\n
![\"\"](\"https:\/\/lingbo.online\/wp-content\/uploads\/2023\/08\/tree1.png\")
\n\u5219\u524d\u3001\u4e2d\u3001\u540e\u904d\u5386\u5bf9\u5e94\u7684\u89c4\u5219\u53ef\u4ee5\u8868\u793a\u4e3a\uff1a<\/p>\n
\u6709\u4e00\u68f5\u4e8c\u53c9\u6811\u7684\u7ed3\u6784\u5982\u4e0b\u56fe\u6240\u793a\uff1a
\n
\n\u5219\u524d\u3001\u4e2d\u3001\u540e\u904d\u5386\u5bf9\u5e94\u7684\u89c4\u5219\u53ef\u4ee5\u8868\u793a\u4e3a\uff1a<\/p>\n
\u524d\u3001\u4e2d\u3001\u540e\u5e8f\u7684\u904d\u5386\u53ef\u4ee5\u7528\u6df1\u5ea6\u4f18\u5148\u641c\u7d22\u89e3\u51b3\uff0c\u53ef\u4ee5\u4f7f\u7528\u9012\u5f52\u51fd\u6570\u6216\u8005\u5355\u8c03\u6808\u89e3\u51b3\u3002\u9012\u5f52\u51fd\u6570\u5728\u8ba1\u7b97\u673a\u4e2d\u5b9e\u73b0\u9690\u5f0f\u7684\u5229\u7528\u4e86\u88ab\u79f0\u4e3a\u8c03\u7528\u6808\u7684\u6808<\/strong>\uff0c\u5373\u9012\u5f52\u5229\u7528\u4e86\u6808\uff0c\u53ea\u662f\u9690\u5f0f\u7684\u5229\u7528\u4e86\u6808\uff0c\u6ca1\u6709\u663e\u793a\u7684\u8ba9\u4f60\u770b\u5230\u5176\u4f7f\u7528\u4e86\u6808\u3002\u4ee5\u4e2d\u5e8f\u904d\u5386\u4e3a\u4f8b\uff0c\u6574\u4f53\u8fc7\u7a0b\u4e3a\u8bbf\u95ee\u7ed3\u70b9\u5e76\u5165\u6808\u904d\u5386\u5de6\u5b50\u6811\uff0c\u51fa\u6808\u904d\u5386\u53f3\u5b50\u6811<\/strong>\u3002<\/p>\n \u4e5f\u53ef\u4ee5\u8f85\u52a9\u6808\u5c06\u4e0a\u9762\u9012\u5f52\u51fd\u6570\u9690\u5f0f\u8c03\u7528\u6808\u7684\u8fc7\u7a0b\u663e\u793a\u8868\u793a\u3002\u4ee5\u4e2d\u5e8f\u904d\u5386\u4e3a\u4f8b\uff0c\u5b9e\u73b0\u8bbf\u95ee\u7ed3\u70b9\u5e76\u5165\u6808\u904d\u5386\u5de6\u5b50\u6811\uff0c\u7ed3\u70b9\u51fa\u6808\u904d\u5386\u53f3\u5b50\u6811\u3002<\/strong><\/p>\n \u5c42\u5e8f\u904d\u5386\u53ef\u4ee5\u4f7f\u7528\u5bbd\u5ea6\u4f18\u5148\u641c\u7d22\u7b97\u6cd5\u89e3\u51b3\uff0c\u5373\u6784\u9020\u4e00\u4e2a\u8f85\u52a9\u961f\u5217\uff0c\u5f53\u961f\u5217\u4e0d\u4e3a\u7a7a\u65f6\uff0c\u5f39\u51fa\u5f53\u524d\u8282\u70b9\uff0c\u5e76\u5c06\u5f53\u524d\u8282\u70b9\u7684\u5de6\u53f3\u8282\u70b9\u52a0\u5165\u5230\u961f\u5217\u4e2d\u3002<\/strong><\/p>\n \u53ef\u4ee5\u4f7f\u7528\u6808\u8fdb\u884c\u8fed\u4ee3\uff0c\u4ee5\u524d\u5e8f\u904d\u5386\u4e3a\u4f8b\uff0c\u8fc7\u7a0b\u8868\u793a\u5982\u4e0b\uff1a<\/p>\n \u5c42\u5e8f\u904d\u5386\u4f7f\u7528\u5e7f\u5ea6\u4f18\u5148\u641c\u7d22\uff0c\u6b65\u9aa4\u4e3a\uff1a<\/p>\n \u9898\u76ee\u94fe\u63a5\uff1ahttps:\/\/leetcode.cn\/problems\/merge-two-binary-trees\/description\/<\/a><\/p>\n \u7ed9\u4f60\u4e24\u68f5\u4e8c\u53c9\u6811\uff1a \u60f3\u8c61\u4e00\u4e0b\uff0c\u5f53\u4f60\u5c06\u5176\u4e2d\u4e00\u68f5\u8986\u76d6\u5230\u53e6\u4e00\u68f5\u4e4b\u4e0a\u65f6\uff0c\u4e24\u68f5\u6811\u4e0a\u7684\u4e00\u4e9b\u8282\u70b9\u5c06\u4f1a\u91cd\u53e0\uff08\u800c\u53e6\u4e00\u4e9b\u4e0d\u4f1a\uff09\u3002\u4f60\u9700\u8981\u5c06\u8fd9\u4e24\u68f5\u6811\u5408\u5e76\u6210\u4e00\u68f5\u65b0\u4e8c\u53c9\u6811\u3002\u5408\u5e76\u7684\u89c4\u5219\u662f\uff1a\u5982\u679c\u4e24\u4e2a\u8282\u70b9\u91cd\u53e0\uff0c\u90a3\u4e48\u5c06\u8fd9\u4e24\u4e2a\u8282\u70b9\u7684\u503c\u76f8\u52a0\u4f5c\u4e3a\u5408\u5e76\u540e\u8282\u70b9\u7684\u65b0\u503c\uff1b\u5426\u5219\uff0c\u4e0d\u4e3a \u8fd4\u56de\u5408\u5e76\u540e\u7684\u4e8c\u53c9\u6811\u3002<\/p>\n \u6ce8\u610f:<\/strong> \u5408\u5e76\u8fc7\u7a0b\u5fc5\u987b\u4ece\u4e24\u4e2a\u6811\u7684\u6839\u8282\u70b9\u5f00\u59cb\u3002<\/p>\n \u793a\u4f8b1\uff1a<\/strong><\/p>\n \u4f7f\u7528\u6df1\u5ea6\u4f18\u5148\u641c\u7d22\u904d\u5386\u5e76\u5408\u5e76\u4e24\u4e2a\u4e8c\u53c9\u6811\uff0c\u4ece\u6839\u8282\u70b9\u5f00\u59cb\u540c\u65f6\u904d\u5386\u4e24\u4e2a\u4e8c\u53c9\u6811\uff0c\u5c06\u5bf9\u5e94\u7684\u8282\u70b9\u8fdb\u884c\u76f8\u52a0\u5408\u5e76\u3002<\/p>\n \u5728\u904d\u5386\u4e8c\u53c9\u6811\u7684\u5404\u4e2a\u8282\u70b9\u65f6\uff0c\u4e00\u5171\u4f1a\u51fa\u73b0\u5982\u4e0b\u4e09\u79cd\u60c5\u51b5\uff1a<\/p>\n \u5728\u4e00\u4e2a\u8282\u70b9\u5408\u5e76\u5b8c\u6210\u540e\uff0c\u8fd8\u9700\u8981\u5bf9\u8be5\u8282\u70b9\u7684\u5de6\u53f3\u5b57\u6570\u8fdb\u884c\u76f8\u540c\u64cd\u4f5c\uff0c\u76f4\u81f3\u4e8c\u53c9\u6811\u4e3a\u7a7a\uff0c\u8be5\u8fc7\u7a0b\u662f\u4e00\u4e2a\u9012\u5f52\u8fc7\u7a0b\u3002<\/p>\n \u65f6\u95f4\u590d\u6742\u5ea6\uff1a<\/strong>O(min(m,n))\uff0c\u5176\u4e2dm\u548cn\u5206\u522b\u662f\u4e24\u4e2a\u4e8c\u53c9\u6811\u7684\u8282\u70b9\u4e2a\u6570\u3002 \u9898\u76ee\u94fe\u63a5\uff1ahttps:\/\/leetcode.cn\/problems\/binary-trees-with-factors\/description\/<\/a><\/p>\n \u7ed9\u51fa\u4e00\u4e2a\u542b\u6709\u4e0d\u91cd\u590d\u6574\u6570\u5143\u7d20\u7684\u6570\u7ec4 \u7528\u8fd9\u4e9b\u6574\u6570\u6765\u6784\u5efa\u4e8c\u53c9\u6811\uff0c\u6bcf\u4e2a\u6574\u6570\u53ef\u4ee5\u4f7f\u7528\u4efb\u610f\u6b21\u6570\u3002\u5176\u4e2d\uff1a\u6bcf\u4e2a\u975e\u53f6\u7ed3\u70b9\u7684\u503c\u5e94\u7b49\u4e8e\u5b83\u7684\u4e24\u4e2a\u5b50\u7ed3\u70b9\u7684\u503c\u7684\u4e58\u79ef\u3002<\/p>\n \u6ee1\u8db3\u6761\u4ef6\u7684\u4e8c\u53c9\u6811\u4e00\u5171\u6709\u591a\u5c11\u4e2a\uff1f\u7b54\u6848\u53ef\u80fd\u5f88\u5927\uff0c\u8fd4\u56de \u5bf9 \u793a\u4f8b\uff1a<\/p>\n \u8f93\u5165\uff1aarr=[2,4] \u52a8\u6001\u89c4\u5212+\u53cc\u6307\u9488 \u5f53arr[i]\u6ca1\u6709\u5b50\u8282\u70b9\u65f6\uff0c\u5bf9\u5e941\u4e2a\u5e26\u56e0\u5b50\u4e8c\u53c9\u6811\u3002\u56e0\u6b64\uff0c\u72b6\u6001\u8f6c\u79fb\u65b9\u7a0b\u4e3a\uff1a<\/p>\n $$dp[i]=1+\\sum_{(left,right)}dp[left]*dp[right]*(1+f(left,right))$$<\/p>\n \u5176\u4e2d\uff0cleft=right<\/span>\u65f6\uff0cf(left,right)=0<\/span>\uff0cleft \\neq right<\/span>\u65f6\uff0cf(left,right)=1<\/span><\/p>\n \u9898\u76ee\u94fe\u63a5\uff1ahttps:\/\/leetcode.cn\/problems\/er-cha-shu-de-shen-du-lcof\/description\/<\/a> \u4e8c\u53c9\u6811\u7684\u5c42\u5e8f\u904d\u5386\uff0c\u904d\u5386\u65f6\u5bf9\u6bcf\u4e00\u5c42\u8ba1\u6570<\/p>\n\u6848\u4f8b\u4ee3\u7801<\/h4>\n
\u9012\u5f52\u601d\u8def<\/h5>\n
#\u524d\u5e8f\u904d\u5386\nclass Solution:\n def preorderTraversal(self, root: TreeNode) -> List[int]:\n def preorder(root: TreeNode):\n if not root:\n return\n res.append(root.val)\n preorder(root.left)\n preorder(root.right)\n\n res = list()\n preorder(root)\n return res\n\n# \u4e2d\u5e8f\u904d\u5386\nclass Solution:\n def inorderTraversal(self, root: TreeNode) -> List[int]:\n def inorder(root: TreeNode):\n if not root:\n return\n inorder(root.left)\n res.append(root.val)\n inorder(root.right)\n\n res = list()\n inorder(root)\n return res\n\n# \u540e\u5e8f\u904d\u5386\nclass Solution:\n def postorderTraversal(self, root: TreeNode) -> List[int]:\n def postorder(root: TreeNode):\n if not root:\n return\n postorder(root.left)\n postorder(root.right)\n res.append(root.val)\n\n res = list()\n postorder(root)\n return res<\/code><\/pre>\n\u8fed\u4ee3\u601d\u8def<\/h5>\n
\n
\n
Node<\/code>\uff0c\u5e76\u5c06\u503c\u6dfb\u52a0\u5230\u7ed3\u679c\u4e2d\uff1b<\/li>\nNode<\/code>\u7684\u53f3\u5b50\u6811\u975e\u7a7a\uff0c\u5c06\u53f3\u5b50\u6811\u5165\u6808<\/li>\nNode<\/code>\u7684\u5de6\u5b50\u6811\u975e\u7a7a\uff0c\u5c06\u5de6\u5b50\u6811\u5165\u6808<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n![\"\"](\"https:\/\/lingbo.online\/wp-content\/uploads\/2023\/08\/preorder.gif\")
<\/p>\n#\u524d\u5e8f\u904d\u5386\nclass Solution:\n def preorderTraversal(self, root: TreeNode) -> List[int]:\n if not root:\n return []\n stack,res=[root],[]\n while stack:\n node=stack.pop()\n if node:\n res.append(node)\n if node.right:\n stack.append(node.right)\n if node.left:\n stack.append(node.left)\n return res\n\n# \u4e2d\u5e8f\u904d\u5386\nclass Solution:\n def inorderTraversal(self, root: TreeNode) -> List[int]:\n if not root:\n return []\n cur,stack,res=root,[],[]\n while stack or cur:\n while cur: #cur\u5165\u6808\uff0c\u5e76\u5230\u8fbe\u6700\u5de6\u7aef\u7684\u53f6\u5b50\u7ed3\u70b9\n stack.append(cur)\n cur=cur.left\n tmp=stack.pop()\n res.append(tmp.val)\n cur=tmp.right\n return res\n\n# \u540e\u5e8f\u904d\u5386\nclass Solution:\n def inorderTraversal(self, root: TreeNode) -> List[int]:\n if not root:\n return []\n cur,stack,res=root,[],[]\n while stack or cur:\n while cur: #\u6700\u5148\u5230\u8fbe\u53f3\u7aef\n res.append(cur.val)\n stack.append(cur)\n cur=cur.right\n tmp=stack.pop()\n cur=tmp.left\n return res[::-1]<\/code><\/pre>\n\u5c42\u5e8f\u904d\u5386<\/h5>\n
\n
q<\/code>\uff0c\u5e76\u5c06\u6839\u8282\u70b9root<\/code>\u52a0\u5165\u5230\u961f\u5217\u4e2d<\/li>\n\n
node<\/code>,\u52a0\u5165\u5230\u7ed3\u679c\u4e2d\uff1b<\/li>\nclass Solution:\n def levelOrder(self, root: Optional[TreeNode]) -> List[List[int]]:\n if not root:\n return []\n\n queue=deque()\n queue.append(root)\n\n result=[]\n while queue:\n tmp=[]\n num=len(queue)\n for i in range(num):\n node=queue.popleft()\n tmp.append(node.val)\n if node.left:\n queue.append(node.left)\n if node.right:\n queue.append(node.right)\n result.append(tmp)\n\n return result<\/code><\/pre>\nLeecode.617 \u5408\u5e76\u4e8c\u53c9\u6811<\/h3>\n
root1<\/code> \u548c root2<\/code> \u3002<\/p>\nnull<\/code>\u7684\u8282\u70b9\u5c06\u76f4\u63a5\u4f5c\u4e3a\u65b0\u4e8c\u53c9\u6811\u7684\u8282\u70b9\u3002<\/p>\n![\"\"](\"https:\/\/lingbo.online\/wp-content\/uploads\/2023\/08\/merge.jpg\")
<\/p>\n\u8f93\u5165\uff1aroot1 = [1,3,2,5], root2 = [2,1,3,null,4,null,7]\n\u8f93\u51fa\uff1a[3,4,5,5,4,null,7]<\/code><\/pre>\n\u89e3\u9898\u601d\u8def<\/h4>\n
\u6df1\u5ea6\u4f18\u5148\u641c\u7d22<\/h5>\n
\n
\u590d\u6742\u5ea6\u5206\u6790<\/h5>\n
\n\u7a7a\u95f4\u590d\u6742\u5ea6\uff1a<\/strong>O(min(m,n))\uff0c\u5176\u4e2dm\u548cn\u5206\u522b\u662f\u4e24\u4e2a\u4e8c\u53c9\u6811\u7684\u8282\u70b9\u4e2a\u6570\u3002<\/p>\n\u6848\u4f8b\u4ee3\u7801<\/h5>\n
class Solution:\n def mergeTrees(self, t1: TreeNode, t2: TreeNode) -> TreeNode:\n #\u5982\u679c\u6709\u7a7a\u8282\u70b9\uff1a\n if not t1:\n return t2\n if not t2:\n return t1\n\n #\u5982\u679c\u4e24\u9897\u6811\u7684\u8282\u70b9\u5747\u4e0d\u4e3a\u7a7a\uff0c\u5bf9\u4e24\u8282\u70b9\u503c\u8fdb\u884c\u5408\u5e76\n Node=TreeNode(t1.val+t2.val)\n #\u9012\u5f52\uff0c\u904d\u5386\u5de6\u53f3\u8282\u70b9\n Node.left=mergeTrees(t1.left,t2.left)\n Node.right=mergeTrees(t1.right,t2.right)\n return Node<\/code><\/pre>\nLeecode.823 \u5e26\u56e0\u5b50\u7684\u4e8c\u53c9\u6811<\/h3>\n
arr<\/code>\uff0c\u6bcf\u4e2a\u6574\u6570arr[i]<\/code>\u5747\u5927\u4e8e 1\u3002<\/p>\n10^9 + 7<\/code>\u53d6\u4f59\u7684\u7ed3\u679c\u3002<\/p>\n\n
\n\u8f93\u51fa\uff1a3
\n\u89e3\u91ca\uff1a\u53ef\u4ee5\u5f97\u5230\u8fd9\u4e9b\u4e8c\u53c9\u6811\uff1a[2],[4],[4,2,2]<\/code><\/p>\n<\/blockquote>\n\u89e3\u9898\u601d\u8def<\/h4>\n
\n\u9898\u76ee\u4e2d\u6bcf\u4e2a\u6574\u6570arr[i]\u90fd\u5927\u4e8e1\uff0c\u56e0\u6b64\u6bcf\u4e2a\u975e\u5b50\u53f6\u8282\u70b9\u7684\u503c\u90fd\u5927\u4e8e\u5b83\u5b50\u53f6\u8282\u70b9\u7684\u503c\u3002<\/p>\n\n
\n
\u590d\u6742\u5ea6\u5206\u6790<\/h4>\n
\n
\u6848\u4f8b\u4ee3\u7801<\/h4>\n
class Solution:\n def numFactoredBinaryTrees(self, arr: List[int]) -> int:\n n=len(arr)\n arr=sorted(arr)\n\n dp=[1]*n\n res,mod=0,10**9+7\n\n for i in range(n):\n left,right=0,i-1\n\n while left<=right:\n while right>=left and arr[left]*arr[right]>arr[i]:\n right-=1\n if right>=left and arr[left]*arr[right]==arr[i]:\n #\u5982\u679c\u4e24\u4e2a\u8282\u70b9\u4e0d\u76f8\u7b49\uff0c\u53ef\u4ee5\u5de6\u53f3\u4ea4\u6362\uff0c\u56e0\u6b64\u4e8c\u53c9\u6811\u6570\u76ee*2\n if right!=left:\n dp[i]=(dp[i]+dp[left]*dp[right]*2)%mod\n #\u76f8\u7b49\u65f6\u4e0d\u80fd\u4ea4\u6362\n else:\n dp[i]=(dp[i]+dp[left]*dp[right])%mod\n left+=1\n res=(res+dp[i])%mod\n return res<\/code><\/pre>\n\u4e8c\u53c9\u6811\u7684\u6700\u5927\u6df1\u5ea6<\/h3>\n
\n\u67d0\u516c\u53f8\u67b6\u6784\u4ee5\u4e8c\u53c9\u6811\u5f62\u5f0f\u8bb0\u5f55\uff0c\u8bf7\u8fd4\u56de\u8be5\u516c\u53f8\u7684\u5c42\u7ea7\u6570\u3002<\/p>\n\u89e3\u9898\u601d\u8def<\/h4>\n
\u6848\u4f8b\u4ee3\u7801<\/h4>\n
# Definition for a binary tree node.\n# class TreeNode:\n# def __init__(self, val=0, left=None, right=None):\n# self.val = val\n# self.left = left\n# self.right = right\nclass Solution:\n def calculateDepth(self, root: Optional[TreeNode]) -> int:\n if not root:\n return 0\n queue=[]\n\n queue.append(root)\n\n count=0\n while queue:\n temp=queue\n queue=[]\n count+=1\n for i in temp:\n if i.left:\n queue.append(i.left)\n if i.right:\n queue.append(i.right)\n\n return count<\/code><\/pre>\nLeecode 589. N\u53c9\u6811\u7684\u524d\u5e8f\u904d\u5386<\/h3>\n
![\"\"](\"https:\/\/lingbo.online\/wp-content\/uploads\/2023\/08\/flaten.jpg\")
<\/p>\n