Add implementation of array binary tree.

Rewrite the tree serialization and deserialization methods.
Add applications of array and linked list.

codes/python/chapter_tree/array_binary_tree.py

@@ -0,0 +1,118 @@
+"""
+File: array_binary_tree.py
+Created Time: 2023-07-19
+Author: Krahets (krahets@163.com)
+"""
+
+import sys, os.path as osp
+
+sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__))))
+from modules import *
+
+
+class ArrayBinaryTree:
+    """数组表示下的二叉树类"""
+
+    def __init__(self, arr: list[int | None]):
+        """构造方法"""
+        self.__tree = list(arr)
+
+    def size(self):
+        """节点数量"""
+        return len(self.__tree)
+
+    def val(self, i: int) -> int:
+        """获取索引为 i 节点的值"""
+        # 若索引越界，则返回 None ，代表空位
+        if i < 0 or i >= self.size():
+            return None
+        return self.__tree[i]
+
+    def left(self, i: int) -> int | None:
+        """获取索引为 i 节点的左子节点的索引"""
+        return 2 * i + 1
+
+    def right(self, i: int) -> int | None:
+        """获取索引为 i 节点的右子节点的索引"""
+        return 2 * i + 2
+
+    def parent(self, i: int) -> int | None:
+        """获取索引为 i 节点的父节点的索引"""
+        return (i - 1) // 2
+
+    def level_order(self) -> list[int]:
+        """层序遍历"""
+        self.res = []
+        # 直接遍历数组
+        for i in range(self.size()):
+            if self.val(i) is not None:
+                self.res.append(self.val(i))
+        return self.res
+
+    def __dfs(self, i: int, order: str):
+        """深度优先遍历"""
+        if self.val(i) is None:
+            return
+        # 前序遍历
+        if order == "pre":
+            self.res.append(self.val(i))
+        self.__dfs(self.left(i), order)
+        # 中序遍历
+        if order == "in":
+            self.res.append(self.val(i))
+        self.__dfs(self.right(i), order)
+        # 后序遍历
+        if order == "post":
+            self.res.append(self.val(i))
+
+    def pre_order(self) -> list[int]:
+        """前序遍历"""
+        self.res = []
+        self.__dfs(0, order="pre")
+        return self.res
+
+    def in_order(self) -> list[int]:
+        """中序遍历"""
+        self.res = []
+        self.__dfs(0, order="in")
+        return self.res
+
+    def post_order(self) -> list[int]:
+        """后序遍历"""
+        self.res = []
+        self.__dfs(0, order="post")
+        return self.res
+
+
+"""Driver Code"""
+if __name__ == "__main__":
+    # 初始化二叉树
+    # 这里借助了一个从数组直接生成二叉树的函数
+    arr = [1, 2, 3, 4, None, 6, 7, 8, 9, None, None, 12, None, None, 15]
+    root = list_to_tree(arr)
+    print("\n初始化二叉树\n")
+    print(f"二叉树的数组表示：")
+    print(arr)
+    print(f"二叉树的链表表示：")
+    print_tree(root)
+
+    # 数组表示下的二叉树类
+    abt = ArrayBinaryTree(arr)
+
+    # 访问节点
+    i = 1
+    l, r, p = abt.left(i), abt.right(i), abt.parent(i)
+    print(f"\n当前节点的索引为 {i} ，值为 {abt.val(i)}")
+    print(f"其左子节点的索引为 {l} ，值为 {abt.val(l)}")
+    print(f"其右子节点的索引为 {r} ，值为 {abt.val(r)}")
+    print(f"其父节点的索引为 {p} ，值为 {abt.val(p)}")
+
+    # 遍历树
+    res = abt.level_order()
+    print("\n层序遍历为：", res)
+    res = abt.pre_order()
+    print("前序遍历为：", res)
+    res = abt.in_order()
+    print("中序遍历为：", res)
+    res = abt.post_order()
+    print("后序遍历为：", res)

codes/python/modules/__init__.py

@@ -3,13 +3,13 @@
 from __future__ import annotations
 
 # Import common libs here to simplify the codes by `from module import *`
-from .linked_list import (
+from .list_node import (
     ListNode,
     list_to_linked_list,
     linked_list_to_list,
     get_list_node,
 )
-from .binary_tree import TreeNode, list_to_tree, tree_to_list, get_tree_node
+from .tree_node import TreeNode, list_to_tree, tree_to_list, get_tree_node
 from .vertex import Vertex, vals_to_vets, vets_to_vals
 from .print_util import (
     print_matrix,

codes/python/modules/binary_tree.py

@@ -1,72 +0,0 @@
-"""
-File: binary_tree.py
-Created Time: 2021-12-11
-Author: Krahets (krahets@163.com)
-"""
-
-from collections import deque
-
-
-class TreeNode:
-    """Definition for a binary tree node"""
-
-    def __init__(self, val: int = 0):
-        self.val: int = val  # 节点值
-        self.height: int = 0  # 节点高度
-        self.left: TreeNode | None = None  # 左子节点引用
-        self.right: TreeNode | None = None  # 右子节点引用
-
-
-def list_to_tree(arr: list[int]) -> TreeNode | None:
-    """Generate a binary tree with a list"""
-    if not arr:
-        return None
-
-    i = 0
-    root = TreeNode(arr[0])
-    queue: deque[TreeNode] = deque([root])
-    while queue:
-        node: TreeNode = queue.popleft()
-        i += 1
-        if i >= len(arr):
-            break
-        if arr[i] != None:
-            node.left = TreeNode(arr[i])
-            queue.append(node.left)
-        i += 1
-        if i >= len(arr):
-            break
-        if arr[i] != None:
-            node.right = TreeNode(arr[i])
-            queue.append(node.right)
-
-    return root
-
-
-def tree_to_list(root: TreeNode | None) -> list[int]:
-    """Serialize a tree into an array"""
-    if not root:
-        return []
-    queue: deque[TreeNode] = deque()
-    queue.append(root)
-    res: list[int] = []
-    while queue:
-        node: TreeNode | None = queue.popleft()
-        if node:
-            res.append(node.val)
-            queue.append(node.left)
-            queue.append(node.right)
-        else:
-            res.append(None)
-    return res
-
-
-def get_tree_node(root: TreeNode | None, val: int) -> TreeNode | None:
-    """Get a tree node with specific value in a binary tree"""
-    if not root:
-        return
-    if root.val == val:
-        return root
-    left: TreeNode | None = get_tree_node(root.left, val)
-    right: TreeNode | None = get_tree_node(root.right, val)
-    return left if left else right

codes/python/modules/list_node.py

@@ -1,5 +1,5 @@
 """
-File: linked_list.py
+File: list_node.py
 Created Time: 2021-12-11
 Author: Krahets (krahets@163.com)
 """

codes/python/modules/print_util.py

@@ -4,8 +4,8 @@ Created Time: 2021-12-11
 Author: Krahets (krahets@163.com), msk397 (machangxinq@gmail.com)
 """
 
-from .binary_tree import TreeNode, list_to_tree
-from .linked_list import ListNode, linked_list_to_list
+from .tree_node import TreeNode, list_to_tree
+from .list_node import ListNode, linked_list_to_list
 
 
 def print_matrix(mat: list[list[int]]) -> None:

codes/python/modules/tree_node.py

@@ -0,0 +1,80 @@
+"""
+File: tree_node.py
+Created Time: 2021-12-11
+Author: Krahets (krahets@163.com)
+"""
+
+from collections import deque
+
+
+class TreeNode:
+    """二叉树节点类"""
+
+    def __init__(self, val: int = 0):
+        self.val: int = val  # 节点值
+        self.height: int = 0  # 节点高度
+        self.left: TreeNode | None = None  # 左子节点引用
+        self.right: TreeNode | None = None  # 右子节点引用
+
+    # 序列化编码规则请参考：
+    # https://www.hello-algo.com/chapter_tree/array_representation_of_tree/
+    # 二叉树的数组表示：
+    # [1, 2, 3, 4, None, 6, 7, 8, 9, None, None, 12, None, None, 15]
+    # 二叉树的链表表示：
+    #             /——— 15
+    #         /——— 7
+    #     /——— 3
+    #    |    \——— 6
+    #    |        \——— 12
+    # ——— 1
+    #     \——— 2
+    #        |    /——— 9
+    #         \——— 4
+    #             \——— 8
+
+
+def list_to_tree_dfs(arr: list[int], i: int) -> TreeNode | None:
+    """将列表反序列化为二叉树：递归"""
+    # 如果索引超出数组长度，或者对应的元素为 None，返回 None
+    if i < 0 or i >= len(arr) or arr[i] is None:
+        return None
+    # 构建当前节点
+    root = TreeNode(arr[i])
+    # 递归构建左右子树
+    root.left = list_to_tree_dfs(arr, 2 * i + 1)
+    root.right = list_to_tree_dfs(arr, 2 * i + 2)
+    return root
+
+
+def list_to_tree(arr: list[int]) -> TreeNode | None:
+    """将列表反序列化为二叉树"""
+    return list_to_tree_dfs(arr, 0)
+
+
+def tree_to_list_dfs(root: TreeNode, i: int, res: list[int]) -> list[int]:
+    """将二叉树序列化为列表：递归"""
+    if root is None:
+        return
+    if i >= len(res):
+        res += [None] * (i - len(res) + 1)
+    res[i] = root.val
+    tree_to_list_dfs(root.left, 2 * i + 1, res)
+    tree_to_list_dfs(root.right, 2 * i + 2, res)
+
+
+def tree_to_list(root: TreeNode | None) -> list[int]:
+    """将二叉树序列化为列表"""
+    res = []
+    tree_to_list_dfs(root, 0, res)
+    return res
+
+
+def get_tree_node(root: TreeNode | None, val: int) -> TreeNode | None:
+    """Get a tree node with specific value in a binary tree"""
+    if not root:
+        return
+    if root.val == val:
+        return root
+    left: TreeNode | None = get_tree_node(root.left, val)
+    right: TreeNode | None = get_tree_node(root.right, val)
+    return left if left else right