You can not select more than 25 topics
Topics must start with a letter or number, can include dashes ('-') and can be up to 35 characters long.
120 lines
3.3 KiB
120 lines
3.3 KiB
"""
|
|
File: array_binary_tree.py
|
|
Created Time: 2023-07-19
|
|
Author: krahets (krahets@163.com)
|
|
"""
|
|
|
|
import sys
|
|
from pathlib import Path
|
|
|
|
sys.path.append(str(Path(__file__).parent.parent))
|
|
from modules import TreeNode, list_to_tree, print_tree
|
|
|
|
|
|
class ArrayBinaryTree:
|
|
"""陣列表示下的二元樹類別"""
|
|
|
|
def __init__(self, arr: list[int | None]):
|
|
"""建構子"""
|
|
self._tree = list(arr)
|
|
|
|
def size(self):
|
|
"""串列容量"""
|
|
return len(self._tree)
|
|
|
|
def val(self, i: int) -> int | None:
|
|
"""獲取索引為 i 節點的值"""
|
|
# 若索引越界，則返回 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:
|
|
"""獲取索引為 i 節點的左子節點的索引"""
|
|
return 2 * i + 1
|
|
|
|
def right(self, i: int) -> int | None:
|
|
"""獲取索引為 i 節點的右子節點的索引"""
|
|
return 2 * i + 2
|
|
|
|
def parent(self, i: int) -> int | None:
|
|
"""獲取索引為 i 節點的父節點的索引"""
|
|
return (i - 1) // 2
|
|
|
|
def level_order(self) -> list[int]:
|
|
"""層序走訪"""
|
|
self.res = []
|
|
# 直接走訪陣列
|
|
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):
|
|
"""深度優先走訪"""
|
|
if self.val(i) is None:
|
|
return
|
|
# 前序走訪
|
|
if order == "pre":
|
|
self.res.append(self.val(i))
|
|
self.dfs(self.left(i), order)
|
|
# 中序走訪
|
|
if order == "in":
|
|
self.res.append(self.val(i))
|
|
self.dfs(self.right(i), order)
|
|
# 後序走訪
|
|
if order == "post":
|
|
self.res.append(self.val(i))
|
|
|
|
def pre_order(self) -> list[int]:
|
|
"""前序走訪"""
|
|
self.res = []
|
|
self.dfs(0, order="pre")
|
|
return self.res
|
|
|
|
def in_order(self) -> list[int]:
|
|
"""中序走訪"""
|
|
self.res = []
|
|
self.dfs(0, order="in")
|
|
return self.res
|
|
|
|
def post_order(self) -> list[int]:
|
|
"""後序走訪"""
|
|
self.res = []
|
|
self.dfs(0, order="post")
|
|
return self.res
|
|
|
|
|
|
"""Driver Code"""
|
|
if __name__ == "__main__":
|
|
# 初始化二元樹
|
|
# 這裡藉助了一個從陣列直接生成二元樹的函式
|
|
arr = [1, 2, 3, 4, None, 6, 7, 8, 9, None, None, 12, None, None, 15]
|
|
root = list_to_tree(arr)
|
|
print("\n初始化二元樹\n")
|
|
print("二元樹的陣列表示：")
|
|
print(arr)
|
|
print("二元樹的鏈結串列表示：")
|
|
print_tree(root)
|
|
|
|
# 陣列表示下的二元樹類別
|
|
abt = ArrayBinaryTree(arr)
|
|
|
|
# 訪問節點
|
|
i = 1
|
|
l, r, p = abt.left(i), abt.right(i), abt.parent(i)
|
|
print(f"\n當前節點的索引為 {i} ，值為 {abt.val(i)}")
|
|
print(f"其左子節點的索引為 {l} ，值為 {abt.val(l)}")
|
|
print(f"其右子節點的索引為 {r} ，值為 {abt.val(r)}")
|
|
print(f"其父節點的索引為 {p} ，值為 {abt.val(p)}")
|
|
|
|
# 走訪樹
|
|
res = abt.level_order()
|
|
print("\n層序走訪為：", res)
|
|
res = abt.pre_order()
|
|
print("前序走訪為：", res)
|
|
res = abt.in_order()
|
|
print("中序走訪為：", res)
|
|
res = abt.post_order()
|
|
print("後序走訪為：", res)
|