Lowest Common Ancestor Of A Binary Tree

0236.Lowest-Common-Ancestor-of-a-Binary-Tree/memo.md

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+# 236. Lowest Common Ancestor of a Binary Tree
+
+## step1
+pとqが見つかるまで木を探索し、見つかったら
+以前"Lowest Common Ancestor of a Binary Search Tree"で書いた解法。
+
+## 他の人のコード
+https://github.com/huyfififi/coding-challenges/pull/46
+
+かなりシンプルな解法になっている。自分の解法が冗長であったことを認識した。
+
+左右に分岐する点を求める解法は計算量的に O(N^2)になってしまう(step2_top_down.py)。
+この解法はtop-downであると言えるだろう。
+
+> lowest common ancestorの解釈を少し変えているのでやや邪道な感じがするが、`p`と`q`が左右に分かれているパターンを判定するために、`q`を含まない`p`をrootとした部分木においても、`p`がlowest common ancestorだとしておく（`q`が部分木のrootの場合も同様に）。
+
+この広義の定義と狭義の定義を区別した解法が「Cracking The Coding Interviewに載っていた」という解法であることも認識した。
+
+この解法はbottom-upといえる(step2_bottom_up.py)。
+時間計算量O(N)、空間計算量O(h)（最悪O(N)）
+
+top-down、bottom-upという観点でいえば、step1の解法はハイブリッドと言える。
+再帰を使っていない点では優れている。

0236.Lowest-Common-Ancestor-of-a-Binary-Tree/step1_hybrid.py

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+# Definition for a binary tree node.
+class TreeNode:
+    def __init__(self, x):
+        self.val = x
+        self.left = None
+        self.right = None
+
+
+class Solution:
+    def lowestCommonAncestor(
+        self, root: TreeNode, p: TreeNode, q: TreeNode
+    ) -> TreeNode:
+        node_to_depth_and_parent: dict[TreeNode, tuple[int, TreeNode | None]] = {}
+
+        depth = 1
+        frontier = [(root, None)]
+        found_p = False
+        found_q = False
+        while frontier:
+            next_frontier = []
+            for node, parent in frontier:
+                if node is None:
+                    continue
+                node_to_depth_and_parent[node] = (depth, parent)
+                if node == p:
+                    found_p = True
+                if node == q:
+                    found_q = True
+                if found_p and found_q:
+                    break
+                next_frontier.append((node.left, node))
+                next_frontier.append((node.right, node))
+            depth += 1
+            frontier = next_frontier
+
+        depth_p, parent_p = node_to_depth_and_parent[p]
+        depth_q, parent_q = node_to_depth_and_parent[q]
+        if depth_p < depth_q:
+            depth_p, depth_q = depth_q, depth_p
+            parent_p, parent_q = parent_q, parent_p
+            p, q = q, p
+        while depth_p > depth_q:
+            p = parent_p
+            depth_p, parent_p = node_to_depth_and_parent[p]
+        while p != q:
+            p = parent_p
+            depth_p, parent_p = node_to_depth_and_parent[p]
+            q = parent_q
+            depth_q, parent_q = node_to_depth_and_parent[q]
+
+        return p

0236.Lowest-Common-Ancestor-of-a-Binary-Tree/step2_bottom_up.cpp

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+
+// Definition for a binary tree node.
+struct TreeNode {
+    int val;
+    TreeNode *left;
+    TreeNode *right;
+    TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
+};
+
+class Solution {
+  public:
+    TreeNode *lowestCommonAncestor(TreeNode *root, TreeNode *p, TreeNode *q) {
+        if (root == nullptr) {
+            return nullptr;
+        }
+        if (root == p || root == q) {
+            return root;
+        }
+        TreeNode *left_found = lowestCommonAncestor(root->left, p, q);
+        TreeNode *right_found = lowestCommonAncestor(root->right, p, q);
+        if (left_found == nullptr) {
+            return right_found;
+        }
+        if (right_found == nullptr) {
+            return left_found;
+        }
+        return root;
+    }
+};

0236.Lowest-Common-Ancestor-of-a-Binary-Tree/step2_bottom_up.py

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+# Definition for a binary tree node.
+class TreeNode:
+    def __init__(self, x):
+        self.val = x
+        self.left = None
+        self.right = None
+
+
+class Solution:
+    def lowestCommonAncestor(
+        self, root: TreeNode, p: TreeNode, q: TreeNode
+    ) -> TreeNode:
+        if root is None:
+            return None
+        if root == p or root == q:
+            return root
+
+        left_found = self.lowestCommonAncestor(root.left, p, q)
+        right_found = self.lowestCommonAncestor(root.right, p, q)
+
+        if left_found is None:
+            return right_found
+        if right_found is None:
+            return left_found
+        return root

0236.Lowest-Common-Ancestor-of-a-Binary-Tree/step2_top_down.py

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+# Definition for a binary tree node.
+class TreeNode:
+    def __init__(self, x):
+        self.val = x
+        self.left = None
+        self.right = None
+
+
+class Solution:
+    def lowestCommonAncestor(
+        self, root: TreeNode, p: TreeNode, q: TreeNode
+    ) -> TreeNode:
+        def contain(node: TreeNode, target: TreeNode) -> bool:
+            if node is None:
+                return False
+            if node == target:
+                return True
+            return contain(node.left, target) or contain(node.right, target)
+
+        def lowest_common_ancester_helper(
+            node: TreeNode, target1: TreeNode, target2: TreeNode
+        ):
+            if node == target1 or node == target2:
+                return node
+
+            left_contain_1 = contain(node.left, target1)
+            left_contain_2 = contain(node.left, target2)
+
+            if left_contain_1 and left_contain_2:
+                return lowest_common_ancester_helper(node.left, target1, target2)
+            if not (left_contain_1 or left_contain_2):
+                return lowest_common_ancester_helper(node.right, target1, target2)
+            return node
+
+        return lowest_common_ancester_helper(root, p, q)