(NULL) {}
Node(int _val) : val(_val), left(NULL), right(NULL), next(NULL) {}
};
class Solution {
public:
void connectNodes(Node* node) {
if (!node || !node->left) return;
node->left->next = node->right;
if (node->next) node->right->next = node->next->left;
connectNodes(node->left);
connectNodes(node->right);
}
Node* connect(Node* root) {
connectNodes(root);
return root;
}
};The C++ solution uses a helper method 'connectNodes' to recursively connect nodes in the left and right subtrees, maintaining the recursive call depth with the log of the number of nodes.