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This approach leverages Depth First Search (DFS) to explore the binary tree. The key idea is to maintain the minimum and maximum values observed along the path from the root to the current node. By comparing the current node's value with these min/max values, we can compute potential maximum differences. As we backtrack, we use these values to determine the maximum difference possible for subtree paths.
Time Complexity: O(n), where n is the number of nodes in the binary tree, because we visit each node exactly once.
Space Complexity: O(h), where h is the height of the tree, due to the recursive stack usage.
1class TreeNode:
2 def __init__(self, val=0, left=None, right=None):
3 self.val = val
4 self.left = left
5 self.right = right
6
7class Solution:
8 def maxAncestorDiff(self, root: TreeNode) -> int:
9 def dfs(node, min_val, max_val):
10 if not node:
11 return max_val - min_val
12 min_val = min(min_val, node.val)
13 max_val = max(max_val, node.val)
14 left_diff = dfs(node.left, min_val, max_val)
15 right_diff = dfs(node.right, min_val, max_val)
16 return max(left_diff, right_diff)
17 return dfs(root, root.val, root.val)The Python implementation makes use of a nested function dfs, focusing on recursion and maintaining path min/max values to discover maximum differences.
This approach utilizes an iterative Breadth First Search (BFS) paradigm using a queue to traverse the tree. Queue elements consist of a node and associated min/max values for the path leading to this node. As nodes are processed, the difference between node values and min/max path values are calculated to find the maximum difference.
Time Complexity: O(n), as each node is visited once.
Space Complexity: O(n), for the queue storing the nodes in the worst case (when the tree is bushy).
1from collections import deque
2
3class Solution:
4 def In this solution, a queue is used for BFS traversal, storing node and path min/max values. For each node, we compute current possible differences and keep track of the maximum difference encountered. The solution efficiently processes tree traversal iteratively.