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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.
1class Node:
2 def __init__(self, val=0, left=None, right=None, next=None):
3 self.val = val
4 self.left = left
5 self.right = right
6 self.next = next
7
8class Solution:
9 def connect(self, root: 'Node') -> 'Node':
10 if not root:
11 return None
12 current = root
13 while current.left:
14 head = current
15 while head:
16 head.left.next = head.right
17 if head.next:
18 head.right.next = head.next.left
19 head = head.next
20 current = current.left
21 return rootThis Python solution uses two pointers, 'current' for moving level-wise and 'head' for node-wise traversal within a level to connect subsequent next pointers.
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.