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)