mirror of
https://github.com/krahets/hello-algo.git
synced 2025-07-11 09:30:53 +08:00
Merge branch 'master' of github.com:krahets/hello-algo
This commit is contained in:
@ -48,7 +48,21 @@ G. M. Adelson-Velsky 和 E. M. Landis 在其 1962 年发表的论文 "An algorit
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=== "Python"
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```python title="avl_tree.py"
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""" AVL 树结点类 """
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class TreeNode:
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def __init__(self, val=None, left=None, right=None):
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self.val = val # 结点值
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self.height = 0 # 结点高度, avl 树会用到
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self.left = left # 左子结点引用
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self.right = right # 右子结点引用
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def __str__(self): # 直接print时会好看一点
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val = self.val
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left_node_val = self.left.val if self.left else None
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right_node_val = self.right.val if self.right else None
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return "<TreeNode: {}, leftTreeNode: {}, rightTreeNode: {}>".format(val, left_node_val, right_node_val)
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__repr__ = __str__
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```
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=== "Go"
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@ -115,7 +129,17 @@ G. M. Adelson-Velsky 和 E. M. Landis 在其 1962 年发表的论文 "An algorit
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=== "Python"
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```python title="avl_tree.py"
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""" 获取结点高度 """
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def height(self, node: typing.Optional[TreeNode]) -> int:
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# 空结点高度为 -1 ,叶结点高度为 0
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if node is not None:
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return node.height
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return -1
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""" 更新结点高度 """
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def __update_height(self, node: TreeNode):
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# 结点高度等于最高子树高度 + 1
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node.height = max([self.height(node.left), self.height(node.right)]) + 1
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```
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=== "Go"
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@ -185,7 +209,13 @@ G. M. Adelson-Velsky 和 E. M. Landis 在其 1962 年发表的论文 "An algorit
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=== "Python"
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```python title="avl_tree.py"
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""" 获取平衡因子 """
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def balance_factor(self, node: TreeNode) -> int:
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# 空结点平衡因子为 0
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if node is None:
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return 0
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# 结点平衡因子 = 左子树高度 - 右子树高度
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return self.height(node.left) - self.height(node.right)
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```
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=== "Go"
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@ -281,7 +311,18 @@ AVL 树的独特之处在于「旋转 Rotation」的操作,其可 **在不影
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=== "Python"
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```python title="avl_tree.py"
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""" 右旋操作 """
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def __right_rotate(self, node: TreeNode) -> TreeNode:
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child = node.left
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grand_child = child.right
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# 以 child 为原点,将 node 向右旋转
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child.right = node
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node.left = grand_child
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# 更新结点高度
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self.__update_height(node)
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self.__update_height(child)
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# 返回旋转后子树的根节点
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return child
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```
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=== "Go"
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@ -363,7 +404,18 @@ AVL 树的独特之处在于「旋转 Rotation」的操作,其可 **在不影
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=== "Python"
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```python title="avl_tree.py"
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""" 左旋操作 """
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def __left_rotate(self, node: TreeNode) -> TreeNode:
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child = node.right
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grand_child = child.left
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# 以 child 为原点,将 node 向左旋转
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child.left = node
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node.right = grand_child
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# 更新结点高度
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self.__update_height(node)
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self.__update_height(child)
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# 返回旋转后子树的根节点
|
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return child
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```
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|
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=== "Go"
|
||||
@ -485,7 +537,30 @@ AVL 树的独特之处在于「旋转 Rotation」的操作,其可 **在不影
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=== "Python"
|
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|
||||
```python title="avl_tree.py"
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""" 执行旋转操作,使该子树重新恢复平衡 """
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def __rotate(self, node: TreeNode) -> TreeNode:
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# 获取结点 node 的平衡因子
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balance_factor = self.balance_factor(node)
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# 左偏树
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if balance_factor > 1:
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if self.balance_factor(node.left) >= 0:
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# 右旋
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return self.__right_rotate(node)
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else:
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# 先左旋后右旋
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node.left = self.__left_rotate(node.left)
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return self.__right_rotate(node)
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# 右偏树
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elif balance_factor < -1:
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if self.balance_factor(node.right) <= 0:
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# 左旋
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return self.__left_rotate(node)
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else:
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# 先右旋后左旋
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node.right = self.__right_rotate(node.right)
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return self.__left_rotate(node)
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# 平衡树,无需旋转,直接返回
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return node
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```
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=== "Go"
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||||
@ -597,7 +672,27 @@ AVL 树的独特之处在于「旋转 Rotation」的操作,其可 **在不影
|
||||
=== "Python"
|
||||
|
||||
```python title="avl_tree.py"
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||||
|
||||
""" 插入结点 """
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def insert(self, val) -> TreeNode:
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self.root = self.__insert_helper(self.root, val)
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return self.root
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""" 递归插入结点(辅助函数)"""
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def __insert_helper(self, node: typing.Optional[TreeNode], val: int) -> TreeNode:
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if node is None:
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return TreeNode(val)
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# 1. 查找插入位置,并插入结点
|
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if val < node.val:
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node.left = self.__insert_helper(node.left, val)
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elif val > node.val:
|
||||
node.right = self.__insert_helper(node.right, val)
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||||
else:
|
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# 重复结点不插入,直接返回
|
||||
return node
|
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# 更新结点高度
|
||||
self.__update_height(node)
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||||
# 2. 执行旋转操作,使该子树重新恢复平衡
|
||||
return self.__rotate(node)
|
||||
```
|
||||
|
||||
=== "Go"
|
||||
@ -717,7 +812,46 @@ AVL 树的独特之处在于「旋转 Rotation」的操作,其可 **在不影
|
||||
=== "Python"
|
||||
|
||||
```python title="avl_tree.py"
|
||||
|
||||
""" 删除结点 """
|
||||
def remove(self, val: int):
|
||||
root = self.__remove_helper(self.root, val)
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||||
return root
|
||||
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||||
""" 递归删除结点(辅助函数) """
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||||
def __remove_helper(self, node: typing.Optional[TreeNode], val: int) -> typing.Optional[TreeNode]:
|
||||
if node is None:
|
||||
return None
|
||||
# 1. 查找结点,并删除之
|
||||
if val < node.val:
|
||||
node.left = self.__remove_helper(node.left, val)
|
||||
elif val > node.val:
|
||||
node.right = self.__remove_helper(node.right, val)
|
||||
else:
|
||||
if node.left is None or node.right is None:
|
||||
child = node.left or node.right
|
||||
# 子结点数量 = 0 ,直接删除 node 并返回
|
||||
if child is None:
|
||||
return None
|
||||
# 子结点数量 = 1 ,直接删除 node
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||||
else:
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||||
node = child
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||||
else: # 子结点数量 = 2 ,则将中序遍历的下个结点删除,并用该结点替换当前结点
|
||||
temp = self.min_node(node.right)
|
||||
node.right = self.__remove_helper(node.right, temp.val)
|
||||
node.val = temp.val
|
||||
# 更新结点高度
|
||||
self.__update_height(node)
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||||
# 2. 执行旋转操作,使该子树重新恢复平衡
|
||||
return self.__rotate(node)
|
||||
|
||||
""" 获取最小结点 """
|
||||
def min_node(self, node: typing.Optional[TreeNode]) -> typing.Optional[TreeNode]:
|
||||
if node is None:
|
||||
return None
|
||||
# 循环访问左子结点,直到叶结点时为最小结点,跳出
|
||||
while node.left is not None:
|
||||
node = node.left
|
||||
return node
|
||||
```
|
||||
|
||||
=== "Go"
|
||||
|
@ -82,7 +82,21 @@ comments: true
|
||||
=== "Python"
|
||||
|
||||
```python title="binary_search_tree.py"
|
||||
|
||||
""" 查找结点 """
|
||||
def search(self, num: int) -> typing.Optional[TreeNode]:
|
||||
cur = self.root
|
||||
# 循环查找,越过叶结点后跳出
|
||||
while cur is not None:
|
||||
# 目标结点在 root 的右子树中
|
||||
if cur.val < num:
|
||||
cur = cur.right
|
||||
# 目标结点在 root 的左子树中
|
||||
elif cur.val > num:
|
||||
cur = cur.left
|
||||
# 找到目标结点,跳出循环
|
||||
else:
|
||||
break
|
||||
return cur
|
||||
```
|
||||
|
||||
=== "Go"
|
||||
@ -244,7 +258,35 @@ comments: true
|
||||
=== "Python"
|
||||
|
||||
```python title="binary_search_tree.py"
|
||||
""" 插入结点 """
|
||||
def insert(self, num: int) -> typing.Optional[TreeNode]:
|
||||
root = self.root
|
||||
# 若树为空,直接提前返回
|
||||
if root is None:
|
||||
return None
|
||||
|
||||
cur = root
|
||||
pre = None
|
||||
|
||||
# 循环查找,越过叶结点后跳出
|
||||
while cur is not None:
|
||||
# 找到重复结点,直接返回
|
||||
if cur.val == num:
|
||||
return None
|
||||
pre = cur
|
||||
|
||||
if cur.val < num: # 插入位置在 root 的右子树中
|
||||
cur = cur.right
|
||||
else: # 插入位置在 root 的左子树中
|
||||
cur = cur.left
|
||||
|
||||
# 插入结点 val
|
||||
node = TreeNode(num)
|
||||
if pre.val < num:
|
||||
pre.right = node
|
||||
else:
|
||||
pre.left = node
|
||||
return node
|
||||
```
|
||||
|
||||
=== "Go"
|
||||
@ -525,7 +567,60 @@ comments: true
|
||||
=== "Python"
|
||||
|
||||
```python title="binary_search_tree.py"
|
||||
""" 删除结点 """
|
||||
def remove(self, num: int) -> typing.Optional[TreeNode]:
|
||||
root = self.root
|
||||
# 若树为空,直接提前返回
|
||||
if root is None:
|
||||
return None
|
||||
|
||||
cur = root
|
||||
pre = None
|
||||
|
||||
# 循环查找,越过叶结点后跳出
|
||||
while cur is not None:
|
||||
# 找到待删除结点,跳出循环
|
||||
if cur.val == num:
|
||||
break
|
||||
pre = cur
|
||||
if cur.val < num: # 待删除结点在 root 的右子树中
|
||||
cur = cur.right
|
||||
else: # 待删除结点在 root 的左子树中
|
||||
cur = cur.left
|
||||
|
||||
# 若无待删除结点,则直接返回
|
||||
if cur is None:
|
||||
return None
|
||||
|
||||
# 子结点数量 = 0 or 1
|
||||
if cur.left is None or cur.right is None:
|
||||
# 当子结点数量 = 0 / 1 时, child = null / 该子结点
|
||||
child = cur.left or cur.right
|
||||
# 删除结点 cur
|
||||
if pre.left == cur:
|
||||
pre.left = child
|
||||
else:
|
||||
pre.right = child
|
||||
# 子结点数量 = 2
|
||||
else:
|
||||
# 获取中序遍历中 cur 的下一个结点
|
||||
nex = self.min(cur.right)
|
||||
tmp = nex.val
|
||||
# 递归删除结点 nex
|
||||
self.remove(nex.val)
|
||||
# 将 nex 的值复制给 cur
|
||||
cur.val = tmp
|
||||
return cur
|
||||
|
||||
""" 获取最小结点 """
|
||||
def min(self, root: typing.Optional[TreeNode]) -> typing.Optional[TreeNode]:
|
||||
if root is None:
|
||||
return root
|
||||
|
||||
# 循环访问左子结点,直到叶结点时为最小结点,跳出
|
||||
while root.left is not None:
|
||||
root = root.left
|
||||
return root
|
||||
```
|
||||
|
||||
=== "Go"
|
||||
|
@ -35,7 +35,7 @@ comments: true
|
||||
```python title=""
|
||||
""" 链表结点类 """
|
||||
class TreeNode:
|
||||
def __init__(self, val=0, left=None, right=None):
|
||||
def __init__(self, val=None, left=None, right=None):
|
||||
self.val = val # 结点值
|
||||
self.left = left # 左子结点指针
|
||||
self.right = right # 右子结点指针
|
||||
@ -175,7 +175,18 @@ comments: true
|
||||
=== "Python"
|
||||
|
||||
```python title="binary_tree.py"
|
||||
|
||||
""" 初始化二叉树 """
|
||||
# 初始化节点
|
||||
n1 = TreeNode(val=1)
|
||||
n2 = TreeNode(val=2)
|
||||
n3 = TreeNode(val=3)
|
||||
n4 = TreeNode(val=4)
|
||||
n5 = TreeNode(val=5)
|
||||
# 构建引用指向(即指针)
|
||||
n1.left = n2
|
||||
n1.right = n3
|
||||
n2.left = n4
|
||||
n2.right = n5
|
||||
```
|
||||
|
||||
=== "Go"
|
||||
@ -284,7 +295,13 @@ comments: true
|
||||
=== "Python"
|
||||
|
||||
```python title="binary_tree.py"
|
||||
|
||||
""" 插入与删除结点 """
|
||||
p = TreeNode(0)
|
||||
# 在 n1 -> n2 中间插入结点 P
|
||||
n1.left = p
|
||||
p.left = n2
|
||||
# 删除节点 P
|
||||
n1.left = n2
|
||||
```
|
||||
|
||||
=== "Go"
|
||||
@ -437,7 +454,7 @@ comments: true
|
||||
=== "Python"
|
||||
|
||||
```python title=""
|
||||
“”“ 二叉树的数组表示 ”“”
|
||||
""" 二叉树的数组表示 """
|
||||
# 直接使用 None 来表示空位
|
||||
tree = [1, 2, 3, 4, None, 6, 7, 8, 9, None, None, 12, None, None, 15]
|
||||
```
|
||||
|
@ -51,12 +51,12 @@ comments: true
|
||||
vector<int> vec;
|
||||
while (!queue.empty()) {
|
||||
TreeNode* node = queue.front();
|
||||
queue.pop(); // 队列出队
|
||||
vec.push_back(node->val); // 保存结点
|
||||
queue.pop(); // 队列出队
|
||||
vec.push_back(node->val); // 保存结点
|
||||
if (node->left != nullptr)
|
||||
queue.push(node->left); // 左子结点入队
|
||||
queue.push(node->left); // 左子结点入队
|
||||
if (node->right != nullptr)
|
||||
queue.push(node->right); // 右子结点入队
|
||||
queue.push(node->right); // 右子结点入队
|
||||
}
|
||||
return vec;
|
||||
}
|
||||
@ -65,7 +65,21 @@ comments: true
|
||||
=== "Python"
|
||||
|
||||
```python title="binary_tree_bfs.py"
|
||||
|
||||
""" 层序遍历 """
|
||||
def hier_order(root: TreeNode):
|
||||
# 初始化队列,加入根结点
|
||||
queue = collections.deque()
|
||||
queue.append(root)
|
||||
# 初始化一个列表,用于保存遍历序列
|
||||
res = []
|
||||
while queue:
|
||||
node = queue.popleft() # 队列出队
|
||||
res.append(node.val) # 保存节点值
|
||||
if node.left is not None:
|
||||
queue.append(node.left) # 左子结点入队
|
||||
if node.right is not None:
|
||||
queue.append(node.right) # 右子结点入队
|
||||
return res
|
||||
```
|
||||
|
||||
=== "Go"
|
||||
@ -256,7 +270,32 @@ comments: true
|
||||
=== "Python"
|
||||
|
||||
```python title="binary_tree_dfs.py"
|
||||
|
||||
""" 前序遍历 """
|
||||
def pre_order(root: typing.Optional[TreeNode]):
|
||||
if root is None:
|
||||
return
|
||||
# 访问优先级:根结点 -> 左子树 -> 右子树
|
||||
res.append(root.val)
|
||||
pre_order(root=root.left)
|
||||
pre_order(root=root.right)
|
||||
|
||||
""" 中序遍历 """
|
||||
def in_order(root: typing.Optional[TreeNode]):
|
||||
if root is None:
|
||||
return
|
||||
# 访问优先级:左子树 -> 根结点 -> 右子树
|
||||
in_order(root=root.left)
|
||||
res.append(root.val)
|
||||
in_order(root=root.right)
|
||||
|
||||
""" 后序遍历 """
|
||||
def post_order(root: typing.Optional[TreeNode]):
|
||||
if root is None:
|
||||
return
|
||||
# 访问优先级:左子树 -> 右子树 -> 根结点
|
||||
post_order(root=root.left)
|
||||
post_order(root=root.right)
|
||||
res.append(root.val)
|
||||
```
|
||||
|
||||
=== "Go"
|
||||
@ -402,7 +441,6 @@ comments: true
|
||||
postOrder(root.right);
|
||||
list.Add(root.val);
|
||||
}
|
||||
|
||||
```
|
||||
|
||||
!!! note
|
||||
|
Reference in New Issue
Block a user