![\"python](\"https:\/\/cdn-kb.worktile.com\/kb\/wp-content\/uploads\/2024\/04\/24212601\/b56d1e14-be5b-4a3f-a266-920b465b9999.webp\")
<\/p>\n<\/p>\n
Python\u904d\u5386\u4e8c\u53c9\u6811\u7684\u65b9\u6cd5\u4e3b\u8981\u6709\u4e09\u79cd\uff1a\u524d\u5e8f\u904d\u5386\u3001\u4e2d\u5e8f\u904d\u5386\u3001\u540e\u5e8f\u904d\u5386<\/strong>\uff0c\u5176\u4e2d\uff0c\u4e2d\u5e8f\u904d\u5386\u662f\u6700\u5e38\u7528\u7684\u4e00\u79cd\u65b9\u6cd5\u3002\u524d\u5e8f\u904d\u5386\u5148\u8bbf\u95ee\u6839\u8282\u70b9\uff0c\u518d\u8bbf\u95ee\u5de6\u5b50\u6811\uff0c\u6700\u540e\u8bbf\u95ee\u53f3\u5b50\u6811<\/strong>\u3002\u4e0b\u9762\u5c31\u8be6\u7ec6\u8bb2\u89e3\u524d\u5e8f\u904d\u5386\u3002<\/p>\n<\/p>\n \u524d\u5e8f\u904d\u5386\u7684\u5177\u4f53\u6b65\u9aa4\u5982\u4e0b\uff1a<\/p>\n<\/p>\n def __init__(self, value=0, left=None, right=None):<\/p>\n self.value = value<\/p>\n self.left = left<\/p>\n self.right = right<\/p>\n def preorder_traversal(root):<\/p>\n if root:<\/p>\n print(root.value, end=' ')<\/p>\n preorder_traversal(root.left)<\/p>\n preorder_traversal(root.right)<\/p>\n root = TreeNode(1)<\/p>\n root.left = TreeNode(2)<\/p>\n root.right = TreeNode(3)<\/p>\n root.left.left = TreeNode(4)<\/p>\n root.left.right = TreeNode(5)<\/p>\n preorder_traversal(root)<\/p>\n <\/code><\/pre>\n<\/p>\n \u4e00\u3001\u524d\u5e8f\u904d\u5386\uff08Preorder Traversal\uff09<\/p>\n<\/p>\n \u524d\u5e8f\u904d\u5386\u662f\u4e00\u79cd\u6df1\u5ea6\u4f18\u5148\u904d\u5386\uff0c\u5b83\u4f1a\u9996\u5148\u8bbf\u95ee\u6839\u8282\u70b9\uff0c\u7136\u540e\u904d\u5386\u5de6\u5b50\u6811\uff0c\u6700\u540e\u904d\u5386\u53f3\u5b50\u6811\u3002\u524d\u5e8f\u904d\u5386\u7684\u4ee3\u7801\u5b9e\u73b0\u53ef\u4ee5\u901a\u8fc7\u9012\u5f52\u548c\u8fed\u4ee3\u4e24\u79cd\u65b9\u5f0f\u6765\u5b8c\u6210\u3002<\/p>\n<\/p>\n \u9012\u5f52\u5b9e\u73b0\u524d\u5e8f\u904d\u5386\u6bd4\u8f83\u76f4\u89c2\uff0c\u76f4\u63a5\u6309\u7167\u524d\u5e8f\u904d\u5386\u7684\u5b9a\u4e49\u8fdb\u884c\u9012\u5f52\u8c03\u7528\u5373\u53ef\uff1a<\/p>\n<\/p>\n if root:<\/p>\n print(root.value, end=' ')<\/p>\n preorder_traversal(root.left)<\/p>\n preorder_traversal(root.right)<\/p>\n <\/code><\/pre>\n<\/p>\n \u8fed\u4ee3\u5b9e\u73b0\u524d\u5e8f\u904d\u5386\u5219\u9700\u8981\u501f\u52a9\u4e00\u4e2a\u6808\u6765\u6a21\u62df\u9012\u5f52\u8c03\u7528\u7684\u8fc7\u7a0b\uff1a<\/p>\n<\/p>\n if not root:<\/p>\n return<\/p>\n stack = [root]<\/p>\n while stack:<\/p>\n node = stack.pop()<\/p>\n print(node.value, end=' ')<\/p>\n if node.right:<\/p>\n stack.append(node.right)<\/p>\n if node.left:<\/p>\n stack.append(node.left)<\/p>\n <\/code><\/pre>\n<\/p>\n \u4e8c\u3001\u4e2d\u5e8f\u904d\u5386\uff08Inorder Traversal\uff09<\/p>\n<\/p>\n \u4e2d\u5e8f\u904d\u5386\u662f\u53e6\u4e00\u79cd\u6df1\u5ea6\u4f18\u5148\u904d\u5386\uff0c\u5b83\u4f1a\u5148\u904d\u5386\u5de6\u5b50\u6811\uff0c\u7136\u540e\u8bbf\u95ee\u6839\u8282\u70b9\uff0c\u6700\u540e\u904d\u5386\u53f3\u5b50\u6811\u3002\u4e2d\u5e8f\u904d\u5386\u540c\u6837\u53ef\u4ee5\u901a\u8fc7\u9012\u5f52\u548c\u8fed\u4ee3\u4e24\u79cd\u65b9\u5f0f\u6765\u5b9e\u73b0\u3002<\/p>\n<\/p>\n \u9012\u5f52\u5b9e\u73b0\u4e2d\u5e8f\u904d\u5386\u4e5f\u6bd4\u8f83\u76f4\u89c2\uff0c\u6309\u7167\u4e2d\u5e8f\u904d\u5386\u7684\u5b9a\u4e49\u8fdb\u884c\u9012\u5f52\u8c03\u7528\u5373\u53ef\uff1a<\/p>\n<\/p>\n if root:<\/p>\n inorder_traversal(root.left)<\/p>\n print(root.value, end=' ')<\/p>\n inorder_traversal(root.right)<\/p>\n <\/code><\/pre>\n<\/p>\n \u8fed\u4ee3\u5b9e\u73b0\u4e2d\u5e8f\u904d\u5386\u5219\u9700\u8981\u501f\u52a9\u4e00\u4e2a\u6808\u6765\u6a21\u62df\u9012\u5f52\u8c03\u7528\u7684\u8fc7\u7a0b\uff1a<\/p>\n<\/p>\n stack = []<\/p>\n current = root<\/p>\n while stack or current:<\/p>\n while current:<\/p>\n stack.append(current)<\/p>\n current = current.left<\/p>\n current = stack.pop()<\/p>\n print(current.value, end=' ')<\/p>\n current = current.right<\/p>\n <\/code><\/pre>\n<\/p>\n \u4e09\u3001\u540e\u5e8f\u904d\u5386\uff08Postorder Traversal\uff09<\/p>\n<\/p>\n \u540e\u5e8f\u904d\u5386\u662f\u7b2c\u4e09\u79cd\u6df1\u5ea6\u4f18\u5148\u904d\u5386\uff0c\u5b83\u4f1a\u5148\u904d\u5386\u5de6\u5b50\u6811\uff0c\u7136\u540e\u904d\u5386\u53f3\u5b50\u6811\uff0c\u6700\u540e\u8bbf\u95ee\u6839\u8282\u70b9\u3002\u540e\u5e8f\u904d\u5386\u4e5f\u53ef\u4ee5\u901a\u8fc7\u9012\u5f52\u548c\u8fed\u4ee3\u4e24\u79cd\u65b9\u5f0f\u6765\u5b9e\u73b0\u3002<\/p>\n<\/p>\n \u9012\u5f52\u5b9e\u73b0\u540e\u5e8f\u904d\u5386\u4f9d\u7136\u6bd4\u8f83\u76f4\u89c2\uff0c\u6309\u7167\u540e\u5e8f\u904d\u5386\u7684\u5b9a\u4e49\u8fdb\u884c\u9012\u5f52\u8c03\u7528\u5373\u53ef\uff1a<\/p>\n<\/p>\n if root:<\/p>\n postorder_traversal(root.left)<\/p>\n postorder_traversal(root.right)<\/p>\n print(root.value, end=' ')<\/p>\n <\/code><\/pre>\n<\/p>\n \u8fed\u4ee3\u5b9e\u73b0\u540e\u5e8f\u904d\u5386\u5219\u9700\u8981\u501f\u52a9\u4e24\u4e2a\u6808\u6765\u6a21\u62df\u9012\u5f52\u8c03\u7528\u7684\u8fc7\u7a0b\uff1a<\/p>\n<\/p>\n if not root:<\/p>\n return<\/p>\n stack1 = [root]<\/p>\n stack2 = []<\/p>\n while stack1:<\/p>\n node = stack1.pop()<\/p>\n stack2.append(node)<\/p>\n if node.left:<\/p>\n stack1.append(node.left)<\/p>\n if node.right:<\/p>\n stack1.append(node.right)<\/p>\n while stack2:<\/p>\n node = stack2.pop()<\/p>\n print(node.value, end=' ')<\/p>\n <\/code><\/pre>\n<\/p>\n \u56db\u3001\u5c42\u5e8f\u904d\u5386\uff08Level Order Traversal\uff09<\/p>\n<\/p>\n \u9664\u4e86\u524d\u5e8f\u3001\u4e2d\u5e8f\u548c\u540e\u5e8f\u904d\u5386\uff0c\u5c42\u5e8f\u904d\u5386\u4e5f\u662f\u4e00\u79cd\u5e38\u7528\u7684\u904d\u5386\u65b9\u5f0f\uff0c\u5b83\u4f1a\u6309\u7167\u5c42\u7ea7\u4f9d\u6b21\u8bbf\u95ee\u6bcf\u4e2a\u8282\u70b9\u3002\u5c42\u5e8f\u904d\u5386\u901a\u5e38\u901a\u8fc7\u961f\u5217\u6765\u5b9e\u73b0\u3002<\/p>\n<\/p>\n def level_order_traversal(root):<\/p>\n if not root:<\/p>\n return<\/p>\n queue = deque([root])<\/p>\n while queue:<\/p>\n node = queue.popleft()<\/p>\n print(node.value, end=' ')<\/p>\n if node.left:<\/p>\n queue.append(node.left)<\/p>\n if node.right:<\/p>\n queue.append(node.right)<\/p>\n <\/code><\/pre>\n<\/p>\n \u4e94\u3001\u904d\u5386\u65b9\u6cd5\u6bd4\u8f83<\/p>\n<\/p>\n \u4e0d\u540c\u7684\u904d\u5386\u65b9\u6cd5\u9002\u7528\u4e8e\u4e0d\u540c\u7684\u5e94\u7528\u573a\u666f\u3002\u524d\u5e8f\u904d\u5386<\/strong>\u53ef\u4ee5\u7528\u4e8e\u590d\u5236\u6811\u7ed3\u6784\uff0c\u56e0\u4e3a\u5b83\u5728\u8bbf\u95ee\u8282\u70b9\u4e4b\u524d\u5df2\u7ecf\u77e5\u9053\u4e86\u5b50\u6811\u7684\u7ed3\u6784\uff1b\u4e2d\u5e8f\u904d\u5386<\/strong>\u53ef\u4ee5\u7528\u4e8e\u8f93\u51fa\u4e8c\u53c9\u641c\u7d22\u6811\u7684\u8282\u70b9\u503c\uff0c\u5b83\u4f1a\u6309\u7167\u8282\u70b9\u503c\u4ece\u5c0f\u5230\u5927\u7684\u987a\u5e8f\u8f93\u51fa\uff1b\u540e\u5e8f\u904d\u5386<\/strong>\u9002\u7528\u4e8e\u5220\u9664\u6811\u7ed3\u6784\uff0c\u56e0\u4e3a\u5b83\u5728\u8bbf\u95ee\u6839\u8282\u70b9\u4e4b\u524d\u5df2\u7ecf\u8bbf\u95ee\u4e86\u6240\u6709\u5b50\u8282\u70b9\uff1b\u5c42\u5e8f\u904d\u5386<\/strong>\u5219\u9002\u7528\u4e8e\u9010\u5c42\u5904\u7406\u8282\u70b9\uff0c\u4f8b\u5982\u5e7f\u5ea6\u4f18\u5148\u641c\u7d22\u4e2d\u7684\u9010\u5c42\u641c\u7d22\u3002<\/p>\n<\/p>\n \u6bcf\u79cd\u904d\u5386\u65b9\u6cd5\u90fd\u6709\u5176\u72ec\u7279\u7684\u7279\u70b9\u548c\u5e94\u7528\u573a\u666f\uff0c\u9009\u62e9\u5408\u9002\u7684\u904d\u5386\u65b9\u6cd5\u53ef\u4ee5\u63d0\u9ad8\u7b97\u6cd5\u7684\u6548\u7387\u548c\u4ee3\u7801\u7684\u53ef\u8bfb\u6027\u3002\u901a\u8fc7\u5bf9\u6bd4\u4e0d\u540c\u904d\u5386\u65b9\u6cd5\u7684\u5b9e\u73b0\u548c\u5e94\u7528\uff0c\u53ef\u4ee5\u66f4\u597d\u5730\u7406\u89e3\u4e8c\u53c9\u6811\u7684\u7ed3\u6784\u548c\u904d\u5386\u65b9\u5f0f\u3002<\/p>\n<\/p>\n \u516d\u3001\u4e8c\u53c9\u6811\u7684\u5176\u4ed6\u64cd\u4f5c<\/p>\n<\/p>\n \u9664\u4e86\u904d\u5386\u4e8c\u53c9\u6811\uff0c\u4e8c\u53c9\u6811\u8fd8\u6709\u8bb8\u591a\u5176\u4ed6\u64cd\u4f5c\uff0c\u4f8b\u5982\u63d2\u5165\u8282\u70b9\u3001\u5220\u9664\u8282\u70b9\u3001\u67e5\u627e\u8282\u70b9\u3001\u8ba1\u7b97\u6811\u7684\u9ad8\u5ea6\u3001\u5224\u65ad\u662f\u5426\u4e3a\u5e73\u8861\u6811\u7b49\u3002\u4e0b\u9762\u5c06\u7b80\u5355\u4ecb\u7ecd\u4e00\u4e9b\u5e38\u89c1\u7684\u4e8c\u53c9\u6811\u64cd\u4f5c\u3002<\/p>\n<\/p>\n \u63d2\u5165\u8282\u70b9\u64cd\u4f5c\u901a\u5e38\u7528\u4e8e\u4e8c\u53c9\u641c\u7d22\u6811\uff0c\u63d2\u5165\u8282\u70b9\u65f6\u9700\u8981\u4fdd\u8bc1\u4e8c\u53c9\u641c\u7d22\u6811\u7684\u6027\u8d28\uff0c\u5373\u5de6\u5b50\u6811\u7684\u8282\u70b9\u503c\u5c0f\u4e8e\u6839\u8282\u70b9\u503c\uff0c\u53f3\u5b50\u6811\u7684\u8282\u70b9\u503c\u5927\u4e8e\u6839\u8282\u70b9\u503c\u3002<\/p>\n<\/p>\n if not root:<\/p>\n return TreeNode(value)<\/p>\n if value < root.value:<\/p>\n root.left = insert_node(root.left, value)<\/p>\n else:<\/p>\n root.right = insert_node(root.right, value)<\/p>\n return root<\/p>\n <\/code><\/pre>\n<\/p>\n \u5220\u9664\u8282\u70b9\u64cd\u4f5c\u4e5f\u901a\u5e38\u7528\u4e8e\u4e8c\u53c9\u641c\u7d22\u6811\uff0c\u5220\u9664\u8282\u70b9\u65f6\u9700\u8981\u8003\u8651\u4e09\u79cd\u60c5\u51b5\uff1a\u5220\u9664\u53f6\u5b50\u8282\u70b9\u3001\u5220\u9664\u53ea\u6709\u4e00\u4e2a\u5b50\u8282\u70b9\u7684\u8282\u70b9\u3001\u5220\u9664\u6709\u4e24\u4e2a\u5b50\u8282\u70b9\u7684\u8282\u70b9\u3002<\/p>\n<\/p>\n if not root:<\/p>\n return None<\/p>\n if value < root.value:<\/p>\n root.left = delete_node(root.left, value)<\/p>\n elif value > root.value:<\/p>\n root.right = delete_node(root.right, value)<\/p>\n else:<\/p>\n if not root.left:<\/p>\n return root.right<\/p>\n if not root.right:<\/p>\n return root.left<\/p>\n min_larger_node = get_min(root.right)<\/p>\n root.value = min_larger_node.value<\/p>\n root.right = delete_node(root.right, min_larger_node.value)<\/p>\n return root<\/p>\n def get_min(node):<\/p>\n while node.left:<\/p>\n node = node.left<\/p>\n return node<\/p>\n <\/code><\/pre>\n<\/p>\n \u67e5\u627e\u8282\u70b9\u64cd\u4f5c\u4e5f\u9002\u7528\u4e8e\u4e8c\u53c9\u641c\u7d22\u6811\uff0c\u901a\u8fc7\u6bd4\u8f83\u8282\u70b9\u503c\u4e0e\u76ee\u6807\u503c\uff0c\u53ef\u4ee5\u5feb\u901f\u5b9a\u4f4d\u76ee\u6807\u8282\u70b9\u3002<\/p>\n<\/p>\n if not root or root.value == value:<\/p>\n return root<\/p>\n if value < root.value:<\/p>\n return search_node(root.left, value)<\/p>\n else:<\/p>\n return search_node(root.right, value)<\/p>\n <\/code><\/pre>\n<\/p>\n \u8ba1\u7b97\u6811\u7684\u9ad8\u5ea6\u662f\u6307\u4ece\u6839\u8282\u70b9\u5230\u53f6\u5b50\u8282\u70b9\u7684\u6700\u957f\u8def\u5f84\u7684\u8282\u70b9\u6570\uff0c\u53ef\u4ee5\u901a\u8fc7\u9012\u5f52\u6765\u5b9e\u73b0\u3002<\/p>\n<\/p>\n if not root:<\/p>\n return 0<\/p>\n return max(tree_height(root.left), tree_height(root.right)) + 1<\/p>\n <\/code><\/pre>\n<\/p>\n \u5e73\u8861\u6811\u662f\u6307\u4efb\u610f\u8282\u70b9\u7684\u5de6\u53f3\u5b50\u6811\u9ad8\u5ea6\u5dee\u4e0d\u8d85\u8fc71\u7684\u4e8c\u53c9\u6811\uff0c\u53ef\u4ee5\u901a\u8fc7\u9012\u5f52\u6765\u5224\u65ad\u662f\u5426\u4e3a\u5e73\u8861\u6811\u3002<\/p>\n<\/p>\n def check(root):<\/p>\n if not root:<\/p>\n return 0<\/p>\n left = check(root.left)<\/p>\n right = check(root.right)<\/p>\n if left == -1 or right == -1 or abs(left - right) > 1:<\/p>\n return -1<\/p>\n return max(left, right) + 1<\/p>\n return check(root) != -1<\/p>\n <\/code><\/pre>\n<\/p>\n \u901a\u8fc7\u5b66\u4e60\u548c\u638c\u63e1\u8fd9\u4e9b\u5e38\u89c1\u7684\u4e8c\u53c9\u6811\u64cd\u4f5c\uff0c\u53ef\u4ee5\u66f4\u597d\u5730\u7406\u89e3\u4e8c\u53c9\u6811\u7684\u7ed3\u6784\u548c\u6027\u8d28\uff0c\u4e3a\u89e3\u51b3\u5404\u79cd\u5b9e\u9645\u95ee\u9898\u63d0\u4f9b\u6709\u6548\u7684\u89e3\u51b3\u65b9\u6848\u3002<\/p>\n<\/p>\n \u5728Python\u4e2d\uff0c\u6709\u54ea\u4e9b\u5e38\u7528\u7684\u65b9\u6cd5\u53ef\u4ee5\u904d\u5386\u4e8c\u53c9\u6811\uff1f<\/strong> \u5982\u4f55\u4f7f\u7528\u9012\u5f52\u65b9\u6cd5\u8fdb\u884c\u4e8c\u53c9\u6811\u7684\u904d\u5386\uff1f<\/strong> \u5728Python\u4e2d\uff0c\u5982\u4f55\u5b9e\u73b0\u5c42\u5e8f\u904d\u5386\u4e8c\u53c9\u6811\uff1f<\/strong>\n
class TreeNode:<\/p>\n\u793a\u4f8b\u4f7f\u7528<\/strong><\/h2>\n
\u8f93\u51fa: 1 2 4 5 3<\/strong><\/h2>\n
\u9012\u5f52\u5b9e\u73b0<\/h3>\n<\/p>\n
def preorder_traversal(root):<\/p>\n\u8fed\u4ee3\u5b9e\u73b0<\/h3>\n<\/p>\n
def preorder_traversal_iterative(root):<\/p>\n\u9012\u5f52\u5b9e\u73b0<\/h3>\n<\/p>\n
def inorder_traversal(root):<\/p>\n\u8fed\u4ee3\u5b9e\u73b0<\/h3>\n<\/p>\n
def inorder_traversal_iterative(root):<\/p>\n\u9012\u5f52\u5b9e\u73b0<\/h3>\n<\/p>\n
def postorder_traversal(root):<\/p>\n\u8fed\u4ee3\u5b9e\u73b0<\/h3>\n<\/p>\n
def postorder_traversal_iterative(root):<\/p>\nfrom collections import deque<\/p>\n\u63d2\u5165\u8282\u70b9<\/h3>\n<\/p>\n
def insert_node(root, value):<\/p>\n\u5220\u9664\u8282\u70b9<\/h3>\n<\/p>\n
def delete_node(root, value):<\/p>\n\u67e5\u627e\u8282\u70b9<\/h3>\n<\/p>\n
def search_node(root, value):<\/p>\n\u8ba1\u7b97\u6811\u7684\u9ad8\u5ea6<\/h3>\n<\/p>\n
def tree_height(root):<\/p>\n\u5224\u65ad\u662f\u5426\u4e3a\u5e73\u8861\u6811<\/h3>\n<\/p>\n
def is_balanced(root):<\/p>\n\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n
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