mirror of
https://github.com/krahets/hello-algo.git
synced 2024-12-25 02:16:28 +08:00
Merge branch 'master' of github.com:krahets/hello-algo
This commit is contained in:
commit
d03980e185
11 changed files with 814 additions and 35 deletions
|
@ -15,12 +15,12 @@ vector<int> hierOrder(TreeNode* root) {
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vector<int> vec;
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while (!queue.empty()) {
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TreeNode* node = queue.front();
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queue.pop(); // 队列出队
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vec.push_back(node->val); // 保存结点
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queue.pop(); // 队列出队
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vec.push_back(node->val); // 保存结点
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if (node->left != nullptr)
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queue.push(node->left); // 左子结点入队
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queue.push(node->left); // 左子结点入队
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if (node->right != nullptr)
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queue.push(node->right); // 右子结点入队
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queue.push(node->right); // 右子结点入队
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}
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return vec;
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}
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208
codes/python/chapter_tree/avl_tree.py
Normal file
208
codes/python/chapter_tree/avl_tree.py
Normal file
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@ -0,0 +1,208 @@
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"""
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File: avl_tree.py
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Created Time: 2022-12-20
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Author: a16su (lpluls001@gmail.com)
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"""
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import sys, os.path as osp
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import typing
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sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__))))
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from include import *
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class AVLTree:
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def __init__(self, root: typing.Optional[TreeNode] = None):
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self.root = root
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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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""" 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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""" 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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""" 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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""" 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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""" 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:
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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
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return node
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# 更新结点高度
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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
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return self.__rotate(node)
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""" 删除结点 """
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def remove(self, val: int):
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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]:
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if node is None:
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return None
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# 1. 查找结点,并删除之
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if val < node.val:
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node.left = self.__remove_helper(node.left, val)
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elif val > node.val:
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node.right = self.__remove_helper(node.right, val)
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else:
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if node.left is None or node.right is None:
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child = node.left or node.right
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# 子结点数量 = 0 ,直接删除 node 并返回
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if child is None:
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return None
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# 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
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temp = self.__min_node(node.right)
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node.right = self.__remove_helper(node.right, temp.val)
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node.val = temp.val
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# 更新结点高度
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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
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return self.__rotate(node)
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""" 获取最小结点 """
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def __min_node(self, node: typing.Optional[TreeNode]) -> typing.Optional[TreeNode]:
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if node is None:
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return None
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# 循环访问左子结点,直到叶结点时为最小结点,跳出
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while node.left is not None:
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node = node.left
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return node
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""" 查找结点 """
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def search(self, val: int):
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cur = self.root
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# 循环查找,越过叶结点后跳出
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while cur is not None:
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# 目标结点在 root 的右子树中
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if cur.val < val:
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cur = cur.right
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# 目标结点在 root 的左子树中
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elif cur.val > val:
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cur = cur.left
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# 找到目标结点,跳出循环
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else:
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break
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# 返回目标结点
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return cur
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""" Driver Code """
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if __name__ == "__main__":
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def test_insert(tree: AVLTree, val: int):
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tree.insert(val)
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print("\n插入结点 {} 后,AVL 树为".format(val))
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print_tree(tree.root)
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def test_remove(tree: AVLTree, val: int):
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tree.remove(val)
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print("\n删除结点 {} 后,AVL 树为".format(val))
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print_tree(tree.root)
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# 初始化空 AVL 树
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avl_tree = AVLTree()
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# 插入结点
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# 请关注插入结点后,AVL 树是如何保持平衡的
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test_insert(avl_tree, 1)
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test_insert(avl_tree, 2)
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test_insert(avl_tree, 3)
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test_insert(avl_tree, 4)
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test_insert(avl_tree, 5)
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test_insert(avl_tree, 8)
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test_insert(avl_tree, 7)
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test_insert(avl_tree, 9)
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test_insert(avl_tree, 10)
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test_insert(avl_tree, 6)
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# 插入重复结点
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test_insert(avl_tree, 7)
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# 删除结点
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# 请关注删除结点后,AVL 树是如何保持平衡的
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test_remove(avl_tree, 8) # 删除度为 0 的结点
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test_remove(avl_tree, 5) # 删除度为 1 的结点
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test_remove(avl_tree, 4) # 删除度为 2 的结点
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result_node = avl_tree.search(7)
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print("\n查找到的结点对象为 {},结点值 = {}".format(result_node, result_node.val))
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@ -1,10 +1,167 @@
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"""
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File: binary_search_tree.py
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Created Time: 2022-11-25
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Author: Krahets (krahets@163.com)
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Created Time: 2022-12-20
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Author: a16su (lpluls001@gmail.com)
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"""
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import sys, os.path as osp
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import typing
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sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__))))
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from include import *
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""" 二叉搜索树 """
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class BinarySearchTree:
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def __init__(self, nums: typing.List[int]) -> None:
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nums.sort()
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self.__root = self.build_tree(nums, 0, len(nums) - 1)
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""" 构建二叉搜索树 """
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def build_tree(self, nums: typing.List[int], start_index: int, end_index: int) -> typing.Optional[TreeNode]:
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if start_index > end_index:
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return None
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# 将数组中间结点作为根结点
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mid = (start_index + end_index) // 2
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root = TreeNode(nums[mid])
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# 递归建立左子树和右子树
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root.left = self.build_tree(nums=nums, start_index=start_index, end_index=mid - 1)
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root.right = self.build_tree(nums=nums, start_index=mid + 1, end_index=end_index)
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return root
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@property
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def root(self) -> typing.Optional[TreeNode]:
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return self.__root
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""" 查找结点 """
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def search(self, num: int) -> typing.Optional[TreeNode]:
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cur = self.root
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# 循环查找,越过叶结点后跳出
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while cur is not None:
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# 目标结点在 root 的右子树中
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if cur.val < num:
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cur = cur.right
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# 目标结点在 root 的左子树中
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elif cur.val > num:
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cur = cur.left
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# 找到目标结点,跳出循环
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else:
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break
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return cur
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""" 插入结点 """
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def insert(self, num: int) -> typing.Optional[TreeNode]:
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root = self.root
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# 若树为空,直接提前返回
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if root is None:
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return None
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|
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cur = root
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pre = None
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# 循环查找,越过叶结点后跳出
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while cur is not None:
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# 找到重复结点,直接返回
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if cur.val == num:
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return None
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pre = cur
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if cur.val < num: # 插入位置在 root 的右子树中
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cur = cur.right
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else: # 插入位置在 root 的左子树中
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cur = cur.left
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|
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# 插入结点 val
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node = TreeNode(num)
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if pre.val < num:
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pre.right = node
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else:
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pre.left = node
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return node
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|
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""" 删除结点 """
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def remove(self, num: int) -> typing.Optional[TreeNode]:
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root = self.root
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# 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
|
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while cur is not None:
|
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# 找到待删除结点,跳出循环
|
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if cur.val == num:
|
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break
|
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pre = cur
|
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if cur.val < num: # 待删除结点在 root 的右子树中
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cur = cur.right
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else: # 待删除结点在 root 的左子树中
|
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cur = cur.left
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|
||||
# 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
|
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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
|
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# 删除结点 cur
|
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if pre.left == cur:
|
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pre.left = child
|
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else:
|
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pre.right = child
|
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# 子结点数量 = 2
|
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else:
|
||||
# 获取中序遍历中 cur 的下一个结点
|
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nex = self.min(cur.right)
|
||||
tmp = nex.val
|
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# 递归删除结点 nex
|
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self.remove(nex.val)
|
||||
# 将 nex 的值复制给 cur
|
||||
cur.val = tmp
|
||||
return cur
|
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|
||||
""" 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
|
||||
|
||||
|
||||
""" Driver Code """
|
||||
if __name__ == "__main__":
|
||||
# 初始化二叉搜索树
|
||||
nums = list(range(1, 16))
|
||||
bst = BinarySearchTree(nums=nums)
|
||||
print("\n初始化的二叉树为\n")
|
||||
print_tree(bst.root)
|
||||
|
||||
# 查找结点
|
||||
node = bst.search(5)
|
||||
print("\n查找到的结点对象为: {},结点值 = {}".format(node, node.val))
|
||||
|
||||
# 插入结点
|
||||
ndoe = bst.insert(16)
|
||||
print("\n插入结点 16 后,二叉树为\n")
|
||||
print_tree(bst.root)
|
||||
|
||||
# 删除结点
|
||||
bst.remove(1)
|
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print("\n删除结点 1 后,二叉树为\n")
|
||||
print_tree(bst.root)
|
||||
|
||||
bst.remove(2)
|
||||
print("\n删除结点 2 后,二叉树为\n")
|
||||
print_tree(bst.root)
|
||||
|
||||
bst.remove(4)
|
||||
print("\n删除结点 4 后,二叉树为\n")
|
||||
print_tree(bst.root)
|
||||
|
|
|
@ -1,10 +1,40 @@
|
|||
"""
|
||||
File: binary_tree.py
|
||||
Created Time: 2022-11-25
|
||||
Author: Krahets (krahets@163.com)
|
||||
Created Time: 2022-12-20
|
||||
Author: a16su (lpluls001@gmail.com)
|
||||
"""
|
||||
|
||||
import sys, os.path as osp
|
||||
|
||||
sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__))))
|
||||
from include import *
|
||||
|
||||
|
||||
""" Driver Code """
|
||||
if __name__ == "__main__":
|
||||
""" 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
|
||||
print("\n初始化二叉树\n")
|
||||
print_tree(n1)
|
||||
|
||||
""" 插入与删除结点 """
|
||||
P = TreeNode(0)
|
||||
# 在 n1 -> n2 中间插入节点 P
|
||||
n1.left = P
|
||||
P.left = n2
|
||||
print("\n插入结点 P 后\n")
|
||||
print_tree(n1)
|
||||
# 删除结点
|
||||
n1.left = n2
|
||||
print("\n删除结点 P 后\n");
|
||||
print_tree(n1)
|
||||
|
|
|
@ -1,10 +1,42 @@
|
|||
"""
|
||||
File: binary_tree_bfs.py
|
||||
Created Time: 2022-11-25
|
||||
Author: Krahets (krahets@163.com)
|
||||
Created Time: 2022-12-20
|
||||
Author: a16su (lpluls001@gmail.com)
|
||||
"""
|
||||
|
||||
import sys, os.path as osp
|
||||
import typing
|
||||
|
||||
sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__))))
|
||||
from include import *
|
||||
|
||||
|
||||
""" 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
|
||||
|
||||
|
||||
""" 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
|
||||
root = list_to_tree(arr=[1, 2, 3, 4, 5, 6, 7, None, None, None, None, None, None, None, None])
|
||||
print("\n初始化二叉树\n")
|
||||
print_tree(root)
|
||||
|
||||
# 层序遍历
|
||||
res = hier_order(root)
|
||||
print("\n层序遍历的结点打印序列 = ", res)
|
||||
assert res == [1, 2, 3, 4, 5, 6, 7]
|
||||
|
|
|
@ -1,10 +1,68 @@
|
|||
"""
|
||||
File: binary_tree_dfs.py
|
||||
Created Time: 2022-11-25
|
||||
Author: Krahets (krahets@163.com)
|
||||
Created Time: 2022-12-20
|
||||
Author: a16su (lpluls001@gmail.com)
|
||||
"""
|
||||
|
||||
import sys, os.path as osp
|
||||
import typing
|
||||
|
||||
sys.path.append(osp.dirname(osp.dirname(osp.abspath(__file__))))
|
||||
from include import *
|
||||
|
||||
|
||||
res = []
|
||||
|
||||
""" 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)
|
||||
|
||||
|
||||
""" 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
|
||||
root = list_to_tree(arr=[1, 2, 3, 4, 5, 6, 7, None, None, None, None, None, None, None, None])
|
||||
print("\n初始化二叉树\n")
|
||||
print_tree(root)
|
||||
|
||||
# 前序遍历
|
||||
res.clear()
|
||||
pre_order(root)
|
||||
print("\n前序遍历的结点打印序列 = ", res)
|
||||
assert res == [1, 2, 4, 5, 3, 6, 7]
|
||||
|
||||
# 中序遍历
|
||||
res.clear()
|
||||
in_order(root)
|
||||
print("\n中序遍历的结点打印序列 = ", res)
|
||||
assert res == [4, 2, 5, 1, 6, 3, 7]
|
||||
|
||||
# 后序遍历
|
||||
res.clear()
|
||||
post_order(root)
|
||||
print("\n后序遍历的结点打印序列 = ", res)
|
||||
assert res == [4, 5, 2, 6, 7, 3, 1]
|
||||
|
|
|
@ -10,9 +10,19 @@ class TreeNode:
|
|||
"""Definition for a binary tree node
|
||||
"""
|
||||
def __init__(self, val=0, left=None, right=None):
|
||||
self.val = val
|
||||
self.left = left
|
||||
self.right = right
|
||||
self.val = val # 结点值
|
||||
self.height = 0 # 结点高度
|
||||
self.left = left # 左子结点引用
|
||||
self.right = right # 右子结点引用
|
||||
|
||||
def __str__(self):
|
||||
val = self.val
|
||||
left_node_val = self.left.val if self.left else None
|
||||
right_node_val = self.right.val if self.right else None
|
||||
return "<TreeNode: {}, leftTreeNode: {}, rightTreeNode: {}>".format(val, left_node_val, right_node_val)
|
||||
|
||||
__repr__ = __str__
|
||||
|
||||
|
||||
def list_to_tree(arr):
|
||||
"""Generate a binary tree with a list
|
||||
|
|
|
@ -48,7 +48,21 @@ G. M. Adelson-Velsky 和 E. M. Landis 在其 1962 年发表的论文 "An algorit
|
|||
=== "Python"
|
||||
|
||||
```python title="avl_tree.py"
|
||||
|
||||
""" AVL 树结点类 """
|
||||
class TreeNode:
|
||||
def __init__(self, val=None, left=None, right=None):
|
||||
self.val = val # 结点值
|
||||
self.height = 0 # 结点高度, avl 树会用到
|
||||
self.left = left # 左子结点引用
|
||||
self.right = right # 右子结点引用
|
||||
|
||||
def __str__(self): # 直接print时会好看一点
|
||||
val = self.val
|
||||
left_node_val = self.left.val if self.left else None
|
||||
right_node_val = self.right.val if self.right else None
|
||||
return "<TreeNode: {}, leftTreeNode: {}, rightTreeNode: {}>".format(val, left_node_val, right_node_val)
|
||||
|
||||
__repr__ = __str__
|
||||
```
|
||||
|
||||
=== "Go"
|
||||
|
@ -115,7 +129,17 @@ G. M. Adelson-Velsky 和 E. M. Landis 在其 1962 年发表的论文 "An algorit
|
|||
=== "Python"
|
||||
|
||||
```python title="avl_tree.py"
|
||||
|
||||
""" 获取结点高度 """
|
||||
def height(self, node: typing.Optional[TreeNode]) -> int:
|
||||
# 空结点高度为 -1 ,叶结点高度为 0
|
||||
if node is not None:
|
||||
return node.height
|
||||
return -1
|
||||
|
||||
""" 更新结点高度 """
|
||||
def __update_height(self, node: TreeNode):
|
||||
# 结点高度等于最高子树高度 + 1
|
||||
node.height = max([self.height(node.left), self.height(node.right)]) + 1
|
||||
```
|
||||
|
||||
=== "Go"
|
||||
|
@ -185,7 +209,13 @@ G. M. Adelson-Velsky 和 E. M. Landis 在其 1962 年发表的论文 "An algorit
|
|||
=== "Python"
|
||||
|
||||
```python title="avl_tree.py"
|
||||
|
||||
""" 获取平衡因子 """
|
||||
def balance_factor(self, node: TreeNode) -> int:
|
||||
# 空结点平衡因子为 0
|
||||
if node is None:
|
||||
return 0
|
||||
# 结点平衡因子 = 左子树高度 - 右子树高度
|
||||
return self.height(node.left) - self.height(node.right)
|
||||
```
|
||||
|
||||
=== "Go"
|
||||
|
@ -281,7 +311,18 @@ 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"
|
||||
|
||||
""" 右旋操作 """
|
||||
def __right_rotate(self, node: TreeNode) -> TreeNode:
|
||||
child = node.left
|
||||
grand_child = child.right
|
||||
# 以 child 为原点,将 node 向右旋转
|
||||
child.right = node
|
||||
node.left = grand_child
|
||||
# 更新结点高度
|
||||
self.__update_height(node)
|
||||
self.__update_height(child)
|
||||
# 返回旋转后子树的根节点
|
||||
return child
|
||||
```
|
||||
|
||||
=== "Go"
|
||||
|
@ -363,7 +404,18 @@ 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"
|
||||
|
||||
""" 左旋操作 """
|
||||
def __left_rotate(self, node: TreeNode) -> TreeNode:
|
||||
child = node.right
|
||||
grand_child = child.left
|
||||
# 以 child 为原点,将 node 向左旋转
|
||||
child.left = node
|
||||
node.right = grand_child
|
||||
# 更新结点高度
|
||||
self.__update_height(node)
|
||||
self.__update_height(child)
|
||||
# 返回旋转后子树的根节点
|
||||
return child
|
||||
```
|
||||
|
||||
=== "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
|
|||
=== "Python"
|
||||
|
||||
```python title="avl_tree.py"
|
||||
|
||||
""" 执行旋转操作,使该子树重新恢复平衡 """
|
||||
def __rotate(self, node: TreeNode) -> TreeNode:
|
||||
# 获取结点 node 的平衡因子
|
||||
balance_factor = self.balance_factor(node)
|
||||
# 左偏树
|
||||
if balance_factor > 1:
|
||||
if self.balance_factor(node.left) >= 0:
|
||||
# 右旋
|
||||
return self.__right_rotate(node)
|
||||
else:
|
||||
# 先左旋后右旋
|
||||
node.left = self.__left_rotate(node.left)
|
||||
return self.__right_rotate(node)
|
||||
# 右偏树
|
||||
elif balance_factor < -1:
|
||||
if self.balance_factor(node.right) <= 0:
|
||||
# 左旋
|
||||
return self.__left_rotate(node)
|
||||
else:
|
||||
# 先右旋后左旋
|
||||
node.right = self.__right_rotate(node.right)
|
||||
return self.__left_rotate(node)
|
||||
# 平衡树,无需旋转,直接返回
|
||||
return node
|
||||
```
|
||||
|
||||
=== "Go"
|
||||
|
@ -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"
|
||||
|
||||
""" 插入结点 """
|
||||
def insert(self, val) -> TreeNode:
|
||||
self.root = self.__insert_helper(self.root, val)
|
||||
return self.root
|
||||
|
||||
""" 递归插入结点(辅助函数)"""
|
||||
def __insert_helper(self, node: typing.Optional[TreeNode], val: int) -> TreeNode:
|
||||
if node is None:
|
||||
return TreeNode(val)
|
||||
# 1. 查找插入位置,并插入结点
|
||||
if val < node.val:
|
||||
node.left = self.__insert_helper(node.left, val)
|
||||
elif val > node.val:
|
||||
node.right = self.__insert_helper(node.right, val)
|
||||
else:
|
||||
# 重复结点不插入,直接返回
|
||||
return node
|
||||
# 更新结点高度
|
||||
self.__update_height(node)
|
||||
# 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)
|
||||
return root
|
||||
|
||||
""" 递归删除结点(辅助函数) """
|
||||
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
|
||||
else:
|
||||
node = child
|
||||
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)
|
||||
# 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
|
||||
|
|
Loading…
Reference in a new issue