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73 lines
2.3 KiB
Plaintext
73 lines
2.3 KiB
Plaintext
---
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title: '1448. Count Good Nodes in Binary Tree'
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description: Given a binary tree root, a node X in the tree is named good if in the path from root to X there are no nodes with a value greater than X
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sidebar:
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label: 'Count Good Nodes in Binary Tree'
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badge: 'Medium'
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---
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<Badge variant="accent">Tree BFS</Badge>
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### Example 1:
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- Input: `root = [3,1,4,3,null,1,5]`
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- Output: `4`
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- Explanation: Nodes in blue are good. Root Node `(3`) is always a good node. Node `4` -> (3,4) is the maximum value in the path starting from the `root`. Node `5` -> (3,4,5) is the maximum value in the path Node `3` -> (3,1,3) is the maximum value in the path.
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### Example 2:
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- Input: `root = [3,3,null,4,2]`
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- Output: `3`
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- Explanation: Node `2` -> `(3`, `3`, `2`) is not good, because `"3`" is higher than it.
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### Example 3:
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- Input: `root = [1]`
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- Output: `1`
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- Explanation: Root is considered as good.
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### Constraints:
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- The number of nodes in the binary tree is in the range [1, 10^5].
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- Each node's value is between [-10^4, 10^4].
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## Approach
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```mermaid
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flowchart TD
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S(["goodNodes(root)"]) --> C["dfs(root, root.val) — the root is always good"]
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C --> E(["return that count"])
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subgraph dfs["dfs(node, max_val)"]
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D1{"node is None?"} -- yes --> D2(["return 0"])
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D1 -- no --> D3["is_good = 1 if node.val >= max_val else 0 — max_val is the largest value on the path so far"]
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D3 --> D4["new_max = max(max_val, node.val)"]
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D4 --> D5["l = dfs(node.left, new_max), r = dfs(node.right, new_max)"]
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D5 --> D6(["return is_good + l + r"])
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end
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C --> dfs
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```
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## Solution
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```py
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# Definition for a binary tree node.
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# class TreeNode:
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# def __init__(self, val=0, left=None, right=None):
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# self.val = val
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# self.left = left
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# self.right = right
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class Solution:
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def goodNodes(self, root: TreeNode) -> int:
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def dfs(node, max_val):
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if not node:
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return 0
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is_good = 1 if node.val >= max_val else 0
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new_max = max(max_val, node.val)
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return is_good + dfs(node.left, new_max) + dfs(node.right, new_max)
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return dfs(root, root.val)
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```
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## Explanation
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<YouTube id="7cp5imvDzl4" title="Microsoft's Most Asked Question 2021 - Count Good Nodes in a Binary Tree - Leetcode 1448 - Python" />
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