![\"\u5fae\u4fe1\u622a\u56fe_20241203200949.png\"](\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250810125111-689895bf4371b.jpg\")
<\/p>\n\u7ed9\u5b9a\u4e00\u4e2a\u4e8c\u53c9\u6811，\u627e\u51fa\u5176\u6700\u5c0f\u6df1\u5ea6\u3002<\/p>\n
\u6700\u5c0f\u6df1\u5ea6\u662f\u4ece\u6839\u8282\u70b9\u5230\u6700\u8fd1\u53f6\u5b50\u8282\u70b9\u7684\u6700\u77ed\u8def\u5f84\u4e0a\u7684\u8282\u70b9\u6570\u91cf\u3002<\/p>\n
\u8bf4\u660e：\u53f6\u5b50\u8282\u70b9\u662f\u6307\u6ca1\u6709\u5b50\u8282\u70b9\u7684\u8282\u70b9\u3002<\/p>\n
\u793a\u4f8b 1： <\/p>\n
\u8f93\u5165：root = [3,9,20,null,null,15,7] \u8f93\u51fa：2 \u793a\u4f8b 2：<\/p>\n
\u8f93\u5165：root = [2,null,3,null,4,null,5,null,6] \u8f93\u51fa：5<\/p>\n
\u63d0\u793a：<\/p>\n
\u6811\u4e2d\u8282\u70b9\u6570\u7684\u8303\u56f4\u5728 [0, 10^5] \u5185 -1000 <= Node.val <= 1000<\/p>\n
\u6d89\u53ca\u6811\u7684\u5de6\u53f3\u8282\u70b9\u95ee\u9898，\u6211\u4eec\u53ef\u4ee5\u501f\u9274\u95eb\u6c0fDP\u7684\u601d\u60f3，\u4e5f\u5c31\u662f\u6bcf\u6b21\u53ea\u662f\u770b\u5f53\u524d\u6839\u8282\u70b9\u8ddf\u5de6\u53f3\u5b50\u8282\u70b9（\u5de6\u53f3\u5b50\u8282\u70b9\u4e0b\u53ef\u80fd\u5b58\u5728\u5b50\u6811），\u6211\u4eec\u9700\u8981\u770b\u600e\u4e48\u53bb\u7ef4\u62a4\u5f53\u524d\u5de6\u53f3\u5b50\u8282\u70b9\u7684\u4fe1\u606f \u6bd4\u5982\u8fd9\u9898： \u6211\u4eec\u9700\u8981\u6c42\u7684\u662f\u6700\u5c0f\u7684\u6df1\u5ea6，\u90a3\u4e48\u6211\u4eec\u5c31\u5f53\u524d\u6839\u8282\u70b9\u4ee5\u53ca\u5b83\u7684\u5de6\u53f3\u5b50\u8282\u70b9\u6765\u770b，\u6839\u8282\u70b9\u7684\u6700\u5c0f\u6df1\u5ea6\u770b\u6210f(n), \u5de6\u53f3\u5b50\u8282\u70b9\u5206\u522b\u770b\u6210f(a), f(b)，\u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u5206\u60c5\u51b5\u8ba8\u8bbaf(n)\u8ddff(a), f(b)\u4e4b\u95f4\u7684\u5173\u7cfb： 1.a\u548cb\u90fd\u5b58\u5728： \u90a3\u4e48f(n) = min(f(a), f(b)) + 1 2.a\u5b58\u5728b\u4e0d\u5b58\u5728： f(n) = min(f(a)) + 1 3.a\u4e0d\u5b58\u5728b\u5b58\u5728： f(n) = min(f(b)) + 1 4.a\u548cb\u90fd\u4e0d\u5b58\u5728： \u90a3\u4e48f(n) = 1 \u4e8e\u662f\u6211\u4eec\u53ef\u4ee5\u53d1\u73b0\u5f53\u524d\u8ddf\u8282\u70b9\u7684\u6700\u5c0f\u6df1\u5ea6\u53ea\u8ddf\u5de6\u53f3\u5b50\u8282\u70b9\u7684\u60c5\u51b5\u6709\u5173，\u6240\u4ee5\u6211\u4eec\u53ef\u4ee5\u9012\u5f52\u5904\u7406\u6bcf\u4e2a\u5b50\u6811\u7684\u5173\u7cfb，\u6700\u7ec8\u5c06\u7ed3\u679c\u805a\u5408\u5230\u6839\u8282\u70b9\u4e0b ![\"\u5fae\u4fe1\u622a\u56fe_20241203202719.png\"](\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250810125111-689895bf83d8d.jpg\")
<\/p>\n
\u6bcf\u4e2a\u8282\u70b9\u4f1a\u67e5\u8be2\u4e00\u6b21，\u6240\u4ee5\u603b\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u662fO(n)\u7684<\/p>\n
\/**
\n * Definition for a binary tree node.
\n * struct TreeNode {
\n * int val;
\n * TreeNode *left;
\n * TreeNode *right;
\n * TreeNode() : val(0), left(nullptr), right(nullptr) {}
\n * TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
\n * TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
\n * };
\n *\/
\nclass Solution {
\npublic:
\n int minDepth(TreeNode* root) {
\n if(!root) return 0; \/\/\u5f53\u524d\u8282\u70b9\u4e0d\u5b58\u5728，\u8fd4\u56de0
\n if(!root -> right && !root -> left) return 1; \/\/\u6ca1\u6709\u5de6\u53f3\u8282\u70b9，\u8bf4\u660e\u5f53\u524d\u662f\u53f6\u5b50\u8282\u70b9
\n if(root -> right && root -> left) return min(minDepth(root -> left), minDepth(root -> right)) + 1; \/\/\u4e24\u8005\u90fd\u5b58\u5728\u5219\u8fd4\u56de\u6df1\u5ea6\u6700\u5c0f\u7684
\n if(root -> left) return minDepth(root -> left) + 1; \/\/\u5b58\u5de6\u5b50\u8282\u70b9\u90a3\u4e48\u8fd4\u56de\u5de6\u5b50\u6811\u4e2d\u6700\u5c0f\u7684\u6df1\u5ea6+ 1（\u5f53\u524d\u8282\u70b9）
\n return minDepth(root -> right) + 1; \/\/\u5426\u5219\u5c31\u662f\u5b58\u5728\u53f3\u5b50\u8282\u70b9，\u90a3\u4e48\u8fd4\u56de\u53f3\u5b50\u6811\u4e2d\u6700\u5c0f\u7684\u6df1\u5ea6+ 1，\u4ee5\u6b64\u9012\u5f52
\n }
\n};<\/p>\n
\/**
\n * Definition for a binary tree node.
\n * struct TreeNode {
\n * int val;
\n * TreeNode *left;
\n * TreeNode *right;
\n * TreeNode() : val(0), left(nullptr), right(nullptr) {}
\n * TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
\n * TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
\n * };
\n *\/
\nclass Solution {
\npublic:
\n int minDepth(TreeNode* root) {
\n if(!root) return 0;
\n if(!root -> left && !root -> right) return 1;
\n if(root -> left && root -> right) return min(minDepth(root -> left), minDepth(root -> right)) + 1;
\n if(root -> left) return minDepth(root -> left) + 1;
\n return minDepth(root -> right) + 1;
\n }
\n};<\/p>\n
\u7ed9\u4f60\u4e8c\u53c9\u6811\u7684\u6839\u8282\u70b9 root \u548c\u4e00\u4e2a\u8868\u793a\u76ee\u6807\u548c\u7684\u6574\u6570 targetSum \u3002\u5224\u65ad\u8be5\u6811\u4e2d\u662f\u5426\u5b58\u5728 \u6839\u8282\u70b9\u5230\u53f6\u5b50\u8282\u70b9 \u7684\u8def\u5f84，\u8fd9\u6761\u8def\u5f84\u4e0a\u6240\u6709\u8282\u70b9\u503c\u76f8\u52a0\u7b49\u4e8e\u76ee\u6807\u548c targetSum \u3002\u5982\u679c\u5b58\u5728，\u8fd4\u56de true ；\u5426\u5219，\u8fd4\u56de false \u3002<\/p>\n
\u53f6\u5b50\u8282\u70b9 \u662f\u6307\u6ca1\u6709\u5b50\u8282\u70b9\u7684\u8282\u70b9\u3002<\/p>\n
\u793a\u4f8b 1：<\/p>\n
![\"\u5fae\u4fe1\u622a\u56fe_20241204194222.png\"](\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250810125112-689895c02b280.jpg\")
\u8f93\u5165：root = [5,4,8,11,null,13,4,7,2,null,null,null,1], targetSum = 22 \u8f93\u51fa：true \u89e3\u91ca：\u7b49\u4e8e\u76ee\u6807\u548c\u7684\u6839\u8282\u70b9\u5230\u53f6\u8282\u70b9\u8def\u5f84\u5982\u4e0a\u56fe\u6240\u793a\u3002<\/p>\n
\u793a\u4f8b 2：<\/p>\n
![\"\u5fae\u4fe1\u622a\u56fe_20241204194229.png\"](\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250810125112-689895c08cde2.jpg\")
\u8f93\u5165：root = [1,2,3], targetSum = 5 \u8f93\u51fa：false \u89e3\u91ca：\u6811\u4e2d\u5b58\u5728\u4e24\u6761\u6839\u8282\u70b9\u5230\u53f6\u5b50\u8282\u70b9\u7684\u8def\u5f84： (1 –> 2): \u548c\u4e3a 3 (1 –> 3): \u548c\u4e3a 4 \u4e0d\u5b58\u5728 sum = 5 \u7684\u6839\u8282\u70b9\u5230\u53f6\u5b50\u8282\u70b9\u7684\u8def\u5f84\u3002<\/p>\n
\u793a\u4f8b 3：<\/p>\n
\u8f93\u5165：root = [], targetSum = 0 \u8f93\u51fa：false \u89e3\u91ca：\u7531\u4e8e\u6811\u662f\u7a7a\u7684，\u6240\u4ee5\u4e0d\u5b58\u5728\u6839\u8282\u70b9\u5230\u53f6\u5b50\u8282\u70b9\u7684\u8def\u5f84\u3002<\/p>\n
\u63d0\u793a：<\/p>\n
\u6811\u4e2d\u8282\u70b9\u7684\u6570\u76ee\u5728\u8303\u56f4 [0, 5000] \u5185 -1000 <= Node.val <= 1000 -1000 <= targetSum <= 1000<\/p>\n
\u8fd9\u7c7b\u9700\u8981\u6839\u636e\u7236\u5b50\u8282\u70b9\u7684\u503c\u6765\u5f97\u51fa\u7b54\u6848\u7684\u9898\u578b\u4e00\u822c\u6709\u4e24\u79cd\u601d\u8def： \u4e00\u79cd\u81ea\u4e0b\u5411\u4e0a： \u5c31\u662f\u5229\u7528\u513f\u5b50\u8282\u70b9\u6765\u5f97\u51fa\u7236\u4eb2\u8282\u70b9\u7684\u76ee\u6807\u503c； \u4e00\u79cd\u662f\u81ea\u4e0a\u5411\u4e0b： \u4f7f\u7528\u7236\u4eb2\u8282\u70b9\u7684\u503c\u6765\u5f97\u51fa\u513f\u5b50\u8282\u70b9\u4e0a\u7684\u76ee\u6807\u503c； \u8fd9\u9898\u5c31\u662f\u5229\u7528\u81ea\u4e0a\u5411\u4e0b\u7684\u601d\u8def： \u8bbe\u5b9a\u7236\u8282\u70b9u, \u5de6\u53f3\u513f\u5b50\u8282\u70b9\u5206\u522b\u4e3aa, b ： \u90a3\u4e48f(a) \u548c f(b) \u7684\u8def\u5f84\u503c\u5c31\u662f\u5728\u7236\u4eb2\u8282\u70b9\u7684\u57fa\u7840\u4e0a\u52a0\u4e0a\u81ea\u5df1\u672c\u8eab\u7684\u8282\u70b9\u503c\u4e5f\u5c31\u662f f(a) = f(u) + a -> val f(b) = f(u) + b -> val \u4ee5\u6b64\u7c7b\u63a8，\u76f4\u5230\u5ef6\u5c55\u81f3\u53f6\u5b50\u8282\u70b9，\u800c\u8fd9\u91cc\u4e3a\u4e86\u8282\u7701\u53d8\u91cf\u7a7a\u95f4，\u5c06\u539f\u672c\u9700\u8981\u4f7f\u7528sum\u8fdb\u884c\u603b\u548c\u7d2f\u52a0\u7684\u53d8\u91cf\u7701\u53bb，\u6bcf\u6b21\u8ba9targetSum\u51cf\u53bb\u5f53\u524d\u8282\u70b9\u7684\u8282\u70b9\u503c，\u7136\u540e\u5c06\u51cf\u540e\u7684targetSum\u503c\u7ee7\u7eed\u4f5c\u4e3a\u53c2\u6570\u4f20\u4e0b\u53bb，\u4ee5\u6b64\u9012\u5f52，\u76f4\u5230\u5ef6\u5c55\u81f3\u53f6\u5b50\u8282\u70b9\u65f6\u5224\u65ad\u6700\u540e\u7684targetSum\u662f\u5426\u6070\u597d\u4e3a0，\u4e3a0 \u5219\u8bf4\u660e\u8fd9\u6761\u8def\u5f84\u521a\u597d\u6ee1\u8db3\u6761\u4ef6，\u5426\u5219\u8bf4\u660e\u8fd9\u6761\u8def\u5f84\u8282\u70b9\u503c\u603b\u548c\u4e0d\u662ftargetSum<\/p>\n
\u6bcf\u4e2a\u8282\u70b9\u4ec5\u88ab\u904d\u5386\u4e00\u6b21，\u4e14\u9012\u5f52\u8fc7\u7a0b\u4e2d\u7ef4\u62a4 targetSum\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u662f O(1)，\u6240\u4ee5\u603b\u65f6\u95f4\u590d\u6742\u5ea6\u662f O(n)<\/p>\n
\/**
\n * Definition for a binary tree node.
\n * struct TreeNode {
\n * int val;
\n * TreeNode *left;
\n * TreeNode *right;
\n * TreeNode() : val(0), left(nullptr), right(nullptr) {}
\n * TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
\n * TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
\n * };
\n *\/
\nclass Solution {
\npublic:
\n bool hasPathSum(TreeNode* root, int targetSum) {
\n if(!root) return false; \/\/\u5982\u679c\u5f53\u524d\u8282\u70b9\u4e0d\u5b58\u5728\u8fd4\u56defalse
\n targetSum -= root -> val; \/\/\u8ba9target Sum\u51cf\u53bb\u5f53\u524d\u8282\u70b9\u7684\u503c
\n if(!root -> left && !root -> right) return !targetSum; \/\/\u5982\u679c\u662f\u53f6\u5b50\u8282\u70b9\u90a3\u5c31\u5224\u65ad\u5f53\u524dtarget Sum\u7684\u503c\u662f\u5426\u521a\u597d\u51cf\u4e3a0
\n \/\/\u7136\u540e\u5982\u679c\u5f53\u524d\u8282\u70b9\u6709\u5de6\u513f\u5b50\u6216\u8005\u53f3\u513f\u5b50，\u90a3\u4e48\u5728\u5f53\u524d\u8282\u70b9\u548ctargetSum\u7684\u57fa\u7840\u4e0a\u9012\u5f52\u4e0b\u53bb
\n return root -> left && hasPathSum(root -> left, targetSum) || root -> right && hasPathSum(root -> right, targetSum);
\n }
\n};<\/p>\n
\/**
\n * Definition for a binary tree node.
\n * struct TreeNode {
\n * int val;
\n * TreeNode *left;
\n * TreeNode *right;
\n * TreeNode() : val(0), left(nullptr), right(nullptr) {}
\n * TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
\n * TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
\n * };
\n *\/
\nclass Solution {
\npublic:
\n bool hasPathSum(TreeNode* root, int targetSum) {
\n if(!root) return false;
\n targetSum -= root -> val;
\n if(!root -> left && !root -> right && targetSum == 0) return true;
\n return root -> left && hasPathSum(root -> left, targetSum) || root -> right && hasPathSum(root -> right, targetSum);
\n }
\n};<\/p>\n
\u7ed9\u4f60\u4e8c\u53c9\u6811\u7684\u6839\u8282\u70b9 root \u548c\u4e00\u4e2a\u6574\u6570\u76ee\u6807\u548c targetSum ，\u627e\u51fa\u6240\u6709 \u4ece\u6839\u8282\u70b9\u5230\u53f6\u5b50\u8282\u70b9 \u8def\u5f84\u603b\u548c\u7b49\u4e8e\u7ed9\u5b9a\u76ee\u6807\u548c\u7684\u8def\u5f84\u3002<\/p>\n
\u53f6\u5b50\u8282\u70b9 \u662f\u6307\u6ca1\u6709\u5b50\u8282\u70b9\u7684\u8282\u70b9\u3002<\/p>\n
\u793a\u4f8b 1： ![\"\u5fae\u4fe1\u622a\u56fe_20241204200724.png\"](\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250810125112-689895c0a0cc3.jpg\")
<\/p>\n
\u8f93\u5165：root = [5,4,8,11,null,13,4,7,2,null,null,5,1], targetSum = 22 \u8f93\u51fa：[[5,4,11,2],[5,8,4,5]]<\/p>\n
\u793a\u4f8b 2： ![\"\u5fae\u4fe1\u622a\u56fe_20241204194229.png\"](\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250810125113-689895c10a1fd.jpg\")
<\/p>\n
\u8f93\u5165：root = [1,2,3], targetSum = 5 \u8f93\u51fa：[]<\/p>\n
\u793a\u4f8b 3：<\/p>\n
\u8f93\u5165：root = [1,2], targetSum = 0 \u8f93\u51fa：[]<\/p>\n
\u63d0\u793a：<\/p>\n
\u6811\u4e2d\u8282\u70b9\u603b\u6570\u5728\u8303\u56f4 [0, 5000] \u5185 -1000 <= Node.val <= 1000 -1000 <= targetSum <= 1000<\/p>\n
\u8ddf LeetCode12.\u8def\u5f84\u603b\u548c \u601d\u8def\u4e00\u81f4，\u4f46\u662f\u2160\u53ea\u8981\u627e\u5230\u5408\u6cd5\u8def\u5f84\u5c31return\u4e86，\u2161\u5219\u9700\u8981\u5c06\u6240\u6709\u7684\u5408\u6cd5\u8def\u5f84\u5b58\u4e0b\u6765， \u90a3\u4e48\u53ea\u9700\u8981\u5f00\u4e00\u4e2a\u5bb9\u5668\u5e76\u4e14\u8bb0\u5f55\u4f7f\u5f97targetSum\u4e3a0\u7684\u8def\u5f84\u5373\u53ef，\u5f62\u5f0f\u4fbf\u662fdfs\u5f62\u5f0f<\/p>\n
\u6bcf\u4e2a\u8282\u70b9\u4f1a\u641c\u4e00\u6b21，\u5e76\u4e14\u6bcf\u4e2a\u8282\u70b9\u4e0a\u7684\u64cd\u4f5c\u65f6\u95f4\u662fO(1)\u7684，\u603b\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u5c31\u662fO(n)\u7684<\/p>\n
\/**
\n * Definition for a binary tree node.
\n * struct TreeNode {
\n * int val;
\n * TreeNode *left;
\n * TreeNode *right;
\n * TreeNode() : val(0), left(nullptr), right(nullptr) {}
\n * TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
\n * TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
\n * };
\n *\/
\nclass Solution {
\npublic:
\n vector<vector<int>> res;
\n vector<int> path;
\n vector<vector<int>> pathSum(TreeNode* root, int targetSum) {
\n if(root) dfs(root, targetSum);
\n return res;
\n }
\n void dfs(TreeNode* root, int targetSum)
\n {
\n path.push_back(root -> val); \/\/\u5c06\u5f53\u524d\u8282\u70b9\u5b58\u5165\u5f53\u524d\u8def\u5f84
\n targetSum -= root -> val;
\n if(!root -> left && !root -> right) \/\/\u5982\u679c\u5f53\u524d\u8282\u70b9\u662f\u53f6\u5b50\u8282\u70b9
\n {
\n if(targetSum == 0) \/\/\u5e76\u4e14targetSum\u4e3a0，\u8bf4\u660e\u8be5\u8def\u5f84\u662f\u5408\u6cd5\u7684
\n {
\n res.push_back(path); \/\/\u52a0\u5230\u7b54\u6848\u96c6\u5408\u4e2d
\n }
\n }else{
\n if(root -> left) dfs(root -> left, targetSum); \/\/\u5982\u679c\u4e0d\u662f\u53f6\u5b50\u8282\u70b9，\u5e76\u4e14\u5de6\u513f\u5b50\u5b58\u5728\u7684\u8bdd\u9012\u5f52\u5de6\u513f\u5b50
\n if(root -> right) dfs(root -> right, targetSum); \/\/\u4e0d\u662f\u53f6\u5b50\u8282\u70b9\u5e76\u4e14\u53f3\u513f\u5b50\u5b58\u5728\u7684\u8bdd\u9012\u5f52\u53f3\u513f\u5b50
\n }
\n path.pop_back(); \/\/\u6062\u590d\u73b0\u573a
\n }
\n};<\/p>\n
\/**
\n * Definition for a binary tree node.
\n * struct TreeNode {
\n * int val;
\n * TreeNode *left;
\n * TreeNode *right;
\n * TreeNode() : val(0), left(nullptr), right(nullptr) {}
\n * TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
\n * TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
\n * };
\n *\/
\nclass Solution {
\npublic:
\n vector<vector<int>> res;
\n vector<int> path;
\n vector<vector<int>> pathSum(TreeNode* root, int targetSum) {
\n if(root) dfs(root, targetSum);
\n return res;
\n }
\n void dfs(TreeNode* root, int targetSum)
\n {
\n path.push_back(root -> val);
\n targetSum -= root -> val;
\n if(!root -> left && !root -> right)
\n {
\n if(targetSum == 0) res.push_back(path);
\n }else
\n {
\n if(root -> left) dfs(root -> left, targetSum);
\n if(root -> right) dfs(root -> right, targetSum);
\n }
\n path.pop_back();
\n }
\n};<\/p>\n
\u7ed9\u4f60\u4e8c\u53c9\u6811\u7684\u6839\u7ed3\u70b9 root ，\u8bf7\u4f60\u5c06\u5b83\u5c55\u5f00\u4e3a\u4e00\u4e2a\u5355\u94fe\u8868：<\/p>\n
\u5c55\u5f00\u540e\u7684\u5355\u94fe\u8868\u5e94\u8be5\u540c\u6837\u4f7f\u7528 TreeNode ，\u5176\u4e2d right \u5b50\u6307\u9488\u6307\u5411\u94fe\u8868\u4e2d\u4e0b\u4e00\u4e2a\u7ed3\u70b9，\u800c\u5de6\u5b50\u6307\u9488\u59cb\u7ec8\u4e3a null \u3002 \u5c55\u5f00\u540e\u7684\u5355\u94fe\u8868\u5e94\u8be5\u4e0e\u4e8c\u53c9\u6811 \u5148\u5e8f\u904d\u5386 \u987a\u5e8f\u76f8\u540c\u3002<\/p>\n
\u793a\u4f8b 1：<\/p>\n
![\"\u5fae\u4fe1\u622a\u56fe_20241204203751.png\"](\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250810125113-689895c12fb77.jpg\")
<\/p>\n
\u8f93\u5165：root = [1,2,5,3,4,null,6] \u8f93\u51fa：[1,null,2,null,3,null,4,null,5,null,6]<\/p>\n
\u793a\u4f8b 2：<\/p>\n
\u8f93\u5165：root = [] \u8f93\u51fa：[]<\/p>\n
\u793a\u4f8b 3：<\/p>\n
\u8f93\u5165：root = [0] \u8f93\u51fa：[0]<\/p>\n
\u63d0\u793a：<\/p>\n
\u6811\u4e2d\u7ed3\u70b9\u6570\u5728\u8303\u56f4 [0, 2000] \u5185 -100 <= Node.val <= 100<\/p>\n
\u8fdb\u9636：\u4f60\u53ef\u4ee5\u4f7f\u7528\u539f\u5730\u7b97\u6cd5（O(1) \u989d\u5916\u7a7a\u95f4）\u5c55\u5f00\u8fd9\u68f5\u6811\u5417？<\/p>\n
\u8fd9\u91cc\u662f\u4f7f\u7528\u4e8c\u53c9\u6811\u7684\u524d\u5e8f\u904d\u5386： ![\"\u5fae\u4fe1\u622a\u56fe_20241204203954.png\"](\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250810125113-689895c14362c.jpg\")
<\/p>\n
\u7a0d\u5fae\u53d8\u5f62\u4e00\u4e0b\u5c31\u662f\u5982\u679c\u5f53\u524d\u8282\u70b9\u5b58\u5728\u5de6\u513f\u5b50，\u5c31\u627e\u5230\u5f53\u524d\u8282\u70b9\u4e0b\u5de6\u5b50\u6811\u7684\u53f3\u94fe，\u5c06\u5176\u63d2\u5165\u53f3\u5b50\u6811\u4e2d，\u7136\u540e\u8df3\u5230\u53f3\u513f\u5b50\u7ee7\u7eed\u5faa\u73af\u5904\u7406，\u76f4\u5230\u6240\u6709\u8282\u70b9\u90fd\u4e0d\u5b58\u5728\u5de6\u513f\u5b50： ![\"\u5fae\u4fe1\u622a\u56fe_20241204202616.png\"](\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250810125113-689895c198cea.jpg\")
<\/p>\n
\u5f62\u6210\u94fe\u8868\u7684\u505a\u6cd5\u4e5f\u8ddf\u94fe\u8868\u505a\u6cd5\u76f8\u4f3c： \u627e\u5230\u5f53\u524d\u8282\u70b9\u4e0b\u7684\u5de6\u513f\u5b50，\u4ee5\u53ca\u5de6\u5b50\u6811\u7684\u53f3\u94fe\u7684\u6700\u540e\u4e00\u4e2a\u8282\u70b9，\u8ba9\u5de6\u5b50\u6811\u7684\u53f3\u94fe\u6700\u540e\u4e00\u4e2a\u8282\u70b9\u53f3\u513f\u5b50\u6307\u5411\u5f53\u524d\u8282\u70b9\u539f\u5148\u7684\u53f3\u513f\u5b50，\u518d\u8ba9\u5f53\u524d\u8282\u70b9\u7684\u53f3\u513f\u5b50\u6307\u5411\u5f53\u524d\u8282\u70b9\u7684\u5de6\u513f\u5b50，\u5177\u4f53\u5982\u4e0a\u56fe\u6240\u793a<\/p>\n
\u867d\u7136\u4e24\u91cdwhile\u5faa\u73af，\u4f46\u662f\u5916\u5c42\u5faa\u73af\u4f1a\u5c06\u6bcf\u4e2a\u8282\u70b9\u904d\u5386\u4e00\u6b21，\u5185\u5c42\u5faa\u73af\u4f1a\u5c06\u9664\u4e86\u6839\u8282\u70b9\u4e4b\u5916\u7684\u5176\u4ed6\u53f3\u94fe\u5185\u90e8\u8282\u70b9\u904d\u5386\u4e00\u6b21，\u4e5f\u5c31\u662f\u8bf4\u6bcf\u4e2a\u8282\u70b9\u6700\u591a\u904d\u5386\u4e24\u6b21，\u6240\u4ee5\u65f6\u95f4\u590d\u6742\u5ea6\u662fO(n)\u7684<\/p>\n
\/**
\n * Definition for a binary tree node.
\n * struct TreeNode {
\n * int val;
\n * TreeNode *left;
\n * TreeNode *right;
\n * TreeNode() : val(0), left(nullptr), right(nullptr) {}
\n * TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
\n * TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
\n * };
\n *\/
\nclass Solution {
\npublic:
\n void flatten(TreeNode* root) {
\n while(root)
\n {
\n auto p = root -> left; \/\/\u627e\u5230\u5de6\u513f\u5b50
\n if(p) \/\/\u5982\u679c\u5b58\u5728\u5de6\u513f\u5b50，\u90a3\u4e48\u627e\u5230\u5de6\u513f\u5b50\u4e0b\u7684\u53f3\u94fe
\n {
\n while(p -> right) p = p -> right; \/\/\u627e\u5230\u5de6\u5b50\u6811\u7684\u53f3\u94fe
\n p -> right = root -> right; \/\/\u5c06\u53f3\u94fe\u63d2\u5165\u53f3\u5b50\u6811\u4e2d
\n root -> right = root -> left;
\n root -> left = NULL; \/\/\u5f53\u524d\u8282\u70b9\u5c31\u6ca1\u6709\u5de6\u5b50\u6811\u4e86
\n }
\n root = root -> right; \/\/\u5c06\u5f53\u524d\u8282\u70b9\u79fb\u52a8\u5230\u53f3\u8282\u70b9\u7ee7\u7eed\u627e\u5de6\u5b50\u6811\u7684\u53f3\u94fe
\n }
\n }
\n};<\/p>\n
\/**
\n * Definition for a binary tree node.
\n * struct TreeNode {
\n * int val;
\n * TreeNode *left;
\n * TreeNode *right;
\n * TreeNode() : val(0), left(nullptr), right(nullptr) {}
\n * TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
\n * TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
\n * };
\n *\/
\nclass Solution {
\npublic:
\n void flatten(TreeNode* root) {
\n while(root)
\n {
\n auto p = root -> left;
\n if(p)
\n {
\n while(p -> right) p = p -> right;
\n p -> right = root -> right;
\n root -> right = root -> left;
\n root -> left = NULL;
\n }
\n root = root -> right;
\n }
\n }
\n};<\/p>\n
\u7ed9\u4f60\u4e24\u4e2a\u5b57\u7b26\u4e32 s \u548c t ，\u7edf\u8ba1\u5e76\u8fd4\u56de\u5728 s \u7684 \u5b50\u5e8f\u5217 \u4e2d t \u51fa\u73b0\u7684\u4e2a\u6570，\u7ed3\u679c\u9700\u8981\u5bf9 109 + 7 \u53d6\u6a21\u3002<\/p>\n
\u793a\u4f8b 1：<\/p>\n
\u8f93\u5165：s = \u201crabbbit\u201d, t = \u201crabbit\u201d \u8f93\u51fa：3 \u89e3\u91ca： \u5982\u4e0b\u6240\u793a, \u6709 3 \u79cd\u53ef\u4ee5\u4ece s \u4e2d\u5f97\u5230 \u201crabbit\u201d \u7684\u65b9\u6848\u3002 ![\"\u5fae\u4fe1\u622a\u56fe_20241205191219.png\"](\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250810125114-689895c264ef7.jpg\")
<\/p>\n
\u793a\u4f8b 2：<\/p>\n
\u8f93\u5165：s = \u201cbabgbag\u201d, t = \u201cbag\u201d \u8f93\u51fa：5 \u89e3\u91ca： \u5982\u4e0b\u6240\u793a, \u6709 5 \u79cd\u53ef\u4ee5\u4ece s \u4e2d\u5f97\u5230 \u201cbag\u201d \u7684\u65b9\u6848\u3002 ![\"\u5fae\u4fe1\u622a\u56fe_20241205191227.png\"](\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250810125114-689895c26bcd7.jpg\")
<\/p>\n
\u63d0\u793a：<\/p>\n
1 <= s.length, t.length <= 1000 s \u548c t \u7531\u82f1\u6587\u5b57\u6bcd\u7ec4\u6210<\/p>\n
\u8bf8\u5982\u6b64\u7c7b\u5b57\u7b26\u5339\u914d\u7684\u9898\u578b\u4f18\u5148\u8003\u8651\u7528DP： \u901a\u8fc7\u95eb\u6c0fDP\u6cd5： 1.\u8bbe\u5b9a\u96c6\u5408f(i, j): \u8868\u793a\u7531s \u7684\u524d1 ~i \u5b57\u7b26\u7ec4\u6210\u7684\u6240\u6709\u8ddf t\u7684 1~j\u5b57\u7b26\u76f8\u540c\u7684\u5b50\u5e8f\u5217\u6570\u91cf 2.\u96c6\u5408\u5212\u5206： \u5206\u60c5\u51b5\u8003\u8651， DP\u95ee\u9898\u4e00\u822c\u5bf9\u672b\u5c3e\u7684\u4e00\u4f4d\u7684\u60c5\u51b5\u8fdb\u884c\u8ba8\u8bba，\u8fd9\u91cc\u4e5f\u662f，\u5bf9\u4e8e\u8ddft\u7684 1 ~j\u5b57\u7b26\u7ec4\u6210\u7684\u5b57\u7b26\u4e32\u76f8\u540c\u7684\u5b50\u5e8f\u5217\u4e2d，\u662f\u5426\u5305\u542bs\u7684\u7b2ci\u4f4d\u8fdb\u884c\u8ba8\u8bba： (1)\u4e0d\u5305\u542bs[i]\u7684\u5b50\u5e8f\u5217： \u4e5f\u5c31\u662f\u8bf4\u5728\u4e0d\u5305\u542bs[i]\u7684\u60c5\u51b5\u4e0b，\u6240\u6c42\u7684f[i][j]\u4e5f\u5c31\u662f\u7531s\u76841~i\u5b57\u7b26\u4e2d\u7ec4\u6210\u7684\u5b50\u5e8f\u5217\u4e2d\u8ddft\u76841~j\u5b57\u7b26\u4e32\u76f8\u540c\u7684\u6570\u91cf\u662f\u4e0d\u5305\u542bs[i]\u7684\u6570\u91cf，\u4e5f\u5c31\u7b49\u4ef7\u4e8e\u6c42\u7531s\u76841~i-1\u5b57\u7b26\u4e2d\u7ec4\u6210\u7684\u5b50\u5e8f\u5217\u4e2d\u8ddft\u76841~j\u5b57\u7b26\u4e32\u76f8\u540c\u7684\u6570\u91cf： f[i][j] = f[i – 1][j] (2)\u5305\u542bs[i]\u7684\u5b50\u5e8f\u5217: \u9996\u5148\u8981\u6ee1\u8db3s[i] == t[j]\u6761\u4ef6，\u5982\u679c\u9009\u4e86s[i]\u90a3\u4e48， \u6ee1\u8db3\u6761\u4ef6\u7684\u6240\u6709\u5b50\u5e8f\u5217\u90fd\u662f\u5305\u542bs[i]\u7684，\u4e8e\u662f\u53d8\u6210\u4eces\u76841~i-1\u5b57\u7b26\u4e2d\u9009，\u8ba9\u5176\u7ec4\u6210\u7684\u5b50\u5e8f\u5217\u4e2d\u8ddft\u76841~j-1\u5b57\u7b26\u7ec4\u6210\u7684\u5b57\u7b26\u4e32\u76f8\u540c： f[i][j] += f[i – 1][j – 1](\u76f8\u52a0\u662f\u56e0\u4e3a\u6ee1\u8db3\u6761\u4ef6\u7684\u5b50\u5e8f\u5217\u53ef\u4ee5\u5305\u542bs[i] \u4e5f\u53ef\u4ee5\u4e0d\u5305\u542bs[i])<\/p>\n
![\"\u5fae\u4fe1\u622a\u56fe_20241205185215.png\"](\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250810125114-689895c273570.jpg\")
<\/p>\n
![\"\u5fae\u4fe1\u622a\u56fe_20241205193330.png\"](\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250810125115-689895c32887a.jpg\")
<\/p>\n
class Solution {
\npublic:
\n const int mod = 1e9 + 7; \/\/\u8bbe\u5b9amod
\n int numDistinct(string s, string t) {
\n int n = s.size(), m = t.size();
\n s = ' ' + s, t = ' ' + t; \/\/\u4ece1\u5f00\u59cb\u6bd4\u8f83\u597d\u5904\u7406
\n \/\/\u8bbe\u5b9a\u96c6\u5408f(i, j)\u4e3as\u76841~i\u5b57\u7b26\u7ec4\u6210\u7684\u6240\u6709\u5b50\u5e8f\u5217\u4e2d\u7b49\u4e8et\u76841~j\u5b57\u7b26\u4e32\u7684\u5b50\u5e8f\u5217\u4e2a\u6570
\n vector<vector<long long>> f(n + 1, vector<long long> (m + 1));
\n for(int i = 0; i <= n; i++) f[i][0] = 1; \/\/s\u7684\u524d1~i\u4e2a\u5b57\u7b26\u9009\u96f6\u4e2a\u6765\u5339\u914dt\u7684\u524d\u96f6\u4e2a\u5b57\u7b26\u662f\u4e00\u79cd\u65b9\u6848
\n for(int i = 1; i <= n; i++)
\n {
\n for(int j = 1; j <= m; j++)
\n {
\n \/\/\u5f53\u4e0d\u9009s\u7684\u7b2ci\u4e2a\u5b57\u7b26，\u90a3\u4e48s\u76841 ~i\u4e2a\u5b57\u7b26\u4e2d\u5339\u914dt\u76841~j\u7684\u5b50\u5e8f\u5217\u6570\u91cf\u5c31\u4e3as\u76841~i- 1\u4e2a\u5b57\u7b26\u4e2d\u5339\u914dt\u76841~j\u7684\u5b50\u5e8f\u5217\u6570\u91cf
\n f[i][j] = f[i – 1][j] % mod;
\n \/\/\u5982\u679c\u9009s\u7684\u7b2ci\u4e2a\u5b57\u7b26， \u90a3\u4e48\u9996\u5148\u5224\u65ads[i] \u80fd\u4e0d\u80fd\u548ct[j]\u5339\u914d\u4e0a，\u5982\u679c\u80fd\u5339\u914d\u4e0a
\n \/\/\u90a3\u4e48s\u76841 ~i\u4e2a\u5b57\u7b26\u4e2d\u5339\u914dt\u76841~j\u7684\u5b50\u5e8f\u5217\u6570\u91cf\u5c31\u8981\u5728\u672c\u8eab\u7684\u57fa\u7840\u4e0a\u52a0\u4e0as\u76841~i- 1\u4e2a\u5b57\u7b26\u4e2d\u5339\u914dt\u76841~j – 1\u7684\u5b50\u5e8f\u5217\u6570\u91cf
\n if(s[i] == t[j]) f[i][j] += f[i – 1][j – 1] % mod;
\n }
\n }
\n return f[n][m];
\n }
\n};<\/p>\n
class Solution {
\npublic:
\n const int mod = 1e9 + 7;
\n int numDistinct(string s, string t) {
\n int n = s.size(), m = t.size();
\n s = ' ' + s, t = ' ' + t;
\n vector<vector<long long>> f(n + 1, vector<long long> (m + 1));
\n for(int i = 0; i <= n; i++) f[i][0] = 1;
\n for(int i = 1; i <= n; i++)
\n {
\n for(int j = 1; j <= m; j++)
\n {
\n f[i][j] = f[i – 1][j] % mod;
\n if(s[i] == t[j]) f[i][j] += f[i – 1][j – 1] % mod;
\n }
\n }
\n return f[n][m];
\n }
\n};<\/p>\n
\u7ed9\u5b9a\u4e00\u4e2a \u5b8c\u7f8e\u4e8c\u53c9\u6811 ，\u5176\u6240\u6709\u53f6\u5b50\u8282\u70b9\u90fd\u5728\u540c\u4e00\u5c42，\u6bcf\u4e2a\u7236\u8282\u70b9\u90fd\u6709\u4e24\u4e2a\u5b50\u8282\u70b9\u3002\u4e8c\u53c9\u6811\u5b9a\u4e49\u5982\u4e0b：<\/p>\n
struct Node { int val; Node *left; Node *right; Node *next; } \u586b\u5145\u5b83\u7684\u6bcf\u4e2a next \u6307\u9488，\u8ba9\u8fd9\u4e2a\u6307\u9488\u6307\u5411\u5176\u4e0b\u4e00\u4e2a\u53f3\u4fa7\u8282\u70b9\u3002\u5982\u679c\u627e\u4e0d\u5230\u4e0b\u4e00\u4e2a\u53f3\u4fa7\u8282\u70b9，\u5219\u5c06 next \u6307\u9488\u8bbe\u7f6e\u4e3a NULL\u3002<\/p>\n
\u521d\u59cb\u72b6\u6001\u4e0b，\u6240\u6709 next \u6307\u9488\u90fd\u88ab\u8bbe\u7f6e\u4e3a NULL\u3002<\/p>\n
\u793a\u4f8b 1：<\/p>\n
![\"\u5fae\u4fe1\u622a\u56fe_20241205202636.png\"](\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250810125115-689895c34fb7a.jpg\")
<\/p>\n
\u8f93\u5165：root = [1,2,3,4,5,6,7] \u8f93\u51fa：[1,#,2,3,#,4,5,6,7,#] \u89e3\u91ca：\u7ed9\u5b9a\u4e8c\u53c9\u6811\u5982\u56fe A \u6240\u793a，\u4f60\u7684\u51fd\u6570\u5e94\u8be5\u586b\u5145\u5b83\u7684\u6bcf\u4e2a next \u6307\u9488，\u4ee5\u6307\u5411\u5176\u4e0b\u4e00\u4e2a\u53f3\u4fa7\u8282\u70b9，\u5982\u56fe B \u6240\u793a\u3002\u5e8f\u5217\u5316\u7684\u8f93\u51fa\u6309\u5c42\u5e8f\u904d\u5386\u6392\u5217，\u540c\u4e00\u5c42\u8282\u70b9\u7531 next \u6307\u9488\u8fde\u63a5，\u2018#\u2019 \u6807\u5fd7\u7740\u6bcf\u4e00\u5c42\u7684\u7ed3\u675f\u3002<\/p>\n
\u793a\u4f8b 2:<\/p>\n
\u8f93\u5165：root = [] \u8f93\u51fa：[]<\/p>\n
\u63d0\u793a：<\/p>\n
\u6811\u4e2d\u8282\u70b9\u7684\u6570\u91cf\u5728 [0, 2^12 – 1] \u8303\u56f4\u5185 -1000 <= node.val <= 1000<\/p>\n
\u8fdb\u9636：<\/p>\n
\u4f60\u53ea\u80fd\u4f7f\u7528\u5e38\u91cf\u7ea7\u989d\u5916\u7a7a\u95f4\u3002 \u4f7f\u7528\u9012\u5f52\u89e3\u9898\u4e5f\u7b26\u5408\u8981\u6c42，\u672c\u9898\u4e2d\u9012\u5f52\u7a0b\u5e8f\u5360\u7528\u7684\u6808\u7a7a\u95f4\u4e0d\u7b97\u505a\u989d\u5916\u7684\u7a7a\u95f4\u590d\u6742\u5ea6<\/p>\n
\u539f\u672c\u8fd9\u9898\u662f\u53ef\u4ee5\u76f4\u63a5\u4f7f\u7528\u5c42\u5e8f\u904d\u5386\u7684\u505a\u6cd5\u76f4\u63a5\u5728\u6bcf\u4e00\u5c42\u8fdb\u884c\u6307\u5411\u5373\u53ef，\u4f46\u662f\u8fdb\u9636\u505a\u6cd5\u9700\u8981\u4f7f\u7528\u5e38\u6570\u7a7a\u95f4\u7684\u8bdd\u5c31\u53ea\u80fd\u5229\u7528\u539f\u6811\u76f4\u63a5\u8fdb\u884c\u6307\u5411\u4e86，\u90a3\u4e48\u53ef\u4ee5\u53d1\u73b0\u6bcf\u4e00\u5c42\u7684\u8282\u70b9\u6307\u5411\u90fd\u9700\u8981\u7528\u5230\u4e0a\u4e00\u5c42\u7684\u8282\u70b9\u6307\u5411\u624d\u80fd\u5b8c\u6574\u8fde\u63a5\u6bcf\u4e00\u5c42\u7684\u6240\u6709\u8282\u70b9，\u800c\u4e0a\u5c42\u53c8\u9700\u8981\u66f4\u4e0a\u4e00\u5c42\u7684\u8282\u70b9\u6307\u5411，\u6240\u4ee5\u6211\u4eec\u9700\u8981\u4ece\u6839\u8282\u70b9\u5f00\u59cb\u7ef4\u62a4，\u4e00\u5c42\u4e00\u5c42\u5f80\u4e0b\u6307\u5411：（\u8fd9\u91cc\u4e3a\u4e86\u901a\u4fd7\u6613\u61c2\u4e9b\u4f7f\u7528\u6837\u4f8b\u8fdb\u884c\u8bf4\u660e） 1.\u4ece\u6839\u8282\u70b91\u5f00\u59cb，\u5148\u627e\u5230\u6839\u8282\u70b91\u4e0b\u6700\u5de6\u8fb9\u7684\u8282\u70b9，\u4e5f\u5c31\u662f\u5f53\u524d\u6839\u8282\u70b9\u7684\u5de6\u513f\u5b502，\u8ba92\u6307\u5411\u6839\u8282\u70b9\u7684\u53f3\u513f\u5b503： p -> left -> next = p -> right (p \u4f9d\u6b21\u8868\u793a\u4e0a\u4e00\u5c42\u7684\u6bcf\u4e2a\u8282\u70b9) 2.\u8fdb\u5165\u4e0b\u4e00\u5c42，\u540c\u6837\u662f\u627e\u5230\u4e0b\u4e00\u5c42\u7684\u6700\u5de6\u8fb9\u7684\u8282\u70b9，\u4e5f\u5c31\u662f\u4e0a\u4e00\u5c42\u8282\u70b92\u7684\u5de6\u513f\u5b504： root = root -> left，\u540c\u6837\u7684\u8ba94\u6307\u54112\u7684\u53f3\u513f\u5b505 3.\u7531\u4e8e5\u9700\u8981\u6307\u54116，\u8fd9\u91cc\u5c31\u9700\u8981\u5229\u7528\u4e0a\u4e00\u5c42\u7684\u6307\u5411\u5173\u7cfb： \u56e0\u4e3a\u4e0a\u4e00\u5c42\u76842\u540e\u9762\u6709\u6307\u5411\u7684\u8282\u70b93：p -> next\u5b58\u5728， \u5219，\u8ba95\u6307\u54113\u7684\u5de6\u513f\u5b506：p -> left -> next = p -> next -> left， \u7136\u540ep\u5f80\u540e\u79fb\u6307\u5411\u4e0a\u4e00\u5c42\u7684\u540e\u4e00\u4e2a\u8282\u70b93：p = p -> next, \u6700\u540e\u5c31\u662f\u8ba93\u7684\u5de6\u513f\u5b50\u6307\u54113\u7684\u53f3\u513f\u5b50： p -> right -> next = p -> left ,\u7531\u4e8e\u4e0a\u4e00\u5c42\u8282\u70b93\u7684\u540e\u9762\u6ca1\u6709\u540e\u7eed\u8282\u70b9\u4e86，\u6240\u4ee5\u9000\u51fa\u5f53\u524d\u5c42\u7684\u5faa\u73af，\u5224\u65ad\u4e0b\u4e00\u5c42\u7684\u6700\u5de6\u8fb9\u8282\u70b9\u662f\u5426\u5b58\u5728，\u4e0d\u5b58\u5728\u5219\u65e0\u9700\u8fdb\u5165\u4e0b\u4e00\u5c42，\u5faa\u73af\u7ed3\u675f<\/p>\n
\u6bcf\u4e2a\u8282\u70b9\u4ec5\u4f1a\u904d\u5386\u4e00\u6b21，\u904d\u5386\u65f6\u4fee\u6539\u6307\u9488\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u662f O(1)，\u6240\u4ee5\u603b\u65f6\u95f4\u590d\u6742\u5ea6\u662f O(n)<\/p>\n
\/*
\n\/\/ Definition for a Node.
\nclass Node {
\npublic:
\n int val;
\n Node* left;
\n Node* right;
\n Node* next;<\/p>\n
Node() : val(0), left(NULL), right(NULL), next(NULL) {}<\/p>\n
Node(int _val) : val(_val), left(NULL), right(NULL), next(NULL) {}<\/p>\n
Node(int _val, Node* _left, Node* _right, Node* _next)
\n : val(_val), left(_left), right(_right), next(_next) {}
\n};
\n*\/<\/p>\n
class Solution {
\npublic:
\n Node* connect(Node* root) {
\n if(!root) return root;
\n auto cur = root; \/\/\u5b58\u50a8root\u8282\u70b9，\u4f5c\u4e3a\u8fd4\u56de
\n while(root -> left)
\n {
\n for(auto p = root; p ; p = p -> next) \/\/\u904d\u5386\u5f53\u524d\u5c42\u7684\u6bcf\u4e2a\u8282\u70b9
\n {
\n p -> left -> next = p -> right; \/\/\u8ba9\u5f53\u524d\u8282\u70b9\u4e0b\u7684\u5de6\u513f\u5b50\u6307\u5411\u5f53\u524d\u8282\u70b9\u4e0b\u7684\u53f3\u513f\u5b50
\n if(p -> next) p -> right -> next = p -> next -> left; \/\/\u5982\u679c\u5f53\u524d\u8282\u70b9\u5b58\u5728\u540e\u7eed\u8282\u70b9，\u5219\u8ba9\u5f53\u524d\u8282\u70b9\u4e0b\u7684\u53f3\u513f\u5b50\u6307\u5411\u5f53\u524d\u5c42\u7684\u4e0b\u4e00\u4e2a\u8282\u70b9\u7684\u5de6\u513f\u5b50
\n }
\n root = root -> left; \/\/\u8fdb\u5165\u4e0b\u4e00\u5c42\u7684\u6700\u5de6\u8fb9\u8282\u70b9
\n }
\n return cur;
\n }
\n};<\/p>\n
\/*
\n\/\/ Definition for a Node.
\nclass Node {
\npublic:
\n int val;
\n Node* left;
\n Node* right;
\n Node* next;<\/p>\n
Node() : val(0), left(NULL), right(NULL), next(NULL) {}<\/p>\n
Node(int _val) : val(_val), left(NULL), right(NULL), next(NULL) {}<\/p>\n
Node(int _val, Node* _left, Node* _right, Node* _next)
\n : val(_val), left(_left), right(_right), next(_next) {}
\n};
\n*\/<\/p>\n
class Solution {
\npublic:
\n Node* connect(Node* root) {
\n if(!root) return root;
\n auto cur = root;
\n while(root -> left)
\n {
\n for(auto p = root; p; p = p -> next)
\n {
\n p -> left -> next = p -> right;
\n if(p -> next) p -> right -> next = p -> next -> left;
\n }
\n root = root -> left;
\n }
\n return cur;
\n }
\n};<\/p>\n
\u7ed9\u5b9a\u4e00\u4e2a\u4e8c\u53c9\u6811：<\/p>\n
struct Node { int val; Node *left; Node *right; Node *next; } \u586b\u5145\u5b83\u7684\u6bcf\u4e2a next \u6307\u9488，\u8ba9\u8fd9\u4e2a\u6307\u9488\u6307\u5411\u5176\u4e0b\u4e00\u4e2a\u53f3\u4fa7\u8282\u70b9\u3002\u5982\u679c\u627e\u4e0d\u5230\u4e0b\u4e00\u4e2a\u53f3\u4fa7\u8282\u70b9，\u5219\u5c06 next \u6307\u9488\u8bbe\u7f6e\u4e3a NULL \u3002<\/p>\n
\u521d\u59cb\u72b6\u6001\u4e0b，\u6240\u6709 next \u6307\u9488\u90fd\u88ab\u8bbe\u7f6e\u4e3a NULL \u3002<\/p>\n
\u793a\u4f8b 1：<\/p>\n
![\"\u5fae\u4fe1\u622a\u56fe_20241205210556.png\"](\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250810125115-689895c35b6bf.jpg\")
<\/p>\n
\u8f93\u5165：root = [1,2,3,4,5,null,7] \u8f93\u51fa：[1,#,2,3,#,4,5,7,#] \u89e3\u91ca：\u7ed9\u5b9a\u4e8c\u53c9\u6811\u5982\u56fe A \u6240\u793a，\u4f60\u7684\u51fd\u6570\u5e94\u8be5\u586b\u5145\u5b83\u7684\u6bcf\u4e2a next \u6307\u9488，\u4ee5\u6307\u5411\u5176\u4e0b\u4e00\u4e2a\u53f3\u4fa7\u8282\u70b9，\u5982\u56fe B \u6240\u793a\u3002\u5e8f\u5217\u5316\u8f93\u51fa\u6309\u5c42\u5e8f\u904d\u5386\u987a\u5e8f（\u7531 next \u6307\u9488\u8fde\u63a5），\u2018#\u2019 \u8868\u793a\u6bcf\u5c42\u7684\u672b\u5c3e\u3002<\/p>\n
\u793a\u4f8b 2：<\/p>\n
\u8f93\u5165：root = [] \u8f93\u51fa：[]<\/p>\n
\u63d0\u793a：<\/p>\n
\u6811\u4e2d\u7684\u8282\u70b9\u6570\u5728\u8303\u56f4 [0, 6000] \u5185 -100 <= Node.val <= 100 \u8fdb\u9636：<\/p>\n
\u4f60\u53ea\u80fd\u4f7f\u7528\u5e38\u91cf\u7ea7\u989d\u5916\u7a7a\u95f4\u3002 \u4f7f\u7528\u9012\u5f52\u89e3\u9898\u4e5f\u7b26\u5408\u8981\u6c42，\u672c\u9898\u4e2d\u9012\u5f52\u7a0b\u5e8f\u7684\u9690\u5f0f\u6808\u7a7a\u95f4\u4e0d\u8ba1\u5165\u989d\u5916\u7a7a\u95f4\u590d\u6742\u5ea6\u3002<\/p>\n
\u7531\u4e8e\u8fd9\u9898\u7684\u8fdb\u9636\u505a\u6cd5\u4e5f\u540c\u6837\u4e0d\u80fd\u4f7f\u7528\u989d\u5916\u7a7a\u95f4，\u540c\u65f6\u8fd9\u91cc\u8fd8\u662f\u4e0e\u4e0a\u9898\u540c\u6837\u7684\u601d\u60f3，\u4f7f\u7528\u4e0a\u4e00\u5c42\u8282\u70b9\u6765\u7ef4\u62a4\u4e0b\u5c42\u7684\u6307\u5411\u5173\u7cfb，\u4f46\u662f\u53ef\u80fd\u4e0d\u5b58\u5728\u90e8\u5206\u8282\u70b9，\u5c31\u4e0d\u80fd\u4f7f\u7528\u4e0a\u9898\u6240\u8ff0\u65b9\u6cd5\u8fdb\u884c\u94fe\u8868\u8fde\u63a5，\u8fd9\u91cc\u60f3\u5230\u53ea\u9700\u8981\u521b\u5efa\u94fe\u8868\u7684\u5934\u5c3e\u4e24\u4e2a\u8282\u70b9，\u6bcf\u6b21\u53ea\u8981\u53d1\u73b0\u5f53\u524d\u8282\u70b9\u6709\u5de6\u513f\u5b50\u5c31\u4f18\u5148\u5c06\u5de6\u513f\u5b50\u6dfb\u52a0\u5230\u5c3e\u8282\u70b9\u4e4b\u524d，\u7136\u540e\u770b\u53f3\u513f\u5b50，\u4e5f\u8fdb\u884c\u540c\u6837\u64cd\u4f5c，\u8fd9\u6837\u4ece\u524d\u5f80\u540e\u904d\u5386\u4e0a\u4e00\u5c42\u7684\u8282\u70b9，\u5c31\u80fd\u5c06\u4e0b\u4e00\u5c42\u7684\u8282\u70b9\u5168\u90e8\u4f9d\u6b21\u6dfb\u52a0\u5230\u6bcf\u5c42\u521b\u5efa\u7684\u5934\u5c3e\u8282\u70b9\u4e4b\u95f4<\/p>\n
![\"\u5fae\u4fe1\u622a\u56fe_20241205211602.png\"](\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250810125115-689895c36b972.jpg\")
<\/p>\n
\u6bcf\u4e2a\u8282\u70b9\u4ec5\u4f1a\u904d\u5386\u4e00\u6b21\u3002\u5bf9\u4e8e\u6bcf\u4e2a\u8282\u70b9，\u904d\u5386\u65f6\u7ef4\u62a4\u4e0b\u4e00\u5c42\u94fe\u8868\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u662f O(1)，\u6240\u4ee5\u603b\u65f6\u95f4\u590d\u6742\u5ea6\u662f O(n)\u3002<\/p>\n
\/*
\n\/\/ Definition for a Node.
\nclass Node {
\npublic:
\n int val;
\n Node* left;
\n Node* right;
\n Node* next;<\/p>\n
Node() : val(0), left(NULL), right(NULL), next(NULL) {}<\/p>\n
Node(int _val) : val(_val), left(NULL), right(NULL), next(NULL) {}<\/p>\n
Node(int _val, Node* _left, Node* _right, Node* _next)
\n : val(_val), left(_left), right(_right), next(_next) {}
\n};
\n*\/<\/p>\n
class Solution {
\npublic:
\n Node* connect(Node* root) {
\n if(!root) return root;
\n auto cur = root;
\n while(cur)
\n {
\n auto head = new Node(-1); \/\/\u6bcf\u4e00\u5c42\u7684\u5934\u8282\u70b9
\n auto tail = head; \/\/\u6bcf\u4e00\u5c42\u7684\u5c3e\u8282\u70b9
\n for(auto p = cur; p; p = p -> next) \/\/\u904d\u5386\u5f53\u524d\u5c42\u7684\u6bcf\u4e00\u4e2a\u8282\u70b9，\u5229\u7528\u5f53\u524d\u5c42\u66f4\u65b0\u4e0b\u4e00\u5c42\u7684\u94fe\u8868\u6307\u5411
\n {
\n if(p -> left) tail = tail -> next = p -> left; \/\/\u5982\u679c\u5b58\u5728\u5de6\u513f\u5b50\u90a3\u4e48\u5c06\u5de6\u513f\u5b50\u63d2\u5165\u5c3e\u8282\u70b9\u4e4b\u524d
\n if(p -> right) tail = tail -> next = p -> right; \/\/\u5982\u679c\u5b58\u5728\u53f3\u513f\u5b50\u90a3\u4e48\u5c06\u53f3\u513f\u5b50\u63d2\u5165\u5c3e\u8282\u70b9\u4e4b\u524d
\n }
\n cur = head -> next; \/\/\u8f6c\u81f3\u4e0b\u4e00\u5c42\u7684\u5934\u8282\u70b9\u4e0b\u7684\u7b2c\u4e00\u4e2a\u8282\u70b9
\n }
\n return root;
\n }
\n};<\/p>\n
\/*
\n\/\/ Definition for a Node.
\nclass Node {
\npublic:
\n int val;
\n Node* left;
\n Node* right;
\n Node* next;<\/p>\n
Node() : val(0), left(NULL), right(NULL), next(NULL) {}<\/p>\n
Node(int _val) : val(_val), left(NULL), right(NULL), next(NULL) {}<\/p>\n
Node(int _val, Node* _left, Node* _right, Node* _next)
\n : val(_val), left(_left), right(_right), next(_next) {}
\n};
\n*\/<\/p>\n
class Solution {
\npublic:
\n Node* connect(Node* root) {
\n if(!root) return root;
\n auto cur = root;
\n while(cur)
\n {
\n auto head = new Node(-1);
\n auto tail = head;
\n for(auto p = cur; p; p = p -> next)
\n {
\n if(p -> left) tail = tail -> next = p -> left;
\n if(p -> right) tail = tail -> next = p -> right;
\n }
\n cur = head -> next;
\n }
\n return root;
\n }
\n};<\/p>\n
\u7ed9\u5b9a\u4e00\u4e2a\u975e\u8d1f\u6574\u6570 numRows，\u751f\u6210\u300c\u6768\u8f89\u4e09\u89d2\u300d\u7684\u524d numRows \u884c\u3002<\/p>\n
\u5728\u300c\u6768\u8f89\u4e09\u89d2\u300d\u4e2d，\u6bcf\u4e2a\u6570\u662f\u5b83\u5de6\u4e0a\u65b9\u548c\u53f3\u4e0a\u65b9\u7684\u6570\u7684\u548c\u3002<\/p>\n
![\"\u5fae\u4fe1\u622a\u56fe_20241206184955.png\"](\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250810125116-689895c47312d.jpg\")
<\/p>\n
\u793a\u4f8b 1:<\/p>\n
\u8f93\u5165: numRows = 5 \u8f93\u51fa: [[1],[1,1],[1,2,1],[1,3,3,1],[1,4,6,4,1]]<\/p>\n
\u793a\u4f8b 2:<\/p>\n
\u8f93\u5165: numRows = 1 \u8f93\u51fa: [[1]]<\/p>\n
\u63d0\u793a:<\/p>\n
1 <= numRows <= 30<\/p>\n
\u9012\u63a8\u5373\u53ef：\u8fd9\u91cc\u4e3b\u8981\u9700\u8981\u6ce8\u610f\u7684\u662f\u5728\u8f6c\u6362\u6210\u77e9\u9635\u6765\u770b\u7684\u8bdd\u5f53\u524d\u683c\u5b50\u662f\u7531\u4e0a\u4e00\u884c\u7684\u540c\u4e00\u5217\u548c\u4e0a\u4e00\u884c\u524d\u4e00\u5217\u7684\u4e24\u4e2a\u683c\u5b50\u7684\u548c<\/p>\n
![\"\u5fae\u4fe1\u622a\u56fe_20241206185038.png\"](\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250810125116-689895c4d6183.jpg\")
<\/p>\n
\u603b\u5171n\u884c，\u6bcf\u884c\u6700\u591an\u4e2a\u6570，\u603b\u5171n* (n + 1) \/ 2\u4e2a\u6570，\u6bcf\u4e2a\u6570\u8ba1\u7b97\u65f6\u95f4\u662fO(1)\u7684，\u603b\u5171\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u662fO(n^2)\u7684<\/p>\n
class Solution {
\npublic:
\n vector<vector<int>> generate(int n) {
\n vector<vector<int>> f;
\n for(int i = 0; i < n; i++)
\n {
\n vector<int> line(i + 1); \/\/\u6bcf\u4e00\u884c\u7684\u957f\u5ea6
\n line[0] = line[i] = 1; \/\/\u6bcf\u4e00\u884c\u7684\u5f00\u5934\u548c\u7ed3\u5c3e\u90fd\u662f1
\n for(int j = 1; j < i; j++) \/\/\u6bcf\u4e00\u884c\u7684\u6bcf\u4e2a\u4f4d\u7f6e
\n {
\n line[j] = f[i – 1][j – 1] + f[i – 1][j]; \/\/\u6570\u4e3a\u4e0a\u4e00\u884c\u540c\u4e00\u5217\u548c\u4e0a\u4e00\u884c\u524d\u4e00\u5217\u7684\u6570\u4e4b\u548c
\n }
\n f.push_back(line);
\n }
\n return f;
\n }
\n};<\/p>\n
class Solution {
\npublic:
\n vector<vector<int>> generate(int n) {
\n vector<vector<int>> res;
\n for(int i = 0; i < n; i++)
\n {
\n vector<int> line(i + 1);
\n line[0] = line[i] = 1;
\n for(int j = 1; j < i; j++)
\n {
\n line[j] = res[i – 1][j] + res[i – 1][j – 1];
\n }
\n res.push_back(line);
\n }
\n return res;
\n }
\n};<\/p>\n
\u7ed9\u5b9a\u4e00\u4e2a\u975e\u8d1f\u7d22\u5f15 rowIndex，\u8fd4\u56de\u300c\u6768\u8f89\u4e09\u89d2\u300d\u7684\u7b2c rowIndex \u884c\u3002<\/p>\n
\u5728\u300c\u6768\u8f89\u4e09\u89d2\u300d\u4e2d，\u6bcf\u4e2a\u6570\u662f\u5b83\u5de6\u4e0a\u65b9\u548c\u53f3\u4e0a\u65b9\u7684\u6570\u7684\u548c\u3002<\/p>\n
![\"\u5fae\u4fe1\u622a\u56fe_20241206184955.png\"](\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250810125117-689895c57edcd.jpg\")
<\/p>\n
\u793a\u4f8b 1:<\/p>\n
\u8f93\u5165: rowIndex = 3 \u8f93\u51fa: [1,3,3,1] \u793a\u4f8b 2:<\/p>\n
\u8f93\u5165: rowIndex = 0 \u8f93\u51fa: [1]<\/p>\n
\u793a\u4f8b 3:<\/p>\n
\u8f93\u5165: rowIndex = 1 \u8f93\u51fa: [1,1]<\/p>\n
\u63d0\u793a:<\/p>\n
0 <= rowIndex <= 33<\/p>\n
\u8fdb\u9636：<\/p>\n
\u4f60\u53ef\u4ee5\u4f18\u5316\u4f60\u7684\u7b97\u6cd5\u5230 O(rowIndex) \u7a7a\u95f4\u590d\u6742\u5ea6\u5417？<\/p>\n
\u6b63\u5e38\u505a\u6cd5\u5982\u4e0b\u6240\u793a： \u9700\u8981O(n*n)\u7684\u7a7a\u95f4\u590d\u6742\u5ea6， \u8fdb\u9636\u505a\u6cd5\u8981\u6c42\u4f7f\u7528O(n)\u7684\u7a7a\u95f4\u590d\u6742\u5ea6，\u4e8e\u662f\u8003\u8651\u4f7f\u7528\u6eda\u52a8\u6570\u7ec4： \u6eda\u52a8\u6570\u7ec4：\u7531\u4e8e\u6211\u4eec\u4ece\u72b6\u6001\u65b9\u7a0bf[i][j] = f[i – 1][j – 1] + f[i – 1][j]\u53ef\u4ee5\u770b\u51fa，\u5f53\u524d\u884c\u7684\u72b6\u6001\u53ea\u662f\u8ddf\u4e0a\u4e00\u884c\u6709\u5173，\u6240\u4ee5\u5728\u8ba1\u7b97\u5b8c\u5f53\u524d\u884c\u7684\u72b6\u6001\u503c\u4e4b\u540e， \u4e0a\u4e00\u884c\u7684\u72b6\u6001\u503c\u5c31\u6ca1\u7528\u4e86，\u4e3a\u4e86\u8282\u7701\u7a7a\u95f4，\u6211\u4eec\u53ea\u9700\u8981\u5355\u5f00\u4e24\u884c(\u4e3a\u4ec0\u4e48\u8981\u4e24\u884c？ \u4ea4\u66ff\u5b58\u50a8\u5f53\u524d\u884c\u7684\u72b6\u6001\u503c，\u8ba1\u7b97\u65f6\u4e0d\u4f1a\u53d1\u751f\u51b2\u7a81，\u5947\u6570\u884c\u548c\u5076\u6570\u884c\u4ea4\u66ff\u5b58\u50a8\u5c31\u4e0d\u4f1a\u53d1\u751f\u8986\u76d6\u95ee\u9898)（\u600e\u4e48\u5b58\u50a8？ \u5c06\u5f53\u524d\u884c\u533a\u5206\u4e3a\u5947\u6570\u884c\u8fd8\u662f\u5076\u6570\u884c： (i % 2 == 0) -> i & 1: \u5982\u679c\u5f53\u524d\u884c\u662f\u5947\u6570\u884c，\u5b83\u7684\u72b6\u6001\u503c\u5c31\u4f1a\u5b58\u50a8\u5230\u7b2c0\u884c，\u800c\u5229\u7528\u4e0a\u4e00\u884c\u7684\u72b6\u6001\u503c\u4e5f\u5c31\u662f\u5076\u6570\u884c（\u7b2c\u4e00\u884c）\u7684\u503c，\u4ee5\u6b64\u4ea4\u66ff<\/p>\n
![\"\u5fae\u4fe1\u622a\u56fe_20241206190813.png\"](\"https:\/\/www.wsisp.com\/helps\/wp-content\/uploads\/2025\/08\/20250810125117-689895c58f3ed.jpg\")
<\/p>\n
\u603b\u5171n\u5c42，\u603b\u5171：1 + 2 + \u2026+n = n *(n + 1) \/ 2\u4e2a\u6570，\u6bcf\u4e2a\u6570\u7684\u8ba1\u7b97\u65f6\u95f4\u662fO(1)\u7684，\u603b\u5171\u65f6\u95f4\u590d\u6742\u5ea6\u662fO(n * n), \u7a7a\u95f4\u590d\u6742\u5ea6：\u603b\u5171\u5f00\u4e862 * n\u4e2a\u6570\u7ec4\u7a7a\u95f4，2\u4e3a\u5e38\u6570，\u6240\u4ee5\u7a7a\u95f4\u590d\u6742\u5ea6\u8fd8\u662fO(n)\u7684<\/p>\n
class Solution {
\npublic:
\n vector<int> getRow(int n) {
\n vector<vector<int>> f(n + 1, vector<int> (n + 1));
\n for(int i = 0; i <= n; i++)
\n {
\n f[i][0] = f[i][i] = 1;
\n for(int j = 1; j < i; j++)
\n {
\n f[i][j] = f[i – 1][j – 1] + f[i – 1][j];
\n }
\n }
\n return f[n];
\n }
\n};<\/p>\n
class Solution {
\npublic:
\n vector<int> getRow(int n) {
\n vector<vector<int>> f(2, vector<int> (n + 1));
\n for(int i = 0; i <= n; i++)
\n {
\n f[i & 1][0] = f[i & 1][i] = 1;
\n for(int j = 1; j < i; j++)
\n {
\n f[i & 1][j] = f[i – 1 & 1][j – 1] + f[i – 1 & 1][j];
\n }
\n }
\n return f[n & 1];
\n }
\n};<\/p>\n
\u7ed9\u5b9a\u4e00\u4e2a\u4e09\u89d2\u5f62 triangle ，\u627e\u51fa\u81ea\u9876\u5411\u4e0b\u7684\u6700\u5c0f\u8def\u5f84\u548c\u3002<\/p>\n
\u6bcf\u4e00\u6b65\u53ea\u80fd\u79fb\u52a8\u5230\u4e0b\u4e00\u884c\u4e2d\u76f8\u90bb\u7684\u7ed3\u70b9\u4e0a\u3002\u76f8\u90bb\u7684\u7ed3\u70b9 \u5728\u8fd9\u91cc\u6307\u7684\u662f \u4e0b\u6807 \u4e0e \u4e0a\u4e00\u5c42\u7ed3\u70b9\u4e0b\u6807 \u76f8\u540c\u6216\u8005\u7b49\u4e8e \u4e0a\u4e00\u5c42\u7ed3\u70b9\u4e0b\u6807 + 1 \u7684\u4e24\u4e2a\u7ed3\u70b9\u3002\u4e5f\u5c31\u662f\u8bf4，\u5982\u679c\u6b63\u4f4d\u4e8e\u5f53\u524d\u884c\u7684\u4e0b\u6807 i ，\u90a3\u4e48\u4e0b\u4e00\u6b65\u53ef\u4ee5\u79fb\u52a8\u5230\u4e0b\u4e00\u884c\u7684\u4e0b\u6807 i \u6216 i + 1 \u3002<\/p>\n
\u793a\u4f8b 1：<\/p>\n
\u8f93\u5165：triangle = [[2],[3,4],[6,5,7],[4,1,8,3]] \u8f93\u51fa：11 \u89e3\u91ca：\u5982\u4e0b\u9762\u7b80\u56fe\u6240\u793a： 2 3 4 6 5 7 4 1 8 3 \u81ea\u9876\u5411\u4e0b\u7684\u6700\u5c0f\u8def\u5f84\u548c\u4e3a 11（\u5373，2 + 3 + 5 + 1 = 11）\u3002<\/p>\n
\u793a\u4f8b 2：<\/p>\n
\u8f93\u5165：triangle = [[-10]] \u8f93\u51fa：-10<\/p>\n
\u63d0\u793a：<\/p>\n
1 <= triangle.length <= 200 triangle[0].length == 1 triangle[i].length == triangle[i – 1].length + 1 -10^4 <= triangle[i][j] <= 10^4<\/p>\n
\u8fdb\u9636：<\/p>\n
\u4f60\u53ef\u4ee5\u53ea\u4f7f\u7528 O(n) \u7684\u989d\u5916\u7a7a\u95f4（n \u4e3a\u4e09\u89d2\u5f62\u7684\u603b\u884c\u6570）\u6765\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u5417？<\/p>\n
\u6700\u5c0f\u8def\u5f84\u548c\u4e00\u770b\u5c31\u662fDP\u95ee\u9898，\u4f46\u662f\u6709\u4e24\u79cd\u8003\u8651\u65b9\u5f0f： 1.\u4ece\u6700\u4e0b\u8fb9\u5f80\u4e0a：\u8003\u8651\u6700\u4e0b\u8fb9\u5230\u4e0a\u9762\u4efb\u610f\u5143\u7d20\u7684\u6700\u4e0b\u8def\u5f84，\u8fb9\u754c\u6761\u4ef6\u6bd4\u8f83\u591a，\u4e00\u662f\u8981\u6ce8\u610f\u4e24\u8fb9\u662f\u5426\u5b58\u5728\u5143\u7d20，\u4e8c\u662f\u9700\u8981\u5224\u65ad\u8def\u5f84\u662f\u4ece\u54ea\u4e2a\u4f4d\u7f6e\u6765\u7684 2.\u4ece\u4e0a\u5f80\u4e0b：\u8003\u8651\u6bcf\u4e2a\u4f4d\u7f6e\u5230\u6700\u5e95\u5c42\u7684\u6700\u5c0f\u8def\u5f84\u548c：<\/p>\n
\u6bcf\u4e2a\u4f4d\u7f6e\u4f1a\u904d\u5386\u5230，\u603b\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO(n*n), \u7a7a\u95f4\u590d\u6742\u5ea6：O(1):\u6ca1\u6709\u989d\u5916\u5f00\u7a7a\u95f4，\u800c\u662f\u76f4\u63a5\u5c06\u5143\u7d20\u4f4d\u7f6e\u7684\u503c\u6539\u4e3a\u5f53\u524d\u4f4d\u7f6e\u5230\u6700\u5e95\u5c42\u7684\u6700\u5c0f\u8def\u5f84\u548c<\/p>\n
class Solution {
\npublic:
\n int minimumTotal(vector<vector<int>>& f) {
\n for(int i = f.size() – 2; i >= 0; i–)
\n {
\n for(int j = 0; j <= i; j++)
\n {
\n \/\/f[i][j] \u66ff\u6362\u8868\u793a\u4e3a：\u4ece（i, j) \u5230\u6700\u5e95\u5c42\u7684\u6700\u5c0f\u8def\u5f84\u548c
\n f[i][j] += min(f[i + 1][j], f[i + 1][j + 1]);
\n }
\n }
\n return f[0][0]; \/\/\u8fd4\u56de\u6700\u4e0a\u9762\u7684\u70b9:\u4e5f\u5c31\u662f(0, 0)\u5230\u6700\u5e95\u5c42\u7684\u6700\u4e0b\u8def\u5f84\u548c
\n }
\n};<\/p>\n
class Solution {
\npublic:
\n int minimumTotal(vector<vector<int>>& f) {
\n for(int i = f.size() – 2; i >= 0; i–)
\n {
\n for(int j = 0; j <= i; j++)
\n {
\n f[i][j] += min(f[i + 1][j + 1], f[i + 1][j]);
\n }
\n }
\n return f[0][0];
\n }
\n};<\/p>\n
\u7ed9\u5b9a\u4e00\u4e2a\u6570\u7ec4 prices ，\u5b83\u7684\u7b2c i \u4e2a\u5143\u7d20 prices[i] \u8868\u793a\u4e00\u652f\u7ed9\u5b9a\u80a1\u7968\u7b2c i \u5929\u7684\u4ef7\u683c\u3002<\/p>\n
\u4f60\u53ea\u80fd\u9009\u62e9 \u67d0\u4e00\u5929 \u4e70\u5165\u8fd9\u53ea\u80a1\u7968，\u5e76\u9009\u62e9\u5728 \u672a\u6765\u7684\u67d0\u4e00\u4e2a\u4e0d\u540c\u7684\u65e5\u5b50 \u5356\u51fa\u8be5\u80a1\u7968\u3002\u8bbe\u8ba1\u4e00\u4e2a\u7b97\u6cd5\u6765\u8ba1\u7b97\u4f60\u6240\u80fd\u83b7\u53d6\u7684\u6700\u5927\u5229\u6da6\u3002<\/p>\n
\u8fd4\u56de\u4f60\u53ef\u4ee5\u4ece\u8fd9\u7b14\u4ea4\u6613\u4e2d\u83b7\u53d6\u7684\u6700\u5927\u5229\u6da6\u3002\u5982\u679c\u4f60\u4e0d\u80fd\u83b7\u53d6\u4efb\u4f55\u5229\u6da6，\u8fd4\u56de 0 \u3002<\/p>\n
\u793a\u4f8b 1：<\/p>\n
\u8f93\u5165：[7,1,5,3,6,4] \u8f93\u51fa：5 \u89e3\u91ca：\u5728\u7b2c 2 \u5929（\u80a1\u7968\u4ef7\u683c = 1）\u7684\u65f6\u5019\u4e70\u5165，\u5728\u7b2c 5 \u5929（\u80a1\u7968\u4ef7\u683c = 6）\u7684\u65f6\u5019\u5356\u51fa，\u6700\u5927\u5229\u6da6 = 6-1 = 5 \u3002 \u6ce8\u610f\u5229\u6da6\u4e0d\u80fd\u662f 7-1 = 6, \u56e0\u4e3a\u5356\u51fa\u4ef7\u683c\u9700\u8981\u5927\u4e8e\u4e70\u5165\u4ef7\u683c；\u540c\u65f6，\u4f60\u4e0d\u80fd\u5728\u4e70\u5165\u524d\u5356\u51fa\u80a1\u7968\u3002<\/p>\n
\u793a\u4f8b 2：<\/p>\n
\u8f93\u5165：prices = [7,6,4,3,1] \u8f93\u51fa：0 \u89e3\u91ca：\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b, \u6ca1\u6709\u4ea4\u6613\u5b8c\u6210, \u6240\u4ee5\u6700\u5927\u5229\u6da6\u4e3a 0\u3002<\/p>\n
\u63d0\u793a：<\/p>\n
1 <= prices.length <= 10^5 0 <= prices[i] <= 10^4<\/p>\n
\u76f8\u5f53\u4e8e\u4e0a\u5e1d\u89c6\u89d2\u4e70\u80a1\u7968：\u53ea\u8981\u627e\u5230\u5f53\u524di\u4e4b\u524d\u6700\u4f4e\u7684\u65f6\u673a，\u6bcf\u6b21\u6bd4\u8f83\u5f53\u524di\u628a\u80a1\u7968\u5356\u51fa\u53bb\u8d5a\u7684\u4ef7\u503c\u548c\u4e4b\u524d\u5356\u80a1\u7968\u8d5a\u7684\u6700\u5927\u503c，\u540c\u65f6\u4e5f\u8981\u4e0d\u65ad\u66f4\u65b0\u5f53\u524di\u4e4b\u524d\u7684\u6700\u4f4e\u80a1\u7968\u65f6\u673a，\u53d6\u6700\u5c0f\u7684\u80a1\u7968\u65f6\u673a<\/p>\n
\u4f9d\u6b21\u904d\u5386\u6bcf\u4e00\u5929，\u6bcf\u4e00\u5929\u80a1\u7968\u4ef7\u683c\u7684\u8ba1\u7b97\u4e5f\u662fO(1), \u7684\u6240\u4ee5\u603b\u7684\u65f6\u95f4\u6d88\u8017\u4e3aO(n)<\/p>\n
class Solution {
\npublic:
\n int maxProfit(vector<int>& prices) {
\n int res = 0;
\n for(int i = 0, minpr = INT_MAX; i < prices.size(); i++)
\n {
\n res = max(res, prices[i] – minpr);
\n minpr = min(minpr, prices[i]);
\n }
\n return res;
\n }
\n};<\/p>\n
\u7ed9\u4f60\u4e00\u4e2a\u6574\u6570\u6570\u7ec4 prices ，\u5176\u4e2d prices[i] \u8868\u793a\u67d0\u652f\u80a1\u7968\u7b2c i \u5929\u7684\u4ef7\u683c\u3002<\/p>\n
\u5728\u6bcf\u4e00\u5929，\u4f60\u53ef\u4ee5\u51b3\u5b9a\u662f\u5426\u8d2d\u4e70\u548c\/\u6216\u51fa\u552e\u80a1\u7968\u3002\u4f60\u5728\u4efb\u4f55\u65f6\u5019 \u6700\u591a \u53ea\u80fd\u6301\u6709 \u4e00\u80a1 \u80a1\u7968\u3002\u4f60\u4e5f\u53ef\u4ee5\u5148\u8d2d\u4e70，\u7136\u540e\u5728 \u540c\u4e00\u5929 \u51fa\u552e\u3002<\/p>\n
\u8fd4\u56de \u4f60\u80fd\u83b7\u5f97\u7684 \u6700\u5927 \u5229\u6da6 \u3002<\/p>\n
\u793a\u4f8b 1：<\/p>\n
\u8f93\u5165：prices = [7,1,5,3,6,4] \u8f93\u51fa：7 \u89e3\u91ca：\u5728\u7b2c 2 \u5929（\u80a1\u7968\u4ef7\u683c = 1）\u7684\u65f6\u5019\u4e70\u5165，\u5728\u7b2c 3 \u5929（\u80a1\u7968\u4ef7\u683c = 5）\u7684\u65f6\u5019\u5356\u51fa, \u8fd9\u7b14\u4ea4\u6613\u6240\u80fd\u83b7\u5f97\u5229\u6da6 = 5 – 1 = 4\u3002 \u968f\u540e，\u5728\u7b2c 4 \u5929（\u80a1\u7968\u4ef7\u683c = 3）\u7684\u65f6\u5019\u4e70\u5165，\u5728\u7b2c 5 \u5929（\u80a1\u7968\u4ef7\u683c = 6）\u7684\u65f6\u5019\u5356\u51fa, \u8fd9\u7b14\u4ea4\u6613\u6240\u80fd\u83b7\u5f97\u5229\u6da6 = 6 – 3 = 3\u3002 \u6700\u5927\u603b\u5229\u6da6\u4e3a 4 + 3 = 7 \u3002<\/p>\n
\u793a\u4f8b 2：<\/p>\n
\u8f93\u5165：prices = [1,2,3,4,5] \u8f93\u51fa：4 \u89e3\u91ca：\u5728\u7b2c 1 \u5929（\u80a1\u7968\u4ef7\u683c = 1）\u7684\u65f6\u5019\u4e70\u5165，\u5728\u7b2c 5 \u5929 （\u80a1\u7968\u4ef7\u683c = 5）\u7684\u65f6\u5019\u5356\u51fa, \u8fd9\u7b14\u4ea4\u6613\u6240\u80fd\u83b7\u5f97\u5229\u6da6 = 5 – 1 = 4\u3002 \u6700\u5927\u603b\u5229\u6da6\u4e3a 4 \u3002<\/p>\n
\u793a\u4f8b 3：<\/p>\n
\u8f93\u5165：prices = [7,6,4,3,1] \u8f93\u51fa：0 \u89e3\u91ca：\u5728\u8fd9\u79cd\u60c5\u51b5\u4e0b, \u4ea4\u6613\u65e0\u6cd5\u83b7\u5f97\u6b63\u5229\u6da6，\u6240\u4ee5\u4e0d\u53c2\u4e0e\u4ea4\u6613\u53ef\u4ee5\u83b7\u5f97\u6700\u5927\u5229\u6da6，\u6700\u5927\u5229\u6da6\u4e3a 0\u3002<\/p>\n
\u63d0\u793a：<\/p>\n
1 <= prices.length <= 3 * 10^4 0 <= prices[i] <= 10^4<\/p>\n
\u4e3b\u8981\u7406\u89e3\u9898\u610f： \u8fd9\u9898\u53ef\u4ee5\u5f53\u5929\u5356\u5f53\u5929\u5356，\u800c\u4e14\u4e0d\u9650\u5236\u4e70\u5356\u6b21\u6570，\u4f46\u624b\u4e0a\u53ea\u80fd\u6301\u6709\u4e00\u652f\u80a1\u7968，\u4e8e\u662f\u6211\u4eec\u53ef\u4ee5\u53d1\u73b0，\u53ea\u8981\u5373\u5c06\u6709\u4e8f\u635f\u5c31\u7acb\u9a6c\u5c06\u80a1\u7968\u5356\u51fa，\u80fd\u76c8\u5229\u7684\u5c31\u7acb\u9a6c\u4e70\u5165：\u4e8e\u662f\u53ea\u8981\u8bb0\u5f55\u6bcf\u4e24\u5929\u4e4b\u95f4\u662f\u5426\u589e\u52a0，\u589e\u5c31\u7d2f\u8ba1，\u51cf\u5c31\u4e0d\u4e70：<\/p>\n
![\"\u5fae\u4fe1\u622a\u56fe_20241207193920.png\"](\"2025-08-10fxhivbjm1x2.png\")
<\/p>\n
\u6bcf\u5929\u5bf9\u6bd4\u524d\u4e00\u5929\u7684\u72b6\u6001\u4f1a\u8ba1\u7b97\u4e00\u6b21，\u6bcf\u6b21\u8ba1\u7b97\u662fO(1)\u7684， \u603b\u5171\u7684\u65f6\u95f4\u6d88\u8017\u4e3aO(n)<\/p>\n
class Solution {
\npublic:
\n int maxProfit(vector<int>& prices) {
\n int res = 0;
\n for(int i = 0; i < prices.size() – 1; i++)
\n {
\n res += max(0, prices[i + 1] – prices[i]);
\n }
\n return res;
\n }
\n};<\/p>\n
\u7ed9\u5b9a\u4e00\u4e2a\u6570\u7ec4，\u5b83\u7684\u7b2c i \u4e2a\u5143\u7d20\u662f\u4e00\u652f\u7ed9\u5b9a\u7684\u80a1\u7968\u5728\u7b2c i \u5929\u7684\u4ef7\u683c\u3002<\/p>\n
\u8bbe\u8ba1\u4e00\u4e2a\u7b97\u6cd5\u6765\u8ba1\u7b97\u4f60\u6240\u80fd\u83b7\u53d6\u7684\u6700\u5927\u5229\u6da6\u3002\u4f60\u6700\u591a\u53ef\u4ee5\u5b8c\u6210 \u4e24\u7b14 \u4ea4\u6613\u3002<\/p>\n
\u6ce8\u610f：\u4f60\u4e0d\u80fd\u540c\u65f6\u53c2\u4e0e\u591a\u7b14\u4ea4\u6613（\u4f60\u5fc5\u987b\u5728\u518d\u6b21\u8d2d\u4e70\u524d\u51fa\u552e\u6389\u4e4b\u524d\u7684\u80a1\u7968）\u3002<\/p>\n
\u793a\u4f8b 1:<\/p>\n
\u8f93\u5165：prices = [3,3,5,0,0,3,1,4] \u8f93\u51fa：6 \u89e3\u91ca：\u5728\u7b2c 4 \u5929（\u80a1\u7968\u4ef7\u683c = 0）\u7684\u65f6\u5019\u4e70\u5165，\u5728\u7b2c 6 \u5929（\u80a1\u7968\u4ef7\u683c = 3）\u7684\u65f6\u5019\u5356\u51fa，\u8fd9\u7b14\u4ea4\u6613\u6240\u80fd\u83b7\u5f97\u5229\u6da6 = 3-0 = 3 \u3002 \u968f\u540e，\u5728\u7b2c 7 \u5929（\u80a1\u7968\u4ef7\u683c = 1）\u7684\u65f6\u5019\u4e70\u5165，\u5728\u7b2c 8 \u5929 （\u80a1\u7968\u4ef7\u683c = 4）\u7684\u65f6\u5019\u5356\u51fa，\u8fd9\u7b14\u4ea4\u6613\u6240\u80fd\u83b7\u5f97\u5229\u6da6 = 4-1 = 3 \u3002<\/p>\n
\u793a\u4f8b 2：<\/p>\n
\u8f93\u5165：prices = [1,2,3,4,5] \u8f93\u51fa：4 \u89e3\u91ca：\u5728\u7b2c 1 \u5929（\u80a1\u7968\u4ef7\u683c = 1）\u7684\u65f6\u5019\u4e70\u5165，\u5728\u7b2c 5 \u5929 （\u80a1\u7968\u4ef7\u683c = 5）\u7684\u65f6\u5019\u5356\u51fa, \u8fd9\u7b14\u4ea4\u6613\u6240\u80fd\u83b7\u5f97\u5229\u6da6 = 5-1 = 4 \u3002 \u6ce8\u610f\u4f60\u4e0d\u80fd\u5728\u7b2c 1 \u5929\u548c\u7b2c 2 \u5929\u63a5\u8fde\u8d2d\u4e70\u80a1\u7968，\u4e4b\u540e\u518d\u5c06\u5b83\u4eec\u5356\u51fa\u3002 \u56e0\u4e3a\u8fd9\u6837\u5c5e\u4e8e\u540c\u65f6\u53c2\u4e0e\u4e86\u591a\u7b14\u4ea4\u6613，\u4f60\u5fc5\u987b\u5728\u518d\u6b21\u8d2d\u4e70\u524d\u51fa\u552e\u6389\u4e4b\u524d\u7684\u80a1\u7968\u3002<\/p>\n
\u793a\u4f8b 3：<\/p>\n
\u8f93\u5165：prices = [7,6,4,3,1] \u8f93\u51fa：0 \u89e3\u91ca：\u5728\u8fd9\u4e2a\u60c5\u51b5\u4e0b, \u6ca1\u6709\u4ea4\u6613\u5b8c\u6210, \u6240\u4ee5\u6700\u5927\u5229\u6da6\u4e3a 0\u3002 \u793a\u4f8b 4：<\/p>\n
\u8f93\u5165：prices = [1] \u8f93\u51fa：0<\/p>\n
\u63d0\u793a：<\/p>\n
1 <= prices.length <= 10^5 0 <= prices[i] <= 10^5<\/p>\n
\u4e24\u6b21！\u95ee\u9898\u601d\u8def： \u95eb\u6c0f\u524d\u540e\u7f00\u5206\u89e3：\u5c06\u4e24\u6b21\u95ee\u9898\u62c6\u5206\u5f00，\u770b\u51fa\u4e24\u6b21\u7684\u5355\u72ec\u95ee\u9898 \u6bd4\u5982\u8fd9\u9898： \u6211\u4eec\u4ee5i\u4e3a\u5206\u754c，\u5c06\u4e24\u6b21\u4ea4\u6613\u770b\u4f5c： \u4e00\u6b21\u4ea4\u6613\u662f\u5728\u7b2ci\u5929\u4e70\u5165，\u5728i\u5929\u4e4b\u540e\u5356\u51fa，\u90a3\u4e48\u53e6\u5916\u4e00\u6b21\u4ea4\u6613\u5c31\u662f\u57281~i-1\u5929\u4e2d\u4e70\u5165\u548c\u5356\u51fa，\u8fd9\u6837\u7684\u8bdd\u4e24\u6b21\u4ea4\u6613\u5c31\u4e0d\u4f1a\u6709\u4ea4\u9519，\u540c\u65f6\u4e24\u6b21\u90fd\u662f\u9700\u8981\u53d6\u6536\u76ca\u6700\u5927： \u5206\u6bb5\u5206\u6790： \u540e\u4e00\u6b21\u4ea4\u6613\u6bd4\u8f83\u7b80\u5355： \u5982\u679c\u5728\u7b2ci\u5929\u4e70\u5165，\u90a3\u4e48\u5728\u7b2ci\u5929\u4e4b\u540e\u627e\u5230\u540e\u9762\u7684\u6700\u5927\u503cmaxpr \u5356\u51fa\u5c31\u4e00\u5b9a\u662f\u5f53\u524d\u4ea4\u6613\u6536\u76ca\u7684\u6700\u5927\u503c：res = maxpr – price[i] \u524d\u4e00\u6b21\u4ea4\u6613： \u57281 ~ i- 1\u5929\u4e2d\u4ea4\u6613\u4e00\u6b21\u83b7\u53d6\u4ea4\u6613\u6700\u5927\u503c，\u8ddf \u4e70\u5356\u80a1\u7968\u7684\u6700\u4f73\u65f6\u673a \u4e00\u81f4，\u5f53\u7136\u4e5f\u53ef\u4ee5\u770b\u6210\u662f\u4e00\u4e2a\u7b80\u5355DP\u95ee\u9898： \u8bbe\u5b9a\u96c6\u5408f[i]\u8868\u793a\u4e3a\u57281~i\u5929\u4e2d\u4e70\u5165\u548c\u5356\u51fa\u4e00\u6b21\u7684\u6536\u76ca\u6700\u5927\u503c，\u90a3\u4e48\u53ef\u4ee5\u5206\u4e3a\u5728\u7b2ci\u5929\u5356\u51fa\u548c\u4e0d\u5728\u7b2ci\u5929\u5356\u51fa： \u9996\u5148\u7ef4\u62a4\u5f53\u524di\u4e4b\u524d\u7684\u6700\u5c0f\u4ef7\u683cminpr： \u7b2ci\u5929\u5356\u51fa： prices[i] – minpr \u4e0d\u5728\u7b2ci\u5929\u5356\u51fa，\u90a3\u4e48\u5c31\u8868\u793a\u9700\u8981\u57281 ~ i- 1\u5929\u4e2d\u4e70\u5165\u548c\u5356\u51fa\u4e00\u6b21，\u72b6\u6001\u8868\u793a\u4e3af[i – 1] \u6700\u7ec8\u8fd9\u4e00\u6b21\u4ea4\u6613\u7684\u6700\u5927\u6536\u76ca\u5c31\u4e3amax(f[i – 1], prices[i] – minpr)<\/p>\n
![\"\u5fae\u4fe1\u622a\u56fe_20241207202944.png\"](\"2025-08-10yc4jv45kggw.png\")
<\/p>\n
\u4e24\u6b21\u4ea4\u6613\u5747\u904d\u5386\u4e00\u904dprices\u6570\u7ec4，\u6bcf\u4e2a\u5143\u7d20\u904d\u5386\u4e24\u6b21，\u6240\u4ee5\u603b\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u8fd8\u662fO(n)\u7684<\/p>\n
class Solution {
\npublic:
\n int maxProfit(vector<int>& prices) {
\n int n = prices.size(); \/\/\u5929\u6570
\n vector<int> f(n + 2);
\n \/\/\u5c06\u4e24\u6b21\u7684\u4ea4\u6613\u62c6\u5206
\n \/\/\u5c06\u4ea4\u6613\u7b2c\u4e00\u6b21： 1~i\u4e2d\u4e70\u5165\u548c\u5356\u51fa\u4e00\u6b21\u7684\u6700\u5927\u6536\u76ca
\n \/\/\u6c42\u51faf[i]: \u57281~i\u5929\u4e2d\u4e70\u5165\u548c\u5356\u51fa\u4e00\u6b21\u7684\u6700\u5927\u6536\u76ca
\n \/\/\u4ece1\u5f00\u59cb，\u56e0\u4e3a\u6d89\u53ca\u5230f[i – 1]，0\u7684\u8bdd\u4f1a\u8d8a\u754c，\u6240\u4ee5\u5c06prices\u5411\u540e\u79fb\u4e00\u4f4d，f[i] \u4e0d\u53d8
\n for(int i = 1, minpr = INT_MAX; i <= n; i++)
\n {
\n f[i] = max(f[i – 1], prices[i – 1] – minpr);
\n minpr = min(minpr, prices[i – 1]);
\n }<\/p>\n
int res = 0;
\n \/\/\u7b2c\u4e8c\u6b21\u4ea4\u6613\u662f\u7b2ci\u5929\u4e70\u5165，\u5728\u4e4b\u540e\u67d0\u5929\u5356\u51fa
\n \/\/\u4ece\u540e\u5f80\u524d\u627e\u5230i\u4e4b\u540e\u7684\u6700\u5927\u503c
\n \/\/\u56e0\u4e3a\u4e0a\u9762\u79fb\u4e86\u4e00\u4f4d，\u6240\u4ee5\u6574\u4f53\u5411\u540e\u79fb\u4e00\u4f4d
\n for(int i = n, maxpr = 0; i > 0; i–)
\n {
\n cout<<i<<endl;
\n res = max(res, maxpr – prices[i – 1] + f[i – 1]); \/\/\u4e8c\u6b21\u4ea4\u6613\u52a0\u5728\u4e00\u8d77\u7684\u6700\u5927\u6536\u76ca
\n maxpr = max(maxpr, prices[i – 1]); \/\/\u66f4\u65b0i\u4e4b\u540e\u7684\u6700\u5927\u4ef7\u683c
\n }
\n return res;
\n }
\n};<\/p>\n
class Solution {
\npublic:
\n int maxProfit(vector<int>& prices) {
\n int n = prices.size();
\n vector<int> f(n + 2);
\n for(int i = 1, minpr = INT_MAX; i <= n; i++)
\n {
\n f[i] = max(f[i – 1], prices[i – 1] – minpr);
\n minpr = min(minpr, prices[i – 1]);
\n }<\/p>\n
int res = 0;<\/p>\n
for(int i = n, maxpr = 0; i > 0; i–)
\n {
\n res = max(res, maxpr – prices[i – 1] + f[i – 1]);
\n maxpr = max(maxpr, prices[i – 1]);
\n }
\n return res;
\n }
\n};<\/p>\n
\u4e8c\u53c9\u6811\u4e2d\u7684 \u8def\u5f84 \u88ab\u5b9a\u4e49\u4e3a\u4e00\u6761\u8282\u70b9\u5e8f\u5217，\u5e8f\u5217\u4e2d\u6bcf\u5bf9\u76f8\u90bb\u8282\u70b9\u4e4b\u95f4\u90fd\u5b58\u5728\u4e00\u6761\u8fb9\u3002\u540c\u4e00\u4e2a\u8282\u70b9\u5728\u4e00\u6761\u8def\u5f84\u5e8f\u5217\u4e2d \u81f3\u591a\u51fa\u73b0\u4e00\u6b21 \u3002\u8be5\u8def\u5f84 \u81f3\u5c11\u5305\u542b\u4e00\u4e2a \u8282\u70b9，\u4e14\u4e0d\u4e00\u5b9a\u7ecf\u8fc7\u6839\u8282\u70b9\u3002<\/p>\n
\u8def\u5f84\u548c \u662f\u8def\u5f84\u4e2d\u5404\u8282\u70b9\u503c\u7684\u603b\u548c\u3002<\/p>\n
\u7ed9\u4f60\u4e00\u4e2a\u4e8c\u53c9\u6811\u7684\u6839\u8282\u70b9 root ，\u8fd4\u56de\u5176 \u6700\u5927\u8def\u5f84\u548c \u3002<\/p>\n
\u793a\u4f8b 1：<\/p>\n
![\"\u5fae\u4fe1\u622a\u56fe_20241208181509.png\"](\"2025-08-10gf1iuhthc2b.png\")
<\/p>\n
\u8f93\u5165：root = [1,2,3] \u8f93\u51fa：6 \u89e3\u91ca：\u6700\u4f18\u8def\u5f84\u662f 2 -> 1 -> 3 ，\u8def\u5f84\u548c\u4e3a 2 + 1 + 3 = 6<\/p>\n
\u793a\u4f8b 2：<\/p>\n
![\"\u5fae\u4fe1\u622a\u56fe_20241208181458.png\"](\"2025-08-1021c3qvvtxi1.png\")
<\/p>\n
\u8f93\u5165：root = [-10,9,20,null,null,15,7] \u8f93\u51fa：42 \u89e3\u91ca：\u6700\u4f18\u8def\u5f84\u662f 15 -> 20 -> 7 ，\u8def\u5f84\u548c\u4e3a 15 + 20 + 7 = 42<\/p>\n
\u63d0\u793a：<\/p>\n
\u6811\u4e2d\u8282\u70b9\u6570\u76ee\u8303\u56f4\u662f [1, 3 * 10^4] -1000 <= Node.val <= 1000<\/p>\n
\u6700\u5927\u8def\u5f84\u5e76\u4e14\u53ef\u4ee5\u4e0d\u5305\u542b\u6839\u8282\u70b9，\u90a3\u4e48\u4e5f\u5c31\u662f\u9700\u8981\u641c\u7d22\u6bcf\u4e00\u6761\u8def\u5f84，\u4e24\u4e2a\u8282\u70b9\u4e4b\u95f4\u90fd\u5b58\u5728\u8def\u5f84，\u5e38\u7528\u6811\u7684\u8def\u5f84\u641c\u7d22\u65b9\u5f0f： \u679a\u4e3e\u6bcf\u4e2a\u8282\u70b9，\u8003\u8651\u4ee5\u8be5\u8282\u70b9\u4e3a\u6700\u9ad8\u8282\u70b9(\u76f8\u8fde)\u4e0b\u7684\u6240\u6709\u8def\u5f84（\u5982\u56fe\u6240\u793a），\u8fd9\u6837\u7684\u603b\u548c\u5c31\u53ef\u4ee5\u627e\u51fa\u6240\u6709\u8def\u5f84<\/p>\n
![\"\u5fae\u4fe1\u622a\u56fe_20241208182320.png\"](\"2025-08-10vlv5gsldjro.png\")
<\/p>\n
\u6bcf\u6761\u8def\u5f84\u627e\u5230\u4e86，\u63a5\u4e0b\u6765\u7684\u95ee\u9898\u5c31\u662f\u5982\u4f55\u5728\u8fd9\u4e9b\u8def\u5f84\u4e2d\u627e\u5230\u6700\u5927\u7684\u8def\u5f84\u548c，\u9996\u5148\u7edf\u8ba1\u4ee5\u6bcf\u4e2a\u8282\u70b9\u4e3a\u6700\u9ad8\u70b9\u4e0b\u7684\u8def\u5f84\u4e2d\u8def\u5f84\u548c\u7684\u6700\u5927\u503c，\u4ee5\u67d0\u4e2a\u8282\u70b9\u4e3a\u9876\u70b9\u6c42\u5176\u4e0b\u9762\u7684\u6700\u5927\u503c，\u7c7b\u4f3c\u4e8e\u4e4b\u524d\u7684\u6c42\u6839\u8282\u70b9\u4e0b\u7684\u6700\u5927\u503c，\u505a\u6cd5\u5c31\u662f： \u83b7\u53d6\u5230\u5de6\u513f\u5b50\u4e0b\u7684\u8def\u5f84\u6700\u5927\u503c\u548c\u53f3\u513f\u5b50\u4e0b\u7684\u8def\u5f84\u6700\u5927\u503c，\u90a3\u4e48\u4ee5\u5f53\u524d\u8282\u70b9\u4e3a\u6700\u9ad8\u70b9\u7684\u8def\u5f84\u548c\u6700\u5927\u503c\u5c31\u662f\u5f53\u524d\u8282\u70b9\u503c+ \u5de6\u513f\u5b50\u4e0b\u8def\u5f84\u6700\u5927\u503c（\u5927\u4e8e\u96f6\u7684\u524d\u63d0\u4e0b）+\u53f3\u513f\u5b50\u4e0b\u8def\u5f84\u6700\u5927\u503c（\u5927\u4e8e0\u7684\u524d\u63d0\u4e0b），\u800c\u4e3a\u4e86\u6c42\u5de6\u53f3\u513f\u5b50\u4e0b\u7684\u8def\u5f84\u6700\u5927\u503c，\u6df1\u641c\u65e0\u7591\u662f\u6700\u597d\u7684\u65b9\u5f0f，\u4f7f\u7528dfs，\u6bcf\u6b21\u627e\u5230\u5f53\u524d\u8282\u70b9\u4e0b\u7684\u5de6\u513f\u5b50\u548c\u53f3\u513f\u5b50\u7684\u6700\u5927\u8def\u5f84\u548c，\u5f53\u524d\u8282\u70b9\u6700\u5927\u8def\u5f84\u548c\u5c31\u4e3a\u5f53\u524d\u8282\u70b9\u503c+max(\u5de6\u513f\u5b50\u6700\u5927\u8def\u5f84\u548c， \u53f3\u513f\u5b50\u6700\u5927\u8def\u5f84\u548c),\u4ee5\u6b64\u5f80\u4e0b\u641c\u5373\u53ef<\/p>\n
![\"\u5fae\u4fe1\u622a\u56fe_20241208183240.png\"](\"2025-08-10km4ag0xfsfy.png\")
<\/p>\n
\u6bcf\u4e2a\u8282\u70b9\u641c\u4e00\u6b21，\u6bcf\u6b21\u8ba1\u7b97\u65f6\u95f4\u4e3aO(1),\u603b\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO(n)<\/p>\n
\/**
\n * Definition for a binary tree node.
\n * struct TreeNode {
\n * int val;
\n * TreeNode *left;
\n * TreeNode *right;
\n * TreeNode() : val(0), left(nullptr), right(nullptr) {}
\n * TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
\n * TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
\n * };
\n *\/
\nclass Solution {
\npublic:
\n int ans;
\n int maxPathSum(TreeNode* root) {
\n ans = INT_MIN;
\n dfs(root); \/\/\u8fd4\u56de\u4ee5\u5f53\u524d\u8282\u70b9\u4e3a\u6700\u9ad8\u70b9\u4e0b\u7684\u6700\u5927\u8def\u5f84\u548c
\n return ans;
\n }<\/p>\n
int dfs(TreeNode* u)
\n {
\n if(!u) return 0;
\n int left = max(0, dfs(u -> left)); \/\/\u8fd4\u56de\u5de6\u8fb9\u8282\u70b9\u4e0b\u7684\u6700\u5927\u8def\u5f84\u548c
\n int right = max(0, dfs(u -> right)); \/\/\u8fd4\u56de\u53f3\u8fb9\u8282\u70b9\u4e0b\u7684\u6700\u5927\u8def\u5f84\u548c
\n ans = max(ans, u -> val + left + right); \/\/\u7b54\u6848\u662f\u5728\u6bcf\u6b21\u8282\u70b9\u4e0b\u5de6\u53f3\u8282\u70b9\u8fde\u901a\u4e4b\u548c
\n return u -> val + max(left, right); \/\/\u5f53\u524d\u8282\u70b9\u4e0b\u7684\u6700\u5927\u8def\u5f84\u548c\u4e3a： \u5f53\u524d\u8282\u70b9\u503c\u4e0emax(\u5de6\u8fb9\u8282\u70b9，\u53f3\u8fb9\u8282\u70b9)\u6700\u5927\u8def\u5f84
\n }
\n};<\/p>\n
\/**
\n * Definition for a binary tree node.
\n * struct TreeNode {
\n * int val;
\n * TreeNode *left;
\n * TreeNode *right;
\n * TreeNode() : val(0), left(nullptr), right(nullptr) {}
\n * TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
\n * TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
\n * };
\n *\/
\nclass Solution {
\npublic:
\n int res;
\n int maxPathSum(TreeNode* root) {
\n res = INT_MIN;
\n dfs(root);
\n return res;
\n }<\/p>\n
int dfs(TreeNode* u)
\n {
\n if(!u) return 0;
\n int l = max(0, dfs(u -> left));
\n int r = max(0, dfs(u -> right));
\n res = max(res, u -> val + l + r);
\n return u -> val + max(l , r);
\n }
\n};<\/p>\n
\u5982\u679c\u5728\u5c06\u6240\u6709\u5927\u5199\u5b57\u7b26\u8f6c\u6362\u4e3a\u5c0f\u5199\u5b57\u7b26\u3001\u5e76\u79fb\u9664\u6240\u6709\u975e\u5b57\u6bcd\u6570\u5b57\u5b57\u7b26\u4e4b\u540e，\u77ed\u8bed\u6b63\u7740\u8bfb\u548c\u53cd\u7740\u8bfb\u90fd\u4e00\u6837\u3002\u5219\u53ef\u4ee5\u8ba4\u4e3a\u8be5\u77ed\u8bed\u662f\u4e00\u4e2a \u56de\u6587\u4e32 \u3002<\/p>\n
\u5b57\u6bcd\u548c\u6570\u5b57\u90fd\u5c5e\u4e8e\u5b57\u6bcd\u6570\u5b57\u5b57\u7b26\u3002<\/p>\n
\u7ed9\u4f60\u4e00\u4e2a\u5b57\u7b26\u4e32 s，\u5982\u679c\u5b83\u662f \u56de\u6587\u4e32 ，\u8fd4\u56de true ；\u5426\u5219，\u8fd4\u56de false \u3002<\/p>\n
\u793a\u4f8b 1：<\/p>\n
\u8f93\u5165: s = \u201cA man, a plan, a canal: Panama\u201d \u8f93\u51fa：true \u89e3\u91ca：\u201camanaplanacanalpanama\u201d \u662f\u56de\u6587\u4e32\u3002<\/p>\n
\u793a\u4f8b 2：<\/p>\n
\u8f93\u5165：s = \u201crace a car\u201d \u8f93\u51fa：false \u89e3\u91ca：\u201craceacar\u201d \u4e0d\u662f\u56de\u6587\u4e32\u3002<\/p>\n
\u793a\u4f8b 3：<\/p>\n
\u8f93\u5165：s = " " \u8f93\u51fa：true \u89e3\u91ca：\u5728\u79fb\u9664\u975e\u5b57\u6bcd\u6570\u5b57\u5b57\u7b26\u4e4b\u540e，s \u662f\u4e00\u4e2a\u7a7a\u5b57\u7b26\u4e32 \u201c\u201d \u3002 \u7531\u4e8e\u7a7a\u5b57\u7b26\u4e32\u6b63\u7740\u53cd\u7740\u8bfb\u90fd\u4e00\u6837，\u6240\u4ee5\u662f\u56de\u6587\u4e32\u3002<\/p>\n
\u63d0\u793a：<\/p>\n
1 <= s.length <= 2 * 10^5 s \u4ec5\u7531\u53ef\u6253\u5370\u7684 ASCII \u5b57\u7b26\u7ec4\u6210<\/p>\n
\u53cc\u6307\u9488： \u5934\u5c3e\u5206\u522b\u4f7f\u7528\u4e24\u4e2a\u6307\u9488，\u53ea\u8981\u4e0d\u662f\u5927\u5c0f\u5199\u5b57\u6bcd\u6216\u8005\u6570\u5b57\u5b57\u7b26\u5c31\u5f80\u4e2d\u95f4\u8df3<\/p>\n
class Solution {
\npublic:
\n bool check(char c)
\n {
\n return c >= 'a' && c <= 'z' || c >= 'A' && c <= 'Z'|| c >= '0' && c <= '9';
\n }
\n bool isPalindrome(string s) {
\n for(int i = 0, j = s.size() – 1; i < j; i++, j–)
\n {
\n while(i < j && !check(s[i])) i++;
\n while(i < j && !check(s[j])) j–;
\n if(i < j && tolower(s[i]) != tolower(s[j])) return false;
\n }
\n return true;
\n }
\n};<\/p>\n
\u6309\u5b57\u5178 wordList \u5b8c\u6210\u4ece\u5355\u8bcd beginWord \u5230\u5355\u8bcd endWord \u8f6c\u5316，\u4e00\u4e2a\u8868\u793a\u6b64\u8fc7\u7a0b\u7684 \u8f6c\u6362\u5e8f\u5217 \u662f\u5f62\u5f0f\u4e0a\u50cf beginWord -> s1 -> s2 -> \u2026 -> sk \u8fd9\u6837\u7684\u5355\u8bcd\u5e8f\u5217，\u5e76\u6ee1\u8db3：<\/p>\n
\u6bcf\u5bf9\u76f8\u90bb\u7684\u5355\u8bcd\u4e4b\u95f4\u4ec5\u6709\u5355\u4e2a\u5b57\u6bcd\u4e0d\u540c\u3002 \u8f6c\u6362\u8fc7\u7a0b\u4e2d\u7684\u6bcf\u4e2a\u5355\u8bcd si（1 <= i <= k）\u5fc5\u987b\u662f\u5b57\u5178 wordList \u4e2d\u7684\u5355\u8bcd\u3002\u6ce8\u610f，beginWord \u4e0d\u5fc5\u662f\u5b57\u5178 wordList \u4e2d\u7684\u5355\u8bcd\u3002 sk == endWord \u7ed9\u4f60\u4e24\u4e2a\u5355\u8bcd beginWord \u548c endWord ，\u4ee5\u53ca\u4e00\u4e2a\u5b57\u5178 wordList \u3002\u8bf7\u4f60\u627e\u51fa\u5e76\u8fd4\u56de\u6240\u6709\u4ece beginWord \u5230 endWord \u7684 \u6700\u77ed\u8f6c\u6362\u5e8f\u5217 ，\u5982\u679c\u4e0d\u5b58\u5728\u8fd9\u6837\u7684\u8f6c\u6362\u5e8f\u5217，\u8fd4\u56de\u4e00\u4e2a\u7a7a\u5217\u8868\u3002\u6bcf\u4e2a\u5e8f\u5217\u90fd\u5e94\u8be5\u4ee5\u5355\u8bcd\u5217\u8868 [beginWord, s1, s2, \u2026, sk] \u7684\u5f62\u5f0f\u8fd4\u56de\u3002<\/p>\n
\u793a\u4f8b 1：<\/p>\n
\u8f93\u5165：beginWord = \u201chit\u201d, endWord = \u201ccog\u201d, wordList = [\u201chot\u201d,\u201cdot\u201d,\u201cdog\u201d,\u201clot\u201d,\u201clog\u201d,\u201ccog\u201d] \u8f93\u51fa：[[\u201chit\u201d,\u201chot\u201d,\u201cdot\u201d,\u201cdog\u201d,\u201ccog\u201d],[\u201chit\u201d,\u201chot\u201d,\u201clot\u201d,\u201clog\u201d,\u201ccog\u201d]] \u89e3\u91ca：\u5b58\u5728 2 \u79cd\u6700\u77ed\u7684\u8f6c\u6362\u5e8f\u5217： \u201chit\u201d -> \u201chot\u201d -> \u201cdot\u201d -> \u201cdog\u201d -> \u201ccog\u201d \u201chit\u201d -> \u201chot\u201d -> \u201clot\u201d -> \u201clog\u201d -> \u201ccog\u201d<\/p>\n
\u793a\u4f8b 2：<\/p>\n
\u8f93\u5165：beginWord = \u201chit\u201d, endWord = \u201ccog\u201d, wordList = [\u201chot\u201d,\u201cdot\u201d,\u201cdog\u201d,\u201clot\u201d,\u201clog\u201d] \u8f93\u51fa：[] \u89e3\u91ca：endWord \u201ccog\u201d \u4e0d\u5728\u5b57\u5178 wordList \u4e2d，\u6240\u4ee5\u4e0d\u5b58\u5728\u7b26\u5408\u8981\u6c42\u7684\u8f6c\u6362\u5e8f\u5217\u3002<\/p>\n
\u63d0\u793a：<\/p>\n
1 <= beginWord.length <= 5 endWord.length == beginWord.length 1 <= wordList.length <= 500 wordList[i].length == beginWord.length beginWord\u3001endWord \u548c wordList[i] \u7531\u5c0f\u5199\u82f1\u6587\u5b57\u6bcd\u7ec4\u6210 beginWord != endWord wordList \u4e2d\u7684\u6240\u6709\u5355\u8bcd \u4e92\u4e0d\u76f8\u540c<\/p>\n
\u4f7f\u7528\u56fe\u8bba\u77e5\u8bc6，\u5c06\u5f00\u59cb\u5355\u8bcd\u5230\u7ed3\u675f\u5355\u8bcd\u7684\u6240\u6709\u5355\u8bcd\u770b\u6210\u4e00\u4e2a\u70b9，\u4e24\u4e2a\u5355\u8bcd\u4e4b\u95f4\u7684\u53d8\u6362\u5c31\u662f\u8fb9\u6743\u4e3a1\u7684\u8fb9， \u4ece\u5f00\u59cb\u5355\u8bcdbeginWord\u5f00\u59cb，\u4e0d\u65ad\u5f80\u540e\u5224\u65ad\u5f53\u524d\u5355\u8bcd(\u70b9t)\u80fd\u5426\u7531\u4e0a\u4e00\u4e2a\u5355\u8bcd(\u70b9r)\u53d8\u6362\u4e00\u6b21(dist[t] == dist[r] + 1)\u5f97\u5230，\u6700\u540e\u53d8\u6362\u5f97\u5230endWord\u4e3a\u6b62 dist\u5b58\u50a8\u5f53\u524d\u70b9\u5230\u8d77\u70b9\u7684\u8ddd\u79bb,\u7531\u4e8e\u9898\u610f\u9700\u8981\u6c42\u6240\u6709\u4ecebeginWord\u5230endWord\u7684\u6700\u77ed\u8def\u5f84，\u4e8e\u662f\u53d8\u6210\u56fe\u7684\u6700\u77ed\u8def\u95ee\u9898<\/p>\n
class Solution {
\npublic:
\n unordered_set<string> S;
\n unordered_map<string, int> dist;
\n queue<string> q;
\n vector<vector<string>> ans;
\n vector<string> path;
\n string beginWord;
\n vector<vector<string>> findLadders(string _beginWord, string endWord, vector<string>& wordList) {
\n for(auto word : wordList) S.insert(word);
\n beginWord = _beginWord;
\n dist[beginWord] = 0;
\n q.push(beginWord); \/\/\u5c06\u5f00\u59cb\u5355\u8bcd\u52a0\u5165
\n while(q.size())
\n {
\n auto t = q.front(); \/\/\u62ff\u51fa\u961f\u5934
\n q.pop();<\/p>\n
string r = t; \/\/\u8bb0\u5f55\u961f\u5934\u9632\u6b62\u4e22\u5931
\n for(int i = 0; i < t.size(); i++) \/\/\u5bf9\u4e8e\u6bcf\u4e00\u4e2a\u5355\u8bcd\u7684\u6bcf\u4e00\u4f4d
\n {
\n t = r; \/\/\u91cd\u65b0\u7f6e\u4e3a\u539f\u59cb\u7684\u961f\u5934\u5355\u8bcd，\u4e0d\u8ba9\u4e0a\u4e00\u4e2a\u5b57\u6bcd\u7684\u6539\u53d8\u5f71\u54cd\u4e0b\u4e00\u4e2a\u5b57\u6bcd\u7684\u6539\u53d8
\n for(char j = 'a'; j <= 'z'; j++) \/\/\u8981\u5c06\u5f53\u524d\u4e3a\u53d8\u6210\u54ea\u4e2a\u5b57\u6bcd
\n {
\n t[i] = j; \/\/\u5c06\u5176\u4e2d\u4e00\u4e2a\u5b57\u6bcd\u6362\u6389
\n if(S.count(t) && dist.count(t) == 0) \/\/\u5982\u679c\u80fd\u5728\u5b57\u5178\u4e2d\u627e\u5230\u5e76\u4e14\u6ca1\u6709\u51fa\u73b0\u8fc7
\n {
\n dist[t] = dist[r] + 1; \/\/\u5efa\u4e00\u6761\u8fb9，\u8bf4\u660e\u5b57\u5178\u4e2d\u7684\u8fd9\u4e2a\u5355\u8bcd\u5230\u961f\u5934\u5355\u8bcd\u7684\u6539\u53d8\u8ddd\u79bb\u4e3a1
\n if(t == endWord) break; \/\/\u5982\u679c\u6362\u5b8c\u7684\u5355\u8bcd\u4e3a\u7ed3\u675f\u5355\u8bcd，\u8bf4\u660e\u5df2\u7ecf\u627e\u5b8c\u4e86，break
\n q.push(t); \/\/\u4e0d\u7136\u7684\u8bdd\u5c06\u6362\u5b8c\u7684\u5355\u8bcd\u653e\u5230\u961f\u5217\u4e2d
\n }
\n }
\n }
\n }<\/p>\n
if(dist.count(endWord) == 0) return ans; \/\/\u5982\u679cdist\u4e2d\u6ca1\u6709\u7ec8\u70b9，\u5c31\u4e0d\u7528\u641c\u7d22\u4e86
\n path.push_back(endWord); \/\/\u5c06\u7ec8\u70b9\u63d2\u5165\u8def\u5f84
\n dfs(endWord);\/\/\u4ece\u7ec8\u70b9\u5f00\u59cb\u6df1\u5ea6\u641c\u7d22
\n return ans;
\n }<\/p>\n
void dfs(string t)
\n {
\n if(t == beginWord) \/\/\u641c\u5230\u5f00\u59cb\u5355\u8bcd\u7684\u8bdd\u5c31\u610f\u5473\u7740\u641c\u5230\u4e86\u4e00\u6761\u8def\u5f84
\n {
\n reverse(path.begin(), path.end()); \/\/\u7ffb\u8f6c\u4e00\u4e0b
\n ans.push_back(path); \/\/\u653e\u5165\u7b54\u6848\u96c6\u5408
\n reverse(path.begin(), path.end()); \/\/\u7ffb\u8f6c\u56de\u6765，\u9632\u6b62\u4e0b\u4e00\u6b21dfs\u4e71\u5e8f
\n }else{
\n string r = t;
\n for(int i = 0; i < t.size(); i++) \/\/\u770b\u5f53\u524dt\u53ef\u4ee5\u4ece\u54ea\u4e9b\u8fb9\u8fc7\u6765
\n {
\n t = r;
\n for(char j = 'a'; j <= 'z'; j++)
\n {
\n t[i] = j;
\n if(dist.count(t) && dist[t] + 1 == dist[r]) \/\/\u5982\u679c\u5b58\u5728\u8fd9\u6761\u8fb9，\u5e76\u4e14\u80fd\u8d70\u5230\u65b0\u7684t
\n {
\n path.push_back(t); \/\/\u5c31\u5c06\u5f53\u524d\u7684t\u52a0\u5165\u8def\u5f84\u4e2d
\n dfs(t);\/\/\u5e76\u7ee7\u7eed\u641c\u7d22t\u7684\u4e0b\u4e00\u4e2a\u8fb9
\n path.pop_back(); \/\/\u6062\u590d\u73b0\u573a
\n }
\n }
\n }
\n }
\n }
\n};<\/p>\n
class Solution {
\npublic:
\n unordered_map<string, int> dist;
\n vector<vector<string>> res;
\n vector<string> path;
\n unordered_set<string> S;
\n string beginWord;
\n queue<string> q;
\n vector<vector<string>> findLadders(string _beginWord, string endWord, vector<string>& wordList) {
\n for(auto word : wordList) S.insert(word);
\n beginWord = _beginWord;
\n dist[beginWord] = 0;
\n q.push(beginWord);
\n while(q.size())
\n {
\n string t = q.front();
\n q.pop();<\/p>\n
string r = t;
\n for(int i = 0; i < t.size(); i++)
\n {
\n t = r;
\n for(char j = 'a'; j <= 'z'; j++)
\n {
\n t[i] = j;
\n if(S.count(t) && dist.count(t) == 0)
\n {
\n dist[t] = dist[r] + 1;
\n cout<<t<<' ' <<r<<' ';
\n if(t == endWord) break;
\n q.push(t);
\n }
\n }
\n }
\n }<\/p>\n
if(dist.count(endWord) == 0) return res;
\n path.push_back(endWord);
\n dfs(endWord);
\n return res;
\n }<\/p>\n
void dfs(string t)
\n {
\n if(t == beginWord)
\n {
\n reverse(path.begin(), path.end());
\n res.push_back(path);
\n reverse(path.begin(), path.end());
\n }else{
\n string r = t;
\n for(int i = 0; i < t.size(); i++)
\n {
\n t = r;
\n for(char j = 'a'; j <= 'z'; j++)
\n {
\n t[i] = j;
\n if(dist.count(t) && dist[t] + 1 == dist[r])
\n {
\n path.push_back(t);
\n dfs(t);
\n path.pop_back();
\n }
\n }
\n }
\n }
\n }
\n};<\/p>\n
\u5b57\u5178 wordList \u4e2d\u4ece\u5355\u8bcd beginWord \u5230 endWord \u7684 \u8f6c\u6362\u5e8f\u5217 \u662f\u4e00\u4e2a\u6309\u4e0b\u8ff0\u89c4\u683c\u5f62\u6210\u7684\u5e8f\u5217 beginWord -> s1 -> s2 -> \u2026 -> sk：<\/p>\n
\u6bcf\u4e00\u5bf9\u76f8\u90bb\u7684\u5355\u8bcd\u53ea\u5dee\u4e00\u4e2a\u5b57\u6bcd\u3002 \u5bf9\u4e8e 1 <= i <= k \u65f6，\u6bcf\u4e2a si \u90fd\u5728 wordList \u4e2d\u3002\u6ce8\u610f， beginWord \u4e0d\u9700\u8981\u5728 wordList \u4e2d\u3002 sk == endWord \u7ed9\u4f60\u4e24\u4e2a\u5355\u8bcd beginWord \u548c endWord \u548c\u4e00\u4e2a\u5b57\u5178 wordList ，\u8fd4\u56de \u4ece beginWord \u5230 endWord \u7684 \u6700\u77ed\u8f6c\u6362\u5e8f\u5217 \u4e2d\u7684 \u5355\u8bcd\u6570\u76ee \u3002\u5982\u679c\u4e0d\u5b58\u5728\u8fd9\u6837\u7684\u8f6c\u6362\u5e8f\u5217，\u8fd4\u56de 0 \u3002<\/p>\n
\u793a\u4f8b 1：<\/p>\n
\u8f93\u5165：beginWord = \u201chit\u201d, endWord = \u201ccog\u201d, wordList = [\u201chot\u201d,\u201cdot\u201d,\u201cdog\u201d,\u201clot\u201d,\u201clog\u201d,\u201ccog\u201d] \u8f93\u51fa：5 \u89e3\u91ca：\u4e00\u4e2a\u6700\u77ed\u8f6c\u6362\u5e8f\u5217\u662f \u201chit\u201d -> \u201chot\u201d -> \u201cdot\u201d -> \u201cdog\u201d -> \u201ccog\u201d, \u8fd4\u56de\u5b83\u7684\u957f\u5ea6 5\u3002<\/p>\n
\u793a\u4f8b 2：<\/p>\n
\u8f93\u5165：beginWord = \u201chit\u201d, endWord = \u201ccog\u201d, wordList = [\u201chot\u201d,\u201cdot\u201d,\u201cdog\u201d,\u201clot\u201d,\u201clog\u201d] \u8f93\u51fa：0 \u89e3\u91ca：endWord \u201ccog\u201d \u4e0d\u5728\u5b57\u5178\u4e2d，\u6240\u4ee5\u65e0\u6cd5\u8fdb\u884c\u8f6c\u6362\u3002<\/p>\n
\u63d0\u793a：<\/p>\n
1 <= beginWord.length <= 10 endWord.length == beginWord.length 1 <= wordList.length <= 5000 wordList[i].length == beginWord.length beginWord\u3001endWord \u548c wordList[i] \u7531\u5c0f\u5199\u82f1\u6587\u5b57\u6bcd\u7ec4\u6210 beginWord != endWord wordList \u4e2d\u7684\u6240\u6709\u5b57\u7b26\u4e32 \u4e92\u4e0d\u76f8\u540c<\/p>\n
\u5efa\u56fe： \u6839\u636e\u5355\u8bcd\u4e4b\u95f4\u7684\u53d8\u6362\u5173\u7cfb，\u5efa\u7acb\u6bcf\u4e2a\u5355\u8bcd\u5230beginWord\u7684\u53d8\u6362\u64cd\u4f5c\u6b21\u6570，dist\u5b58\u50a8\u5f53\u524d\u5355\u8bcd（\u8282\u70b9）\u8ddf\u5f00\u59cb\u5355\u8bcd（\u8d77\u70b9）\u7684\u8ddd\u79bb，\u901a\u8fc7\u4e0d\u65ad\u6784\u5efa\u4e24\u70b9\u4e4b\u95f4\u7684\u8fb9，\u6700\u540e\u627e\u5230\u7ed3\u675f\u5355\u8bcdendWord\u65f6\u8fd4\u56deendWord\u8ddd\u79bb\u5f00\u59cb\u5355\u8bcd\u7684\u8ddd\u79bb\u5373\u53ef（\u5f53\u7136\u8981\u52a01， \u56e0\u4e3a\u8d77\u70b9\u8bbe\u7f6e\u7684\u8ddd\u79bb\u4e3a0， \u4f46\u662f\u9898\u610f\u8981\u6c42\u8fd4\u56de\u5305\u62ecbegin Word\u5728\u5185\u7684\u957f\u5ea6）<\/p>\n
![\"\u5fae\u4fe1\u622a\u56fe_20241210185758.png\"](\"2025-08-10dkbzg2ewf4j.png\")
<\/p>\n
class Solution {
\npublic:
\n int ladderLength(string beginWord, string endWord, vector<string>& wordList) {
\n unordered_set<string> S;
\n for(auto word : wordList) S.insert(word);
\n queue<string> q;
\n unordered_map<string, int> dist;
\n dist[beginWord] = 0;
\n q.push(beginWord);
\n while(q.size())
\n {
\n string t = q.front();
\n q.pop();<\/p>\n
string r = t;
\n for(int i = 0; i < t.size(); i++)
\n {
\n t = r;
\n for(char j = 'a'; j <= 'z'; j++)
\n {
\n t[i] = j;
\n if(S.count(t) && dist.count(t) == 0)
\n {
\n dist[t] = dist[r] + 1;
\n if(t == endWord) return dist[t] + 1; \/\/dist\u6570\u7ec4\u5c31\u662f\u8868\u793a\u5f53\u524d\u5355\u8bcd\u8ddf\u5f00\u59cb\u5355\u8bcd\u7684\u8ddd\u79bb，\u7531\u4e8edist[beginWord]\u662f0\u5f00\u59cb，\u6240\u4ee5+1
\n q.push(t);
\n }
\n }
\n }
\n }
\n return 0;
\n }
\n};<\/p>\n
class Solution {
\npublic:
\n int ladderLength(string beginWord, string endWord, vector<string>& wordList) {
\n unordered_set<string> S;
\n for(auto word : wordList) S.insert(word);
\n unordered_map<string, int> dist;
\n queue<string> q;
\n dist[beginWord] = 0;
\n q.push(beginWord);
\n while(q.size())
\n {
\n string t = q.front();
\n q.pop();<\/p>\n
string r = t;
\n for(int i = 0; i < t.size(); i++)
\n {
\n t = r;
\n for(char j = 'a'; j <= 'z'; j++)
\n {
\n t[i] = j;
\n if(S.count(t) && dist.count(t) == 0)
\n {
\n dist[t] = dist[r] + 1;
\n if(t == endWord) return dist[t] + 1;
\n q.push(t);
\n }
\n }
\n }
\n }
\n return 0;
\n }
\n};<\/p>\n
\u7ed9\u5b9a\u4e00\u4e2a\u672a\u6392\u5e8f\u7684\u6574\u6570\u6570\u7ec4 nums ，\u627e\u51fa\u6570\u5b57\u8fde\u7eed\u7684\u6700\u957f\u5e8f\u5217（\u4e0d\u8981\u6c42\u5e8f\u5217\u5143\u7d20\u5728\u539f\u6570\u7ec4\u4e2d\u8fde\u7eed）\u7684\u957f\u5ea6\u3002<\/p>\n
\u8bf7\u4f60\u8bbe\u8ba1\u5e76\u5b9e\u73b0\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a O(n) \u7684\u7b97\u6cd5\u89e3\u51b3\u6b64\u95ee\u9898\u3002<\/p>\n
\u793a\u4f8b 1：<\/p>\n
\u8f93\u5165：nums = [100,4,200,1,3,2] \u8f93\u51fa：4 \u89e3\u91ca：\u6700\u957f\u6570\u5b57\u8fde\u7eed\u5e8f\u5217\u662f [1, 2, 3, 4]\u3002\u5b83\u7684\u957f\u5ea6\u4e3a 4\u3002<\/p>\n
\u793a\u4f8b 2：<\/p>\n
\u8f93\u5165：nums = [0,3,7,2,5,8,4,6,0,1] \u8f93\u51fa：9<\/p>\n
\u63d0\u793a：<\/p>\n
0 <= nums.length <= 10^5 -10^9 <= nums[i] <= 10^9<\/p>\n
\u5c06\u5168\u90e8\u5143\u7d20\u63d2\u5165\u54c8\u5e0c\u8868\u4e2d，\u7136\u540e\u904d\u5386\u67e5\u627e\u6570\u7ec4\u5143\u7d20，\u5148\u627e\u5230\u8d77\u70b9： \u6ca1\u6709\u524d\u9762\u4e00\u4e2a\u6570 \u518d\u627e\u5230\u7ec8\u70b9： \u6ca1\u6709\u540e\u9762\u7684\u4e00\u4e2a\u6570，\u8ba1\u7b97\u4e24\u8005\u4e2d\u95f4\u7684\u957f\u5ea6，\u7136\u540e\u53d6\u6700\u5927<\/p>\n
class Solution {
\npublic:
\n int longestConsecutive(vector<int>& nums) {
\n unordered_set<int> S;
\n for(auto x : nums) S.insert(x);
\n int res = 0;
\n for(auto x : nums)
\n {
\n if(S.count(x) && !S.count(x -1)) \/\/\u8d77\u70b9:\u524d\u9762\u6ca1\u6709\u5143\u7d20\u7684\u8bdd
\n {
\n int y = x;
\n S.erase(x); \/\/\u627e\u5230\u8d77\u70b9\u540e\u79fb\u9664，\u9632\u6b62\u91cd\u590d\u67e5\u627e
\n while(S.count(y + 1)) \/\/\u7ec8\u70b9： \u5f80\u540e\u79fb\u52a8，\u76f4\u5230\u540e\u9762\u6ca1\u6709\u5143\u7d20
\n {
\n y++;
\n S.erase(y); \/\/
\n }
\n res = max(res, y – x + 1);
\n }
\n }
\n return res;
\n }
\n};<\/p>\n
class Solution {
\npublic:
\n int longestConsecutive(vector<int>& nums) {
\n unordered_set<int> hash;
\n for(auto x : nums) hash.insert(x);
\n int res = 0;
\n for(auto x : nums)
\n {
\n if(hash.count(x) && !hash.count(x -1))
\n {
\n int y = x;
\n hash.erase(x);
\n while(hash.count(y + 1))
\n {
\n y++;
\n hash.erase(y);
\n }
\n res = max(res, y – x + 1);
\n }
\n }
\n return res;
\n }
\n};<\/p>\n
\u7ed9\u4f60\u4e00\u4e2a\u4e8c\u53c9\u6811\u7684\u6839\u8282\u70b9 root ，\u6811\u4e2d\u6bcf\u4e2a\u8282\u70b9\u90fd\u5b58\u653e\u6709\u4e00\u4e2a 0 \u5230 9 \u4e4b\u95f4\u7684\u6570\u5b57\u3002 \u6bcf\u6761\u4ece\u6839\u8282\u70b9\u5230\u53f6\u8282\u70b9\u7684\u8def\u5f84\u90fd\u4ee3\u8868\u4e00\u4e2a\u6570\u5b57：<\/p>\n
\u4f8b\u5982，\u4ece\u6839\u8282\u70b9\u5230\u53f6\u8282\u70b9\u7684\u8def\u5f84 1 -> 2 -> 3 \u8868\u793a\u6570\u5b57 123 \u3002 \u8ba1\u7b97\u4ece\u6839\u8282\u70b9\u5230\u53f6\u8282\u70b9\u751f\u6210\u7684 \u6240\u6709\u6570\u5b57\u4e4b\u548c \u3002<\/p>\n
\u53f6\u8282\u70b9 \u662f\u6307\u6ca1\u6709\u5b50\u8282\u70b9\u7684\u8282\u70b9\u3002<\/p>\n
\u793a\u4f8b 1：<\/p>\n
![\"\u5fae\u4fe1\u622a\u56fe_20241208181509.png\"](\"2025-08-103zs3cbn3ael.png\")
<\/p>\n
\u8f93\u5165：root = [1,2,3] \u8f93\u51fa：25 \u89e3\u91ca： \u4ece\u6839\u5230\u53f6\u5b50\u8282\u70b9\u8def\u5f84 1->2 \u4ee3\u8868\u6570\u5b57 12 \u4ece\u6839\u5230\u53f6\u5b50\u8282\u70b9\u8def\u5f84 1->3 \u4ee3\u8868\u6570\u5b57 13 \u56e0\u6b64，\u6570\u5b57\u603b\u548c = 12 + 13 = 25<\/p>\n
\u793a\u4f8b 2：<\/p>\n
![\"\u5fae\u4fe1\u622a\u56fe_20241210191127.png\"](\"2025-08-10z5kd0bd4s3d.png\")
<\/p>\n
\u8f93\u5165：root = [4,9,0,5,1] \u8f93\u51fa：1026 \u89e3\u91ca： \u4ece\u6839\u5230\u53f6\u5b50\u8282\u70b9\u8def\u5f84 4->9->5 \u4ee3\u8868\u6570\u5b57 495 \u4ece\u6839\u5230\u53f6\u5b50\u8282\u70b9\u8def\u5f84 4->9->1 \u4ee3\u8868\u6570\u5b57 491 \u4ece\u6839\u5230\u53f6\u5b50\u8282\u70b9\u8def\u5f84 4->0 \u4ee3\u8868\u6570\u5b57 40 \u56e0\u6b64，\u6570\u5b57\u603b\u548c = 495 + 491 + 40 = 1026<\/p>\n
\u63d0\u793a：<\/p>\n
\u6811\u4e2d\u8282\u70b9\u7684\u6570\u76ee\u5728\u8303\u56f4 [1, 1000] \u5185 0 <= Node.val <= 9 \u6811\u7684\u6df1\u5ea6\u4e0d\u8d85\u8fc7 10<\/p>\n
\u8001\u751f\u5e38\u8c08\u7684\u505a\u6cd5\u4e86，\u600e\u4e48\u4e00\u76f4\u4e0d\u4f1a\u7528？ \u6d89\u53ca\u6811\u7684\u4ece\u6839\u5230\u53f6\u5b50\u8282\u70b9\u7684\u95ee\u9898\u4e00\u822c\u53ea\u9700\u8981\u8003\u8651\u5c40\u90e8，\u5c31\u4ee5\u4efb\u610f\u4e00\u4e2a\u8282\u70b9u\u4ee5\u53ca\u5b83\u7684\u5de6\u513f\u5b50a， \u53f3\u513f\u5b50b\u6765\u8bf4，\u5f53\u524du\u7684\u503c\u53ef\u4ee5\u8868\u793a\u4e3a\u4e0a\u9762\u4f20\u4e0b\u6765\u7684number* 10 + \u81ea\u8eab\u8282\u70b9\u503c，\u540c\u65f6\u5462\u5c06\u8fd9\u4e2a\u503c\u4f20\u4e0b\u53bb，\u4ee5\u6b64\u5f80\u4e0b\u63a8，\u76f4\u5230\u53f6\u5b50\u8282\u70b9\u5219\u5c06\u6240\u6709\u53f6\u5b50\u8282\u70b9\u4e0b\u7684\u503c\u7d2f\u52a0\u5230\u4e00\u8d77\u5c31\u662f\u6211\u4eec\u7684\u7b54\u6848<\/p>\n
\/**
\n * Definition for a binary tree node.
\n * struct TreeNode {
\n * int val;
\n * TreeNode *left;
\n * TreeNode *right;
\n * TreeNode() : val(0), left(nullptr), right(nullptr) {}
\n * TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
\n * TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
\n * };
\n *\/
\nclass Solution {
\npublic:
\n int res = 0;
\n int sumNumbers(TreeNode* root) {
\n if(root) dfs(root, 0); \/\/\u4ece\u6839\u8282\u70b9\u5f80\u4e0b\u641c
\n return res;
\n }<\/p>\n
void dfs(TreeNode* root, int number)
\n {
\n number = number * 10 + root -> val; \/\/\u5f53\u524d\u8282\u70b9\u503c\u7b49\u4e8e\u7236\u8282\u70b9\u7684\u503c*10 + \u81ea\u8eab\u8282\u70b9\u503c
\n if(!root -> left && !root -> right) res += number; \/\/\u5982\u679c\u662f\u53f6\u5b50\u8282\u70b9，\u90a3\u4e48\u52a0\u4e0a\u8fd9\u6761\u8def\u5f84\u4e0a\u7684\u603b\u503c
\n if(root -> left) dfs(root -> left, number); \/\/\u5f80\u5de6\u513f\u5b50\u641c
\n if(root -> right) dfs(root -> right, number); \/\/\u5f80\u53f3\u513f\u5b50\u641c
\n }
\n};<\/p>\n
\/**
\n * Definition for a binary tree node.
\n * struct TreeNode {
\n * int val;
\n * TreeNode *left;
\n * TreeNode *right;
\n * TreeNode() : val(0), left(nullptr), right(nullptr) {}
\n * TreeNode(int x) : val(x), left(nullptr), right(nullptr) {}
\n * TreeNode(int x, TreeNode *left, TreeNode *right) : val(x), left(left), right(right) {}
\n * };
\n *\/
\nclass Solution {
\npublic:
\n int res = 0;
\n int sumNumbers(TreeNode* root) {
\n if(root) dfs(root, 0);
\n return res;
\n }<\/p>\n
void dfs(TreeNode* root, int number)
\n {
\n number = number * 10 + root -> val;
\n if(!root -> left && !root -> right) res += number;
\n if(root -> left) dfs(root -> left, number);
\n if(root -> right) dfs(root -> right, number);
\n }
\n};<\/p>\n
\u7ed9\u4f60\u4e00\u4e2a m x n \u7684\u77e9\u9635 board ，\u7531\u82e5\u5e72\u5b57\u7b26 \u2018X\u2019 \u548c \u2018O\u2019 \u7ec4\u6210，\u6355\u83b7 \u6240\u6709 \u88ab\u56f4\u7ed5\u7684\u533a\u57df：<\/p>\n
\u8fde\u63a5：\u4e00\u4e2a\u5355\u5143\u683c\u4e0e\u6c34\u5e73\u6216\u5782\u76f4\u65b9\u5411\u4e0a\u76f8\u90bb\u7684\u5355\u5143\u683c\u8fde\u63a5\u3002 \u533a\u57df：\u8fde\u63a5\u6240\u6709 \u2018O\u2019 \u7684\u5355\u5143\u683c\u6765\u5f62\u6210\u4e00\u4e2a\u533a\u57df\u3002 \u56f4\u7ed5：\u5982\u679c\u60a8\u53ef\u4ee5\u7528 \u2018X\u2019 \u5355\u5143\u683c \u8fde\u63a5\u8fd9\u4e2a\u533a\u57df，\u5e76\u4e14\u533a\u57df\u4e2d\u6ca1\u6709\u4efb\u4f55\u5355\u5143\u683c\u4f4d\u4e8e board \u8fb9\u7f18，\u5219\u8be5\u533a\u57df\u88ab \u2018X\u2019 \u5355\u5143\u683c\u56f4\u7ed5\u3002 \u901a\u8fc7\u5c06\u8f93\u5165\u77e9\u9635 board \u4e2d\u7684\u6240\u6709 \u2018O\u2019 \u66ff\u6362\u4e3a \u2018X\u2019 \u6765 \u6355\u83b7\u88ab\u56f4\u7ed5\u7684\u533a\u57df\u3002<\/p>\n
\u793a\u4f8b 1：<\/p>\n
\u8f93\u5165：board = [[\u201cX\u201d,\u201cX\u201d,\u201cX\u201d,\u201cX\u201d],[\u201cX\u201d,\u201cO\u201d,\u201cO\u201d,\u201cX\u201d],[\u201cX\u201d,\u201cX\u201d,\u201cO\u201d,\u201cX\u201d],[\u201cX\u201d,\u201cO\u201d,\u201cX\u201d,\u201cX\u201d]]<\/p>\n
\u8f93\u51fa：[[\u201cX\u201d,\u201cX\u201d,\u201cX\u201d,\u201cX\u201d],[\u201cX\u201d,\u201cX\u201d,\u201cX\u201d,\u201cX\u201d],[\u201cX\u201d,\u201cX\u201d,\u201cX\u201d,\u201cX\u201d],[\u201cX\u201d,\u201cO\u201d,\u201cX\u201d,\u201cX\u201d]]<\/p>\n
\u89e3\u91ca：<\/p>\n
![\"\u5fae\u4fe1\u622a\u56fe_20241210200502.png\"](\"2025-08-10uneo5z0fxlu.png\")
<\/p>\n
\u5728\u4e0a\u56fe\u4e2d，\u5e95\u90e8\u7684\u533a\u57df\u6ca1\u6709\u88ab\u6355\u83b7，\u56e0\u4e3a\u5b83\u5728 board \u7684\u8fb9\u7f18\u5e76\u4e14\u4e0d\u80fd\u88ab\u56f4\u7ed5\u3002<\/p>\n
\u793a\u4f8b 2：<\/p>\n
\u8f93\u5165：board = [[\u201cX\u201d]]<\/p>\n
\u8f93\u51fa：[[\u201cX\u201d]]<\/p>\n
\u63d0\u793a：<\/p>\n
m == board.length n == board[i].length 1 <= m, n <= 200 board[i][j] \u4e3a \u2018X\u2019 \u6216 \u2018O\u2019<\/p>\n
\u5229\u7528\u9006\u5411\u601d\u7ef4：\u9898\u76ee\u8981\u6c42\u5c06\u6240\u6709\u8fde\u901a\u7684\u56f4\u7ed5O\u533a\u57df\u6362\u6210X，\u90a3\u4e48\u6211\u4eec\u53ef\u4ee5\u5148\u627e\u5230\u6240\u6709\u6ca1\u6709\u88ab\u56f4\u7ed5\u4e5f\u5c31\u662f\u4e0e\u8fb9\u754c\u76f8\u8fde\u6216\u8005\u5728\u8fb9\u754c\u4e0a\u7684O\u5e76\u66ff\u6362\u6210#\u6807\u8bb0\u51fa\u6765，\u901a\u8fc7\u904d\u5386\u5c06\u8fd9\u4e9b\u533a\u57df\u6362\u56deO，\u800c\u5176\u4ed6\u7684\u5219\u5168\u90e8\u4e3aX：<\/p>\n
![\"\u5fae\u4fe1\u56fe\u7247\u7f16\u8f91_20241210200340.jpg\"](\"2025-08-10uvqvdpavvfa.jpg\")
<\/p>\n
\u6bcf\u4e2a\u4f4d\u7f6e\u4ec5\u88ab\u904d\u5386\u4e00\u6b21，\u6240\u4ee5\u65f6\u95f4\u590d\u6742\u5ea6\u662f O(nm)<\/p>\n
class Solution {
\npublic:
\n int n, m;
\n vector<vector<char>> board;
\n int dx[4] = {-1, 0, 1, 0}, dy[4] = {0, 1, 0, -1};
\n void solve(vector<vector<char>>& _board) {
\n board = _board;
\n n = board.size();
\n if(!n) return;
\n m = board[0].size();<\/p>\n
for(int i = 0; i < n; i++) \/\/\u7b2c\u4e00\u5217\u548c\u6700\u540e\u4e00\u5217\u6709\u4e3aO\u7684\u8bdd，\u5c06\u4e0e\u8be5O\u76f8\u8fde\u7684\u6240\u6709O\u627e\u51fa\u6765，\u6807\u8bb0
\n {
\n if(board[i][0] == 'O') dfs(i, 0);
\n if(board[i][m – 1] == 'O') dfs(i, m – 1);
\n }<\/p>\n
for(int i = 0; i < m; i++) \/\/\u7b2c\u4e00\u884c\u548c\u6700\u540e\u4e00\u884c\u6709\u4e3aO\u7684\u8bdd，\u5c06\u4e0e\u8be5O\u76f8\u8fde\u7684\u6240\u6709O\u627e\u51fa\u6765，\u6807\u8bb0
\n {
\n if(board[0][i] == 'O') dfs(0, i);
\n if(board[n – 1][i] == 'O') dfs(n – 1, i);
\n }<\/p>\n
for(int i = 0;i < n; i++)
\n {
\n for(int j = 0; j < m; j++)
\n {
\n if(board[i][j] == '#') board[i][j] = 'O'; \/\/\u5c06\u6240\u6709\u4e0e\u8fb9\u7f18\u76f8\u8fde\u7684\u683c\u5b50\u4e5f\u5c31\u662f\u6807\u8bb0\u4e3a#\u7684\u683c\u5b50\u66ff\u6362\u6210O
\n else board[i][j] = 'X'; \/\/\u5426\u5219\u66ff\u6362\u6210X
\n }
\n }
\n _board = board;
\n }<\/p>\n
void dfs(int x, int y)
\n {
\n board[x][y] = '#'; \/\/\u5c06\u5f53\u524d\u683c\u5b50\u66ff\u6362\u6210#
\n for(int i = 0; i < 4; i++)
\n {
\n int a = x + dx[i], b = y + dy[i];
\n if(a >= 0 && a < n && b >= 0 && b < m && board[a][b] == 'O') \/\/\u627e\u5230\u6240\u6709\u8fde\u5728\u4e00\u8d77\u7684O
\n {
\n dfs(a, b); \/\/\u7ee7\u7eed\u627e\u4e0b\u4e00\u4e2a\u683c\u5b50
\n }
\n }
\n }
\n};<\/p>\n
class Solution {
\npublic:
\n vector<vector<char>> board;
\n int n, m;
\n int dx[4] = {-1, 0, 1, 0}, dy[4] = {0, 1, 0, -1};
\n void solve(vector<vector<char>>& _board) {
\n board = _board;
\n n = board.size();
\n if(!n) return;
\n m = board[0].size();<\/p>\n
for(int i = 0; i < n; i++)
\n {
\n if(board[i][0] == 'O') dfs(i, 0);
\n if(board[i][m – 1] == 'O') dfs(i, m – 1);
\n }<\/p>\n
for(int i = 0; i < m; i++)
\n {
\n if(board[0][i] == 'O') dfs(0, i);
\n if(board[n – 1][i] == 'O') dfs(n – 1, i);
\n }<\/p>\n
for(int i = 0; i < n; i++)
\n {
\n for(int j = 0; j < m; j++)
\n {
\n if(board[i][j] == '#') board[i][j] = 'O';
\n else board[i][j] = 'X';
\n }
\n }
\n _board = board;
\n }<\/p>\n
void dfs(int x, int y)
\n {
\n board[x][y] = '#';
\n for(int i = 0; i < 4; i++)
\n {
\n int a = x + dx[i], b = y + dy[i];
\n if(a >= 0 && a < n && b >= 0 && b < m && board[a][b] == 'O')
\n {
\n dfs(a, b);
\n }
\n }
\n }
\n};<\/p>\n
class Solution {
\npublic:
\n vector<vector<char>> board;
\n int n, m;
\n int dx[4] = {-1, 0, 1, 0}, dy[4] = {0, -1, 0, 1};
\n void solve(vector<vector<char>>& _board) {
\n board = _board;
\n n = board.size(), m = board[0].size();<\/p>\n
for(int i = 0; i < n; i++) \/\/\u7b2c\u4e00\u5217\u548c\u6700\u540e\u4e00\u5217\u7684\u8fb9\u7f18\u8fde\u901a\u5757
\n {
\n if(board[i][0] == 'O') dfs(i, 0);
\n if(board[i][m – 1] == 'O') dfs(i, m – 1);
\n }<\/p>\n
for(int i = 0; i < m; i++) \/\/\u7b2c\u4e00\u884c\u548c\u6700\u540e\u4e00\u884c\u7684\u8fb9\u7f18\u8fde\u901a\u5757
\n {
\n if(board[0][i] == 'O') dfs(0, i);
\n if(board[n – 1][i] == 'O') dfs(n – 1, i);
\n }<\/p>\n
for(int i = 0; i < n; i++)
\n {
\n for(int j = 0; j < m; j++)
\n {
\n if(board[i][j] == '#') board[i][j] = 'O'; \/\/\u5c06\u8fb9\u7f18\u7684\u8fde\u901a\u5757\u4fdd\u7559\u4e0b\u6765
\n else board[i][j] = 'X'; \/\/\u5176\u4ed6\u8fde\u901a\u5757\u586b\u6210X
\n }
\n }
\n _board = board;<\/p>\n
}<\/p>\n
void dfs(int x, int y) \/\/\u627e\u5230\u4ee5x,y\u4e3a\u8d77\u70b9\u7684\u8fde\u901a\u5757
\n {
\n board[x][y] = '#';
\n for(int i = 0; i < 4; i++)
\n {
\n int a = x + dx[i], b = y + dy[i];
\n if(a >= 0 && a < n && b >= 0 && b < m && board[a][b] == 'O')
\n {
\n dfs(a, b);
\n }
\n }
\n }
\n};<\/p>\n
*\u6ce8：\u4e0a\u8ff0\u9898\u89e3\u5747\u6765\u81eaacwing\u8bfe\u7a0b\u8bb2\u89e3\u622a\u56fe，\u4ec5\u4f5c\u4e3a\u5b66\u4e60\u4ea4\u6d41，\u4e0d\u4f5c\u4e3a\u5546\u4e1a\u7528\u9014，\u5982\u6709\u4fb5\u6743，\u8054\u7cfb\u5220\u9664\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"
\u6587\u7ae0\u6d4f\u89c8\u9605\u8bfb604\u6b21\uff0c\u70b9\u8d5e14\u6b21\uff0c\u6536\u85cf7\u6b21\u3002\u7ed9\u5b9a\u4e00\u4e2a\u4e8c\u53c9\u6811\uff0c\u627e\u51fa\u5176\u6700\u5c0f\u6df1\u5ea6\u3002\u6700\u5c0f\u6df1\u5ea6\u662f\u4ece\u6839\u8282\u70b9\u5230\u6700\u8fd1\u53f6\u5b50\u8282\u70b9\u7684\u6700\u77ed\u8def\u5f84\u4e0a\u7684\u8282\u70b9\u6570\u91cf\u3002\u8bf4\u660e\uff1a\u53f6\u5b50\u8282\u70b9\u662f\u6307\u6ca1\u6709\u5b50\u8282\u70b9\u7684\u8282\u70b9\u3002\u793a\u4f8b 1\uff1a\u8f93\u5165\uff1aroot = [3,9,20,null,null,15,7]\u8f93\u51fa\uff1a2\u793a\u4f8b 2\uff1a\u8f93\u5165\uff1aroot = [2,null,3,null,4,null,5,null,6]\u8f93\u51fa\uff1a5\u63d0\u793a\uff1a\u6811\u4e2d\u8282\u70b9\u6570\u7684\u8303\u56f4\u5728 [0, 10^5] \u5185\u3002<\/p>\n","protected":false},"author":2,"featured_media":51290,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[2692,5072,5073,3226,1813,1983,427,2891],"topic":[],"class_list":{"0":"post-51310","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","6":"hentry","7":"category-server","8":"tag-leetcode","10":"tag-5073","11":"tag-3226","12":"tag-1813","13":"tag-1983","14":"tag-427","15":"tag-2891"},"yoast_head":"\n