Binary Tree Maximum Path Sum

0124.Binary-Tree-Maximum-Path-Sum/memo.md

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+# 124. Binary Tree Maximum Path Sum
+
+## step1
+再帰で書く。12mぐらい。
+
+以下の点を間違えた
+- 左右の子ノードを使う最大値を親ノードに返す（pathが分岐する）
+- 関数を呼び出さずにmax_sumを返す
+
+## 他の人のコード
+https://github.com/shining-ai/leetcode/pull/69
+
+考え方自体は同じだが書き方がやや異なる。
+
+## step2
+参考にして改善
+

0124.Binary-Tree-Maximum-Path-Sum/step1.py

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+import math
+
+# Definition for a binary tree node.
+class TreeNode:
+    def __init__(self, val=0, left=None, right=None):
+        self.val = val
+        self.left = left
+        self.right = right
+
+class Solution:
+    def maxPathSum(self, root: TreeNode | None) -> int:
+        max_sum = -math.inf
+
+        def update_max_sum(node):
+            # update the max sum of the tree
+            # return the max sum using the node as the root of the path
+            nonlocal max_sum
+            if node is None:
+                return -math.inf
+            max_sum_left = update_max_sum(node.left)
+            max_sum_right = update_max_sum(node.right)
+            max_sum_self = node.val + max(0, max_sum_left, max_sum_right)
+            max_sum = max(max_sum, max_sum_self, node.val + max_sum_left+max_sum_right)
+            return max_sum_self
+
+        update_max_sum(root)
+        return max_sum

0124.Binary-Tree-Maximum-Path-Sum/step1_revised.py

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+import math
+
+# Definition for a binary tree node.
+class TreeNode:
+    def __init__(self, val=0, left=None, right=None):
+        self.val = val
+        self.left = left
+        self.right = right
+
+class Solution:
+    def maxPathSum(self, root: TreeNode | None) -> int:
+        max_sum = -math.inf
+
+        def update_max_sum(node):
+            # update the max sum of the tree
+            # return the max sum using the node as the root of the path
+            nonlocal max_sum
+            if node is None:
+                return -math.inf
+            max_sum_left = update_max_sum(node.left)
+            max_sum_right = update_max_sum(node.right)
+            max_sum_self = node.val + max(0, max_sum_left, max_sum_right)
+            max_sum = max(max_sum, max_sum_self, node.val + max_sum_left + max_sum_right)
+            return max_sum_self
+
+        update_max_sum(root)
+        return max_sum

0124.Binary-Tree-Maximum-Path-Sum/step2.py

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+import math
+
+# Definition for a binary tree node.
+class TreeNode:
+    def __init__(self, val=0, left=None, right=None):
+        self.val = val
+        self.left = left
+        self.right = right
+
+class Solution:
+    def maxPathSum(self, root: TreeNode | None) -> int:
+
+        def get_max_sums(node):
+            # 返り値: (部分木の最大パス和, 親へ繋げられる片側の枝の最大和)
+            if node is None:
+                return -math.inf, 0
+
+            left_max_sum, left_branch_max = get_max_sums(node.left)
+            right_max_sum, right_branch_max = get_max_sums(node.right)
+
+            subtree_max = max(left_max_sum, right_max_sum, node.val + left_branch_max + right_branch_max)
+            branch_max = max(0, node.val + max(left_branch_max, right_branch_max))
+
+            return subtree_max, branch_max
+
+        max_sum, _ = get_max_sums(root)
+        return max_sum