From 7e7631810ff285b9e259951272288b8e88191864 Mon Sep 17 00:00:00 2001 From: youngyangyang04 <826123027@qq.com> Date: Fri, 16 Oct 2020 08:35:19 +0800 Subject: [PATCH] Update --- README.md | 6 +- ...¸ªèŠ‚ç‚¹çš„ä¸‹ä¸€ä¸ªå³ä¾§èŠ‚ç‚¹æŒ‡é’ˆ.png | Bin 62171 -> 112426 bytes pics/669.ä¿®å‰ªäºŒå‰æœç´¢æ ‘.png | Bin 0 -> 116564 bytes pics/669.ä¿®å‰ªäºŒå‰æœç´¢æ ‘1.png | Bin 0 -> 81402 bytes ...个节点的下一个å³ä¾§èŠ‚ç‚¹æŒ‡é’ˆ.md | 67 ++++- ...ªèŠ‚ç‚¹çš„ä¸‹ä¸€ä¸ªå³ä¾§èŠ‚ç‚¹æŒ‡é’ˆII.md | 2 + .../0236.äºŒå‰æ ‘的最近公共祖先.md | 1 - problems/0501.äºŒå‰æœç´¢æ ‘中的众数.md | 265 ++++++++++++++---- .../0530.äºŒå‰æœç´¢æ ‘的最å°ç»å¯¹å·®.md | 56 +++- problems/0669.ä¿®å‰ªäºŒå‰æœç´¢æ ‘.md | 217 ++++++++++++++ 10 files changed, 540 insertions(+), 74 deletions(-) create mode 100644 pics/669.ä¿®å‰ªäºŒå‰æœç´¢æ ‘.png create mode 100644 pics/669.ä¿®å‰ªäºŒå‰æœç´¢æ ‘1.png create mode 100644 problems/0669.ä¿®å‰ªäºŒå‰æœç´¢æ ‘.md diff --git a/README.md b/README.md index 0eae3978..55434203 100644 --- a/README.md +++ b/README.md @@ -113,6 +113,7 @@ * [本周å°ç»“ï¼ï¼ˆäºŒå‰æ ‘系列三)](https://mp.weixin.qq.com/s/JLLpx3a_8jurXcz6ovgxtg) * [äºŒå‰æ ‘:åˆå¹¶ä¸¤ä¸ªäºŒå‰æ ‘](https://mp.weixin.qq.com/s/3f5fbjOFaOX_4MXzZ97LsQ) * [äºŒå‰æ ‘ï¼šäºŒå‰æœç´¢æ ‘登场ï¼](https://mp.weixin.qq.com/s/vsKrWRlETxCVsiRr8v_hHg) + * [äºŒå‰æ ‘:æœç´¢æ ‘的最å°ç»å¯¹å·®](https://mp.weixin.qq.com/s/Hwzml6698uP3qQCC1ctUQQ) @@ -268,8 +269,8 @@ |[0110.å¹³è¡¡äºŒå‰æ ‘](https://github.com/youngyangyang04/leetcode/blob/master/problems/0110.å¹³è¡¡äºŒå‰æ ‘.md) |æ ‘ |简å•|**递归**| |[0111.äºŒå‰æ ‘çš„æœ€å°æ·±åº¦](https://github.com/youngyangyang04/leetcode/blob/master/problems/0111.äºŒå‰æ ‘çš„æœ€å°æ·±åº¦.md) |æ ‘ |简å•|**递归** **队列/BFS**| |[0112.路径总和](https://github.com/youngyangyang04/leetcode/blob/master/problems/0112.路径总和.md) |æ ‘ |简å•|**深度优先æœç´¢/递归** **回溯** **æ ˆ**| -|[0116.å¡«å……æ¯ä¸ªèŠ‚ç‚¹çš„ä¸‹ä¸€ä¸ªå³ä¾§èŠ‚ç‚¹æŒ‡é’ˆ](https://github.com/youngyangyang04/leetcode/blob/master/problems/0116.å¡«å……æ¯ä¸ªèŠ‚ç‚¹çš„ä¸‹ä¸€ä¸ªå³ä¾§èŠ‚ç‚¹æŒ‡é’ˆ.md) |äºŒå‰æ ‘ |中等|**广度优先æœç´¢**| -|[0117.å¡«å……æ¯ä¸ªèŠ‚ç‚¹çš„ä¸‹ä¸€ä¸ªå³ä¾§èŠ‚ç‚¹æŒ‡é’ˆII](https://github.com/youngyangyang04/leetcode/blob/master/problems/0117.å¡«å……æ¯ä¸ªèŠ‚ç‚¹çš„ä¸‹ä¸€ä¸ªå³ä¾§èŠ‚ç‚¹æŒ‡é’ˆII.md) |äºŒå‰æ ‘ |中等|**广度优先æœç´¢**| +|[0116.å¡«å……æ¯ä¸ªèŠ‚ç‚¹çš„ä¸‹ä¸€ä¸ªå³ä¾§èŠ‚ç‚¹æŒ‡é’ˆ](https://github.com/youngyangyang04/leetcode/blob/master/problems/0116.å¡«å……æ¯ä¸ªèŠ‚ç‚¹çš„ä¸‹ä¸€ä¸ªå³ä¾§èŠ‚ç‚¹æŒ‡é’ˆ.md) |äºŒå‰æ ‘ |中等|**递归** **迭代/广度优先æœç´¢**| +|[0117.å¡«å……æ¯ä¸ªèŠ‚ç‚¹çš„ä¸‹ä¸€ä¸ªå³ä¾§èŠ‚ç‚¹æŒ‡é’ˆII](https://github.com/youngyangyang04/leetcode/blob/master/problems/0117.å¡«å……æ¯ä¸ªèŠ‚ç‚¹çš„ä¸‹ä¸€ä¸ªå³ä¾§èŠ‚ç‚¹æŒ‡é’ˆII.md) |äºŒå‰æ ‘ |中等|**递归** **迭代/广度优先æœç´¢**| |[0131.分割回文串](https://github.com/youngyangyang04/leetcode/blob/master/problems/0131.分割回文串.md) |回溯 |中等|**回溯**| |[0141.环形链表](https://github.com/youngyangyang04/leetcode/blob/master/problems/0141.环形链表.md) |链表 |简å•|**快慢指针/åŒæŒ‡é’ˆ**| |[0142.环形链表II](https://github.com/youngyangyang04/leetcode/blob/master/problems/0142.环形链表II.md) |链表 |中等|**快慢指针/åŒæŒ‡é’ˆ**| @@ -325,6 +326,7 @@ |[0637.äºŒå‰æ ‘的层平å‡å€¼](https://github.com/youngyangyang04/leetcode/blob/master/problems/0637.äºŒå‰æ ‘的层平å‡å€¼.md) |æ ‘ |简å•|**广度优先æœç´¢/队列**| |[0654.æœ€å¤§äºŒå‰æ ‘](https://github.com/youngyangyang04/leetcode/blob/master/problems/0654.æœ€å¤§äºŒå‰æ ‘.md) |æ ‘ |中等|**递归**| |[0685.冗余连接II](https://github.com/youngyangyang04/leetcode/blob/master/problems/0685.冗余连接II.md) | 并查集/æ ‘/图 |å›°éš¾|**并查集**| +|[0669.ä¿®å‰ªäºŒå‰æœç´¢æ ‘](https://github.com/youngyangyang04/leetcode/blob/master/problems/0669.ä¿®å‰ªäºŒå‰æœç´¢æ ‘.md) | äºŒå‰æœç´¢æ ‘/äºŒå‰æ ‘ |简å•|**递归** **迭代**| |[0700.äºŒå‰æœç´¢æ ‘中的æœç´¢](https://github.com/youngyangyang04/leetcode/blob/master/problems/0700.äºŒå‰æœç´¢æ ‘中的æœç´¢.md) |æ ‘ |简å•|**递归** **迭代**| |[0701.äºŒå‰æœç´¢æ ‘中的æ’å…¥æ“作](https://github.com/youngyangyang04/leetcode/blob/master/problems/0701.äºŒå‰æœç´¢æ ‘中的æ’å…¥æ“作.md) |æ ‘ |简å•|**递归** **迭代**| |[0705.设计哈希集åˆ](https://github.com/youngyangyang04/leetcode/blob/master/problems/0705.设计哈希集åˆ.md) |哈希表 |简å•|**模拟**| diff --git a/pics/116.å¡«å……æ¯ä¸ªèŠ‚ç‚¹çš„ä¸‹ä¸€ä¸ªå³ä¾§èŠ‚ç‚¹æŒ‡é’ˆ.png b/pics/116.å¡«å……æ¯ä¸ªèŠ‚ç‚¹çš„ä¸‹ä¸€ä¸ªå³ä¾§èŠ‚ç‚¹æŒ‡é’ˆ.png index 0078731ba77ec42e5faccddba3143e4683926106..bec25c0af991feea02d507b2ce33d3a2731d8baf 100644 GIT binary patch literal 112426 zcmeFZ_dk{YA3u&Lhsvg+NW?K;DP)iAoqghwPC(vo{UGv9dR1WRt!5 zJ}=R$*ZcPQ+`ivG;QK?jigT{(c|D(xaev$&_s12Wq9lER;0gg27S;t>83|P^EIbx0 zEF3@lv*0Ja64Qm?FKkCuX>qLFHkw)R9|@$kteK)B7WfnvJ{I;13oKmdBjC>!@COU) zOaeC68SpnY^s@w<)8FE;B%C?@H;y0lK_Q>~4_H{DSh5mg>aN%evFEDPd&*14zVNBf zN@n^wg>uyU`JF}6ZyF@=Hl<1B$u4mRG^J&XlCOF}IP*ZoSK;?F$u{!p*_k)3sw8HIjQ<%ObW0nfKp6r=X&; 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+``` +if (cur->left) cur->left->next = cur->right; // æ“作1 +if (cur->right) { + if (cur->next) cur->right->next = cur->next->left; // æ“作2 + else cur->right->next = NULL; +} +``` + +ç†è§£åˆ°è¿™é‡Œï¼Œä½¿ç”¨å‰åºé历,那么ä¸éš¾å†™å‡ºå¦‚下代ç ï¼š + +å¦‚æžœå¯¹äºŒå‰æ ‘çš„å‰ä¸­åŽåºä¸äº†è§£çœ‹è¿™ç¯‡:[äºŒå‰æ ‘:一入递归深似海,从此offer是路人](https://mp.weixin.qq.com/s/PwVIfxDlT3kRgMASWAMGhA) + + +``` +class Solution { +private: + void traversal(Node* cur) { + if (cur == NULL) return; + // 中 + if (cur->left) cur->left->next = cur->right; // æ“作1 + if (cur->right) { + if (cur->next) cur->right->next = cur->next->left; // æ“作2 + else cur->right->next = NULL; + } + traversal(cur->left); // å·¦ + traversal(cur->right); // å³ + } +public: + Node* connect(Node* root) { + traversal(root); + return root; + } +}; +``` + +### 迭代(层åºé历) + +本题使用层åºé历是最为直观的,如果对层åºé历ä¸äº†è§£ï¼Œçœ‹è¿™ç¯‡ï¼š[äºŒå‰æ ‘:层åºé历登场ï¼](https://mp.weixin.qq.com/s/Gb3BjakIKGNpup2jYtTzog)。 + +层åºé历本æ¥å°±æ˜¯ä¸€å±‚一层的去é历,记录一层的头结点(nodePre),然åŽè®©nodePre指å‘当å‰é历的节点就å¯ä»¥äº†ã€‚ + +代ç å¦‚下: ``` @@ -20,9 +79,9 @@ public: vector vec; Node* nodePre; Node* node; - for (int i = 0; i < size; i++) { + for (int i = 0; i < size; i++) { // 开始æ¯ä¸€å±‚çš„é历 if (i == 0) { - nodePre = que.front(); // å–出一层的头结点 + nodePre = que.front(); // 记录一层的头结点 que.pop(); node = nodePre; } else { diff --git a/problems/0117.å¡«å……æ¯ä¸ªèŠ‚ç‚¹çš„ä¸‹ä¸€ä¸ªå³ä¾§èŠ‚ç‚¹æŒ‡é’ˆII.md b/problems/0117.å¡«å……æ¯ä¸ªèŠ‚ç‚¹çš„ä¸‹ä¸€ä¸ªå³ä¾§èŠ‚ç‚¹æŒ‡é’ˆII.md index 41d52566..43b56b91 100644 --- a/problems/0117.å¡«å……æ¯ä¸ªèŠ‚ç‚¹çš„ä¸‹ä¸€ä¸ªå³ä¾§èŠ‚ç‚¹æŒ‡é’ˆII.md +++ b/problems/0117.å¡«å……æ¯ä¸ªèŠ‚ç‚¹çš„ä¸‹ä¸€ä¸ªå³ä¾§èŠ‚ç‚¹æŒ‡é’ˆII.md @@ -4,6 +4,8 @@ https://leetcode-cn.com/problems/populating-next-right-pointers-in-each-node-ii/ ## æ€è·¯ +è¿™é“é¢˜ç›®ä½¿ç”¨é€’å½’è¿˜æ˜¯æœ‰éš¾åº¦çš„ï¼Œä¸æ˜¯å®Œç¾ŽäºŒå‰æ ‘,应该怎么办。 + ## C++ä»£ç  ``` diff --git a/problems/0236.äºŒå‰æ ‘的最近公共祖先.md b/problems/0236.äºŒå‰æ ‘的最近公共祖先.md index e222a34a..bcfb336f 100644 --- a/problems/0236.äºŒå‰æ ‘的最近公共祖先.md +++ b/problems/0236.äºŒå‰æ ‘的最近公共祖先.md @@ -21,7 +21,6 @@ public: TreeNode* left = lowestCommonAncestor(root->left, p, q); TreeNode* right = lowestCommonAncestor(root->right, p, q); if (left != NULL && right != NULL) return root; - if (left == NULL) return right; return left; } diff --git a/problems/0501.äºŒå‰æœç´¢æ ‘中的众数.md b/problems/0501.äºŒå‰æœç´¢æ ‘中的众数.md index 2781d5c2..5e727433 100644 --- a/problems/0501.äºŒå‰æœç´¢æ ‘中的众数.md +++ b/problems/0501.äºŒå‰æœç´¢æ ‘中的众数.md @@ -2,20 +2,96 @@ https://leetcode-cn.com/problems/find-mode-in-binary-search-tree/solution/ +> äºŒå‰æ ‘ä¸Šåº”è¯¥æ€Žä¹ˆæ±‚ï¼ŒäºŒå‰æœç´¢æ ‘上有应该怎么求 + +# 501.äºŒå‰æœç´¢æ ‘中的众数 + +给定一个有相åŒå€¼çš„äºŒå‰æœç´¢æ ‘(BST),找出 BST 中的所有众数(出现频率最高的元素)。 + +å‡å®š BST 有如下定义: + +* ç»“ç‚¹å·¦å­æ ‘中所å«ç»“点的值å°äºŽç­‰äºŽå½“å‰ç»“点的值 +* 结点å³å­æ ‘中所å«ç»“点的值大于等于当å‰ç»“点的值 +* 左孿 ‘å’Œå³å­æ ‘éƒ½æ˜¯äºŒå‰æœç´¢æ ‘ + +例如: + +给定 BST [1,null,2,2], + +![501. äºŒå‰æœç´¢æ ‘中的众数](https://img-blog.csdnimg.cn/20201014221532206.png) + +返回[2]. + +æç¤ºï¼šå¦‚果众数超过1个,ä¸éœ€è€ƒè™‘è¾“å‡ºé¡ºåº + +进阶:你å¯ä»¥ä¸ä½¿ç”¨é¢å¤–的空间å—?(å‡è®¾ç”±é€’归产生的éšå¼è°ƒç”¨æ ˆçš„开销ä¸è¢«è®¡ç®—在内) + # æ€è·¯ +è¿™é“题目呢,递归法我从两个维度æ¥è®²ã€‚ -## 暴力统计 +é¦–å…ˆå¦‚æžœä¸æ˜¯äºŒå‰æœç´¢æ ‘çš„è¯ï¼Œåº”è¯¥æ€Žä¹ˆè§£é¢˜ï¼Œæ˜¯äºŒå‰æœç´¢æ ‘,åˆåº”è¯¥å¦‚ä½•è§£é¢˜ï¼Œä¸¤ç§æ–¹å¼åšä¸€ä¸ªæ¯”较,å¯ä»¥åŠ æ·±å¤§å®¶å¯¹äºŒå‰æ ‘çš„ç†è§£ã€‚ -这看到这é“题目,最直观的方法一定是把这个树都é历了,用map统计频率,用vector排个åºï¼Œæœ€åŽå‡ºåŽ»å‰é¢é«˜é¢‘的元素。 +## 递归法 -其实这是å¯ä»¥çš„,也是有效的,é¢è¯•中时间紧张,å¯èƒ½å¿«é€Ÿçš„æŠŠè¿™ä¸ªæ–¹æ³•实现出æ¥ï¼ŒåŽé¢åœ¨è€ƒè™‘满满优化。 +### å¦‚æžœä¸æ˜¯äºŒå‰æœç´¢æ ‘ + +å¦‚æžœä¸æ˜¯äºŒå‰æœç´¢æ ‘,最直观的方法一定是把这个树都é历了,用map统计频率,把频率排个åºï¼Œæœ€åŽå–å‰é¢é«˜é¢‘的元素的集åˆã€‚ + +具体步骤如下: + +1. 这个树都é历了,用map统计频率 + +至于用å‰ä¸­åŽåºé‚£ç§é历也ä¸é‡è¦ï¼Œå› ä¸ºå°±æ˜¯è¦å…¨é历一é,怎么个é历法都行,层åºéåŽ†éƒ½æ²¡æ¯›ç—…ï¼ + +这里采用å‰åºé历,代ç å¦‚下: + +``` +// map key:元素,value:出现频率 +void searchBST(TreeNode* cur, unordered_map& map) { // å‰åºé历 + if (cur == NULL) return ; + map[cur->val]++; // 统计元素频率 + searchBST(cur->left, map); + searchBST(cur->right, map); + return ; +} +``` + +2. 把统计的出æ¥çš„出现频率(å³map中的valueï¼‰æŽ’ä¸ªåº + +有的åŒå­¦å¯èƒ½å¯ä»¥æƒ³ç›´æŽ¥å¯¹map中的value排åºï¼Œè¿˜çœŸåšä¸åˆ°ï¼ŒC++中如果使用std::map或者std::multimapå¯ä»¥å¯¹key排åºï¼Œä½†ä¸èƒ½å¯¹value排åºã€‚ + +æ‰€ä»¥è¦æŠŠmap转化数组å³vector,å†è¿›è¡ŒæŽ’åºï¼Œå½“ç„¶vectoré‡Œé¢æ”¾çš„也是`pair`类型的数æ®ï¼Œç¬¬ä¸€ä¸ªint为元素,第二个int为出现频率。 + +代ç å¦‚下: + +``` +bool static cmp (const pair& a, const pair& b) { + return a.second > b.second; // æŒ‰ç…§é¢‘çŽ‡ä»Žå¤§åˆ°å°æŽ’åº +} + +vector> vec(map.begin(), map.end()); +sort(vec.begin(), vec.end(), cmp); // ç»™é¢‘çŽ‡æŽ’ä¸ªåº +``` + +3. å–å‰é¢é«˜é¢‘的元素 + +此时数组vectorä¸­å·²ç»æ˜¯å­˜æ”¾ç€æŒ‰ç…§é¢‘率排好åºçš„pair,那么把å‰é¢é«˜é¢‘的元素å–出æ¥å°±å¯ä»¥äº†ã€‚ + +代ç å¦‚下: + +``` +result.push_back(vec[0].first); +for (int i = 1; i < vec.size(); i++) { + // å–æœ€é«˜çš„æ”¾åˆ°result数组中 + if (vec[i].second == vec[0].second) result.push_back(vec[i].first); + else break; +} +return result; +``` -至于用å‰ä¸­åŽåºé‚£ç§é历也ä¸é‡è¦ï¼Œå› ä¸ºå°±æ˜¯è¦å…¨é历一é,怎么个é历法都行,层åºéåŽ†éƒ½æ²¡æ¯›ç—…ï¼ - -è¿™ç§æ–¹æ³•C++代ç å¦‚下: - +整体C++代ç å¦‚下: ``` class Solution { @@ -33,14 +109,15 @@ bool static cmp (const pair& a, const pair& b) { } public: vector findMode(TreeNode* root) { - unordered_map map; + unordered_map map; // key:元素,value:出现频率 vector result; if (root == NULL) return result; searchBST(root, map); vector> vec(map.begin(), map.end()); sort(vec.begin(), vec.end(), cmp); // ç»™é¢‘çŽ‡æŽ’ä¸ªåº result.push_back(vec[0].first); - for (int i = 1; i < vec.size(); i++) { + for (int i = 1; i < vec.size(); i++) { + // å–æœ€é«˜çš„æ”¾åˆ°result数组中 if (vec[i].second == vec[0].second) result.push_back(vec[i].first); else break; } @@ -49,15 +126,11 @@ public: }; ``` -**è¿™ç§æ–¹æ³•çš„ç¼ºç‚¹æ˜¯æ²¡æœ‰åˆ©ç”¨ä¸ŠäºŒå‰æœç´¢æ ‘这一特性**ï¼Œå¦‚æžœç”¨è¿™ç§æ–¹æ³•,这é“题就å¯ä»¥æ˜¯æ™®é€šçš„äºŒå‰æ ‘å°±è¡Œäº†ï¼Œåæ­£éƒ½è¦å…¨æ’¸ä¸€é统计频率。 +**æ‰€ä»¥å¦‚æžœæœ¬é¢˜æ²¡æœ‰è¯´æ˜¯äºŒå‰æœç´¢æ ‘çš„è¯ï¼Œé‚£ä¹ˆå°±æŒ‰ç…§ä¸Šé¢çš„æ€è·¯å†™ï¼** -## 中åºé历 +### æ˜¯äºŒå‰æœç´¢æ ‘ -既然是æœç´¢æ ‘,它就是有åºçš„,那么如何有åºå‘¢ï¼Ÿ - -**æœç´¢æ ‘在中åºé历的过程中,就是有åºåºåˆ—,所以此时的问题相当于 ç»™å‡ºå¦‚æžœç»™å‡ºä¸€ä¸ªæœ‰åºæ•°ç»„,求最大频率的元素集åˆã€‚** - -**所以我们è¦é‡‡ç”¨ä¸­åºé历ï¼** +**既然是æœç´¢æ ‘,它中åºé历就是有åºçš„**。 如图: @@ -66,69 +139,82 @@ public: 中åºé历代ç å¦‚下: ``` - void searchBST(TreeNode* cur) { - if (cur == NULL) return ; - searchBST(cur->left); // å·¦ - (处ç†èŠ‚ç‚¹ï¼‰ // 中 - searchBST(cur->right); // å³ - return ; - } +void searchBST(TreeNode* cur) { + if (cur == NULL) return ; + searchBST(cur->left); // å·¦ + (处ç†èŠ‚ç‚¹ï¼‰ // 中 + searchBST(cur->right); // å³ + return ; +} ``` -éåŽ†æœ‰åºæ•°ç»„的元素出现频率,从头éåŽ†ï¼Œé‚£ä¹ˆä¸€å®šæ˜¯ç›¸é‚»ä¸¤ä¸ªå…ƒç´ ä½œæ¯”è¾ƒï¼Œè¦æ˜¯æ•°ç»„çš„è¯ï¼Œå¥½æžï¼Œåœ¨æ ‘上怎么æžå‘¢ï¼Ÿ +éåŽ†æœ‰åºæ•°ç»„的元素出现频率,从头é历,那么一定是相邻两个元素作比较,然åŽå°±æŠŠå‡ºçŽ°é¢‘çŽ‡æœ€é«˜çš„å…ƒç´ è¾“å‡ºå°±å¯ä»¥äº†ã€‚ -需è¦å¼„一个指针指å‘å‰ä¸€ä¸ªèŠ‚ç‚¹ï¼Œè¿™æ ·æ¯æ¬¡cur(当å‰èŠ‚ç‚¹ï¼‰æ‰èƒ½å’Œpre(å‰ä¸€ä¸ªèŠ‚ç‚¹ï¼‰ä½œæ¯”è¾ƒã€‚ +å…³é”®æ˜¯åœ¨æœ‰åºæ•°ç»„上的è¯ï¼Œå¥½æžï¼Œåœ¨æ ‘上怎么æžå‘¢ï¼Ÿ -而且åˆå§‹åŒ–的时候pre = NULL,这样当pre为NULL时候,我们就知é“这是比较的第一个元素,然åŽå†ç»™pre赋值å³pre = cur; +这就考察对树的æ“作了。 + +在[äºŒå‰æ ‘:æœç´¢æ ‘的最å°ç»å¯¹å·®](https://mp.weixin.qq.com/s/Hwzml6698uP3qQCC1ctUQQ)中我们就使用了pre指针和cur指针的技巧,这次åˆç”¨ä¸Šäº†ã€‚ + +弄一个指针指å‘å‰ä¸€ä¸ªèŠ‚ç‚¹ï¼Œè¿™æ ·æ¯æ¬¡cur(当å‰èŠ‚ç‚¹ï¼‰æ‰èƒ½å’Œpre(å‰ä¸€ä¸ªèŠ‚ç‚¹ï¼‰ä½œæ¯”è¾ƒã€‚ + +而且åˆå§‹åŒ–的时候pre = NULL,这样当pre为NULL时候,我们就知é“这是比较的第一个元素。 代ç å¦‚下: ``` - if (pre == NULL) { // 第一个节点 - count = 1; - } else if (pre->val == cur->val) { // 与å‰ä¸€ä¸ªèŠ‚ç‚¹æ•°å€¼ç›¸åŒ - count++; - } else { // 与å‰ä¸€ä¸ªèŠ‚ç‚¹æ•°å€¼ä¸åŒ - count = 1; - } - pre = cur; // 更新上一个节点 +if (pre == NULL) { // 第一个节点 + count = 1; // 频率为1 +} else if (pre->val == cur->val) { // 与å‰ä¸€ä¸ªèŠ‚ç‚¹æ•°å€¼ç›¸åŒ + count++; +} else { // 与å‰ä¸€ä¸ªèŠ‚ç‚¹æ•°å€¼ä¸åŒ + count = 1; +} +pre = cur; // 更新上一个节点 ``` -æ­¤æ—¶åˆæœ‰é—®é¢˜äº†ï¼Œå› ä¸ºè¦æ±‚最大频率的元素集åˆï¼Œç›´è§‚想的想法是è¦å…ˆéåŽ†ä¸€éæ‰¾å‡ºé¢‘率最大的次数maxCount,然åŽåœ¨é‡æ–°é历一éå†æŠŠå‡ºçŽ°é¢‘çŽ‡ä¸ºmaxCount的元素放进集åˆã€‚ +æ­¤æ—¶åˆæœ‰é—®é¢˜äº†ï¼Œå› ä¸ºè¦æ±‚最大频率的元素集åˆï¼ˆæ³¨æ„是集åˆï¼Œä¸æ˜¯ä¸€ä¸ªå…ƒç´ ï¼Œå¯ä»¥æœ‰å¤šä¸ªä¼—数),如果是数组上大家一般怎么办? +应该是先éåŽ†ä¸€éæ•°ç»„,找出最大频率(maxCount),然åŽå†é‡æ–°éåŽ†ä¸€éæ•°ç»„把出现频率为maxCount的元素放进集åˆã€‚(因为众数有多个) + +è¿™ç§æ–¹å¼éåŽ†äº†ä¸¤éæ•°ç»„。 + +那么我们é历两éäºŒå‰æœç´¢æ ‘,把众数集åˆç®—出æ¥ä¹Ÿæ˜¯å¯ä»¥çš„。 + +但这里其实åªéœ€è¦é历一次就å¯ä»¥æ‰¾åˆ°æ‰€æœ‰çš„众数。 那么如何åªé历一é呢? -如果 频率count 等于 maxCountï¼Œå½“ç„¶è¦æŠŠè¿™ä¸ªå…ƒç´ åŠ å…¥åˆ°ç»“æžœé›†ä¸­ï¼ˆä»¥ä¸‹ä»£ç ä¸ºresult数组),代ç å¦‚下: +如果 频率count 等于 maxCountï¼ˆæœ€å¤§é¢‘çŽ‡ï¼‰ï¼Œå½“ç„¶è¦æŠŠè¿™ä¸ªå…ƒç´ åŠ å…¥åˆ°ç»“æžœé›†ä¸­ï¼ˆä»¥ä¸‹ä»£ç ä¸ºresult数组),代ç å¦‚下: ``` - if (count == maxCount) { // 如果和最大值相åŒï¼Œæ”¾è¿›result中 - result.push_back(cur->val); - } +if (count == maxCount) { // 如果和最大值相åŒï¼Œæ”¾è¿›result中 + result.push_back(cur->val); +} ``` -当时感觉这里有问题,result怎么能轻易就把元素放进去了呢,万一,这个maxCountæ­¤æ—¶è¿˜ä¸æ˜¯çœŸæ­£æœ€å¤§å€¼å‘¢ã€‚ +æ˜¯ä¸æ˜¯æ„Ÿè§‰è¿™é‡Œæœ‰é—®é¢˜ï¼Œresult怎么能轻易就把元素放进去了呢,万一,这个maxCountæ­¤æ—¶è¿˜ä¸æ˜¯çœŸæ­£æœ€å¤§é¢‘率呢。 所以下é¢è¦åšå¦‚下æ“作: 频率count 大于 maxCount的时候,ä¸ä»…è¦æ›´æ–°maxCountï¼Œè€Œä¸”è¦æ¸…空结果集(以下代ç ä¸ºresult数组),因为结果集之å‰çš„元素都失效了。 ``` - if (count > maxCount) { // 如果计数大于最大值 - maxCount = count; - result.clear(); // 很关键的一步,ä¸è¦å¿˜è®°æ¸…空result,之å‰result里的元素都失效了 - result.push_back(cur->val); - } +if (count > maxCount) { // 如果计数大于最大值 + maxCount = count; // 更新最大频率 + result.clear(); // 很关键的一步,ä¸è¦å¿˜è®°æ¸…空result,之å‰result里的元素都失效了 + result.push_back(cur->val); +} ``` -关键代ç éƒ½è®²å®Œäº†ï¼Œå®Œæ•´ä»£ç å¦‚下: +关键代ç éƒ½è®²å®Œäº†ï¼Œå®Œæ•´ä»£ç å¦‚下:(**åªéœ€è¦é历一éäºŒå‰æœç´¢æ ‘,就求出了众数的集åˆ**) ``` class Solution { private: - int count; - int maxCount; + int maxCount; // 最大频率 + int count; // 统计频率 TreeNode* pre; vector result; void searchBST(TreeNode* cur) { @@ -149,8 +235,8 @@ private: result.push_back(cur->val); } - if (count > maxCount) { // 如果计数大于最大值 - maxCount = count; + if (count > maxCount) { // 如果计数大于最大值频率 + maxCount = count; // 更新最大频率 result.clear(); // 很关键的一步,ä¸è¦å¿˜è®°æ¸…空result,之å‰result里的元素都失效了 result.push_back(cur->val); } @@ -161,8 +247,8 @@ private: public: vector findMode(TreeNode* root) { - int count = 0; // 记录元素出现次数 - int maxCount = 0; + count = 0; + maxCount = 0; TreeNode* pre = NULL; // 记录å‰ä¸€ä¸ªèŠ‚ç‚¹ result.clear(); @@ -172,8 +258,79 @@ public: }; ``` -此时的è¿è¡Œæ•ˆçŽ‡ï¼š - +## 迭代法 + +åªè¦æŠŠä¸­åºé历转æˆè¿­ä»£ï¼Œä¸­é—´èŠ‚ç‚¹çš„å¤„ç†é€»è¾‘完全一样。 + +äºŒå‰æ ‘å‰ä¸­åŽåºè½¬è¿­ä»£ï¼Œä¼ é€é—¨ï¼š + +* [äºŒå‰æ ‘:å‰ä¸­åŽåºè¿­ä»£æ³•](https://mp.weixin.qq.com/s/c_zCrGHIVlBjUH_hJtghCg) +* [äºŒå‰æ ‘:å‰ä¸­åŽåºç»Ÿä¸€é£Žæ ¼çš„迭代方å¼](https://mp.weixin.qq.com/s/WKg0Ty1_3SZkztpHubZPRg) + +䏋颿ˆ‘给出其中的一ç§ä¸­åºé历的迭代法,其中间处ç†é€»è¾‘一点都没有å˜ï¼ˆæˆ‘从递归法直接粘过æ¥çš„代ç ï¼Œè¿žæ³¨é‡Šéƒ½æ²¡æ”¹ï¼Œå“ˆå“ˆï¼‰ + +代ç å¦‚下: + +``` +class Solution { +public: + vector findMode(TreeNode* root) { + stack st; + TreeNode* cur = root; + TreeNode* pre = NULL; + int maxCount = 0; // 最大频率 + int count = 0; // 统计频率 + vector result; + while (cur != NULL || !st.empty()) { + if (cur != NULL) { // 指针æ¥è®¿é—®èŠ‚ç‚¹ï¼Œè®¿é—®åˆ°æœ€åº•å±‚ + st.push(cur); // 将访问的节点放进栈 + cur = cur->left; // å·¦ + } else { + cur = st.top(); + st.pop(); // 中 + if (pre == NULL) { // 第一个节点 + count = 1; + } else if (pre->val == cur->val) { // 与å‰ä¸€ä¸ªèŠ‚ç‚¹æ•°å€¼ç›¸åŒ + count++; + } else { // 与å‰ä¸€ä¸ªèŠ‚ç‚¹æ•°å€¼ä¸åŒ + count = 1; + } + if (count == maxCount) { // 如果和最大值相åŒï¼Œæ”¾è¿›result中 + result.push_back(cur->val); + } + + if (count > maxCount) { // 如果计数大于最大值频率 + maxCount = count; // 更新最大频率 + result.clear(); // 很关键的一步,ä¸è¦å¿˜è®°æ¸…空result,之å‰result里的元素都失效了 + result.push_back(cur->val); + } + pre = cur; + cur = cur->right; // å³ + } + } + return result; + } +}; +``` + +# 总结 + +æœ¬é¢˜åœ¨é€’å½’æ³•ä¸­ï¼Œæˆ‘ç»™å‡ºäº†å¦‚æžœæ˜¯æ™®é€šäºŒå‰æ ‘,应该怎么求众数。 + +知é“äº†æ™®é€šäºŒå‰æ ‘çš„åšæ³•时候,我å†è¿›ä¸€æ­¥ç»™å‡ºäºŒå‰æœç´¢æ ‘åˆåº”è¯¥æ€Žä¹ˆæ±‚ä¼—æ•°ï¼Œè¿™æ ·é²œæ˜Žçš„å¯¹æ¯”ï¼Œç›¸ä¿¡ä¼šå¯¹äºŒå‰æ ‘åˆæœ‰æ›´æ·±å±‚次的ç†è§£äº†ã€‚ + +在递归éåŽ†äºŒå‰æœç´¢æ ‘的过程中,我还介ç»äº†ä¸€ä¸ªç»Ÿè®¡æœ€é«˜å‡ºçŽ°é¢‘çŽ‡å…ƒç´ é›†åˆçš„æŠ€å·§ï¼Œ è¦ä¸ç„¶å°±è¦éåŽ†ä¸¤æ¬¡äºŒå‰æœç´¢æ ‘æ‰èƒ½æŠŠè¿™ä¸ªæœ€é«˜å‡ºçŽ°é¢‘çŽ‡å…ƒç´ çš„é›†åˆæ±‚出æ¥ã€‚ + + +**为什么没有这个技巧一定è¦é历两次呢? å› ä¸ºè¦æ±‚的是集åˆï¼Œä¼šæœ‰å¤šä¸ªä¼—æ•°ï¼Œå¦‚æžœè§„å®šåªæœ‰ä¸€ä¸ªä¼—数,那么就é历一次稳稳的了。** + +æœ€åŽæˆ‘ä¾ç„¶ç»™å‡ºå¯¹åº”的迭代法,其实就是迭代法中åºé历的模æ¿åŠ ä¸Šé€’å½’æ³•ä¸­ä¸­é—´èŠ‚ç‚¹çš„å¤„ç†é€»è¾‘,分分钟就å¯ä»¥å†™å‡ºæ¥ï¼Œä¸­é—´é€»è¾‘çš„ä»£ç æˆ‘都是从递归法中直接粘过æ¥çš„。 + +**æ±‚äºŒå‰æœç´¢æ ‘中的众数其实是一é“简å•题,但大家å¯ä»¥å‘现我写了这么一大篇幅的文章æ¥è®²è§£ï¼Œä¸»è¦æ˜¯ä¸ºäº†å°½é‡ä»Žå„个角度对本题进剖æžï¼Œå¸®åŠ©å¤§å®¶æ›´å¿«æ›´æ·±å…¥ç†è§£äºŒå‰æ ‘**。 + +**就酱,如果学到了的è¯ï¼Œå°±è½¬å‘给身边需è¦çš„åŒå­¦å§ï¼Œå¯èƒ½ä»–们也需è¦ï¼** + + **需è¦å¼ºè°ƒçš„æ˜¯ leetcode上的耗时统计是éžå¸¸ä¸å‡†ç¡®çš„,看个大概就行,一样的代ç è€—æ—¶å¯ä»¥å·®ç™¾åˆ†ä¹‹50以上**,所以leetcode的耗时统计别太当回事,知é“ç†è®ºä¸Šçš„æ•ˆçŽ‡ä¼˜åŠ£å°±è¡Œäº†ã€‚ diff --git a/problems/0530.äºŒå‰æœç´¢æ ‘的最å°ç»å¯¹å·®.md b/problems/0530.äºŒå‰æœç´¢æ ‘的最å°ç»å¯¹å·®.md index 2cd19592..6a7f8e8e 100644 --- a/problems/0530.äºŒå‰æœç´¢æ ‘的最å°ç»å¯¹å·®.md +++ b/problems/0530.äºŒå‰æœç´¢æ ‘的最å°ç»å¯¹å·®.md @@ -3,21 +3,33 @@ https://leetcode-cn.com/problems/minimum-absolute-difference-in-bst/ -## æ€è·¯ +> åˆ©ç”¨äºŒå‰æœç´¢æ ‘的特性æžèµ·ï¼ + +# 530.äºŒå‰æœç´¢æ ‘的最å°ç»å¯¹å·® + +给你一棵所有节点为éžè´Ÿå€¼çš„äºŒå‰æœç´¢æ ‘,请你计算树中任æ„两节点的差的ç»å¯¹å€¼çš„æœ€å°å€¼ã€‚ + +示例: + +![530äºŒå‰æœç´¢æ ‘的最å°ç»å¯¹å·®](https://img-blog.csdnimg.cn/20201014223400123.png) + +æç¤ºï¼šæ ‘中至少有 2 个节点。 + +# æ€è·¯ é¢˜ç›®ä¸­è¦æ±‚åœ¨äºŒå‰æœç´¢æ ‘上任æ„两节点的差的ç»å¯¹å€¼çš„æœ€å°å€¼ã€‚ -**æ³¨æ„æ˜¯äºŒå‰æœç´¢æ ‘,**äºŒå‰æœç´¢æ ‘坿˜¯æœ‰åºçš„。 +**æ³¨æ„æ˜¯äºŒå‰æœç´¢æ ‘**ï¼ŒäºŒå‰æœç´¢æ ‘坿˜¯æœ‰åºçš„。 é‡åˆ°åœ¨äºŒå‰æœç´¢æ ‘上求什么最值啊,差值之类的,就把它想æˆåœ¨ä¸€ä¸ªæœ‰åºæ•°ç»„上求最值,求差值,这样就简å•多了。 -### 递归 +## 递归 -é‚£ä¹ˆäºŒå‰æœç´¢æ ‘如果采用中åºéåŽ†ï¼Œå…¶å®žå°±æ˜¯ä¸€ä¸ªæœ‰åºæ•°ç»„。 +é‚£ä¹ˆäºŒå‰æœç´¢æ ‘采用中åºéåŽ†ï¼Œå…¶å®žå°±æ˜¯ä¸€ä¸ªæœ‰åºæ•°ç»„。 **åœ¨ä¸€ä¸ªæœ‰åºæ•°ç»„上求两个数最å°å·®å€¼ï¼Œè¿™æ˜¯ä¸æ˜¯å°±æ˜¯ä¸€é“é€åˆ†é¢˜äº†ã€‚** -æœ€ç›´è§‚çš„æƒ³æ³•ï¼Œå°±æ˜¯æŠŠäºŒå‰æœç´¢æ ‘è½¬æ¢æˆæœ‰åºæ•°ç»„,然åŽéåŽ†ä¸€éæ•°ç»„ï¼Œå°±ç»Ÿè®¡å‡ºæ¥æœ€å°å·®å€¼äº† +æœ€ç›´è§‚çš„æƒ³æ³•ï¼Œå°±æ˜¯æŠŠäºŒå‰æœç´¢æ ‘è½¬æ¢æˆæœ‰åºæ•°ç»„,然åŽéåŽ†ä¸€éæ•°ç»„ï¼Œå°±ç»Ÿè®¡å‡ºæ¥æœ€å°å·®å€¼äº†ã€‚ 代ç å¦‚下: @@ -47,12 +59,14 @@ public: ä»¥ä¸Šä»£ç æ˜¯æŠŠäºŒå‰æœç´¢æ ‘è½¬åŒ–ä¸ºæœ‰åºæ•°ç»„äº†ï¼Œå…¶å®žåœ¨äºŒå‰æœç´ æ ‘中åºé历的过程中,我们就å¯ä»¥ç›´æŽ¥è®¡ç®—了。 -需è¦ç”¨ä¸€ä¸ªpre节点记录一下,当å‰èŠ‚ç‚¹çš„å‰ä¸€ä¸ªèŠ‚ç‚¹ã€‚ +需è¦ç”¨ä¸€ä¸ªpre节点记录一下cur节点的å‰ä¸€ä¸ªèŠ‚ç‚¹ã€‚ 如图: +一些åŒå­¦ä¸çŸ¥é“在递归中如何记录å‰ä¸€ä¸ªèŠ‚ç‚¹çš„æŒ‡é’ˆï¼Œå…¶å®žå®žçŽ°èµ·æ¥æ˜¯å¾ˆç®€å•的,大家åªè¦çœ‹è¿‡ä¸€æ¬¡ï¼Œå†™è¿‡ä¸€æ¬¡ï¼Œå°±æŽŒæ¡äº†ã€‚ + 代ç å¦‚下: ``` @@ -62,12 +76,12 @@ int result = INT_MAX; TreeNode* pre; void traversal(TreeNode* cur) { if (cur == NULL) return; - traversal(cur->left); - if (pre != NULL){ + traversal(cur->left); // å·¦ + if (pre != NULL){ // 中 result = min(result, cur->val - pre->val); } pre = cur; // 记录å‰ä¸€ä¸ª - traversal(cur->right); + traversal(cur->right); // å³ } public: int getMinimumDifference(TreeNode* root) { @@ -77,11 +91,13 @@ public: }; ``` -### 迭代 +æ˜¯ä¸æ˜¯çœ‹ä¸ŠåŽ»ä¹Ÿå¹¶ä¸å¤æ‚ï¼ + +## 迭代 看过这两篇[äºŒå‰æ ‘:å¬è¯´é€’归能åšçš„,栈也能åšï¼](https://mp.weixin.qq.com/s/c_zCrGHIVlBjUH_hJtghCg),[äºŒå‰æ ‘:å‰ä¸­åŽåºè¿­ä»£æ–¹å¼çš„写法就ä¸èƒ½ç»Ÿä¸€ä¸€ä¸‹ä¹ˆï¼Ÿ](https://mp.weixin.qq.com/s/WKg0Ty1_3SZkztpHubZPRg)文章之åŽï¼Œä¸éš¾å†™å‡ºä¸¤ç§ä¸­åºé历的迭代法。 -䏋颿ˆ‘给出其中的一ç§ï¼Œä»£ç å¦‚下: +䏋颿ˆ‘给出其中的一ç§ä¸­åºé历的迭代法,代ç å¦‚下: ``` class Solution { @@ -98,8 +114,8 @@ public: } else { cur = st.top(); st.pop(); - if (pre != NULL) { - result = min(result, cur->val - pre->val); // 中 + if (pre != NULL) { // 中 + result = min(result, cur->val - pre->val); } pre = cur; cur = cur->right; // å³ @@ -109,3 +125,17 @@ public: } }; ``` + +# 总结 + +**é‡åˆ°åœ¨äºŒå‰æœç´¢æ ‘ä¸Šæ±‚ä»€ä¹ˆæœ€å€¼ï¼Œæ±‚å·®å€¼ä¹‹ç±»çš„ï¼Œéƒ½è¦æ€è€ƒä¸€ä¸‹äºŒå‰æœç´¢æ ‘坿˜¯æœ‰åºçš„,è¦åˆ©ç”¨å¥½è¿™ä¸€ç‰¹ç‚¹ã€‚** + +åŒæ—¶è¦å­¦ä¼šåœ¨é€’å½’é历的过程中如何记录å‰åŽä¸¤ä¸ªæŒ‡é’ˆï¼Œè¿™ä¹Ÿæ˜¯ä¸€ä¸ªå°æŠ€å·§ï¼Œå­¦ä¼šäº†è¿˜æ˜¯å¾ˆå—用的。 + +åŽé¢æˆ‘将继续介ç»ä¸€ç³»åˆ—åˆ©ç”¨äºŒå‰æœç´¢æ ‘特性的题目。 + +**就酱,感觉学到了,就转å‘给身边需è¦çš„åŒå­¦å§** + + + + diff --git a/problems/0669.ä¿®å‰ªäºŒå‰æœç´¢æ ‘.md b/problems/0669.ä¿®å‰ªäºŒå‰æœç´¢æ ‘.md new file mode 100644 index 00000000..8978424c --- /dev/null +++ b/problems/0669.ä¿®å‰ªäºŒå‰æœç´¢æ ‘.md @@ -0,0 +1,217 @@ + +> 如果ä¸å¯¹é€’归有深刻的ç†è§£ï¼Œæœ¬é¢˜æœ‰ç‚¹éš¾ + +# 669. ä¿®å‰ªäºŒå‰æœç´¢æ ‘ + +ç»™å®šä¸€ä¸ªäºŒå‰æœç´¢æ ‘ï¼ŒåŒæ—¶ç»™å®šæœ€å°è¾¹ç•ŒL 和最大边界 Rã€‚é€šè¿‡ä¿®å‰ªäºŒå‰æœç´¢æ ‘,使得所有节点的值在[L, R]中 (R>=L) 。你å¯èƒ½éœ€è¦æ”¹å˜æ ‘çš„æ ¹èŠ‚ç‚¹ï¼Œæ‰€ä»¥ç»“æžœåº”å½“è¿”å›žä¿®å‰ªå¥½çš„äºŒå‰æœç´¢æ ‘的新的根节点。 + +![669.ä¿®å‰ªäºŒå‰æœç´¢æ ‘](https://img-blog.csdnimg.cn/20201014173115788.png) + +![669.ä¿®å‰ªäºŒå‰æœç´¢æ ‘1](https://img-blog.csdnimg.cn/20201014173219142.png) + +# æ€è·¯ + +相信看到这é“题目大家都感觉是一é“简å•题(事实上leetcode上也表明是简å•)。 + +## 递归法 + +直接想法就是:递归处ç†ï¼Œç„¶åŽé‡åˆ° `root->val < low || root->val > high` 的时候直接return NULL。一波修建,赶紧利è½ã€‚ + +ä¸éš¾å†™å‡ºå¦‚下代ç ï¼š + +``` +class Solution { +public: + TreeNode* trimBST(TreeNode* root, int low, int high) { + if (root == nullptr || root->val < low || root->val > high) return nullptr; + root->left = trimBST(root->left, low, high); + root->right = trimBST(root->right, low, high); + return root; + } +}; +``` + +**然而[1, 3]åŒºé—´åœ¨äºŒå‰æœç´¢æ ‘的中å¯ä¸æ˜¯å•纯的节点3和左孩å­èŠ‚ç‚¹0就决定的,还è¦è€ƒè™‘节点0çš„å³å­æ ‘。** + +æˆ‘ä»¬åœ¨é‡æ–°å…³æ³¨ä¸€ä¸‹ç¬¬äºŒä¸ªç¤ºä¾‹ï¼Œå¦‚图: + + + +**æ‰€ä»¥ä»¥ä¸Šçš„ä»£ç æ˜¯ä¸å¯è¡Œçš„ï¼** + +从图中å¯ä»¥çœ‹å‡ºéœ€è¦é‡æž„äºŒå‰æ ‘ï¼Œæƒ³æƒ³æ˜¯ä¸æ˜¯æœ¬é¢˜å°±æœ‰ç‚¹å¤æ‚了。 + +其实ä¸ç”¨é‡æž„é‚£ä¹ˆå¤æ‚。 + +在上图中我们å‘现节点0å¹¶ä¸ç¬¦åˆåŒºé—´è¦æ±‚,那么将节点0çš„å³å­©å­ 节点2 直接赋给 节点3的左孩å­å°±å¯ä»¥äº†ï¼ˆå°±æ˜¯æŠŠå…ƒç´ 0å‡æŽ‰ï¼‰ï¼Œå¦‚å›¾ï¼š + + + + +ç†è§£äº†æœ€å…³é”®éƒ¨åˆ†äº†æˆ‘们在递归三部曲: + +* ç¡®å®šé€’å½’å‡½æ•°çš„å‚æ•°ä»¥åŠè¿”回值 + +首先**我们è¦è¿”å›žå‡½æ•°å‚æ•°èŠ‚ç‚¹ï¼ˆroot)为根节点的树 修剪完之åŽçš„ æ–°çš„æ ¹èŠ‚ç‚¹**,这里我们为什么需è¦è¿”回值呢? + + +因为是è¦é历整棵树,åšä¿®æ”¹ï¼Œå…¶å®žä¸éœ€è¦è¿”回值也å¯ä»¥ï¼Œæˆ‘们也å¯ä»¥å®Œæˆä¿®å‰ªï¼ˆå…¶å®žå°±æ˜¯è¦åˆ é™¤èŠ‚ç‚¹ï¼‰çš„æ“作。 + +但是有返回值,更方便,å¯ä»¥é€šè¿‡ 这样的赋值语å¥ï¼š`root->left = trimBST(root->left, int low, int high)` 直接删除root的左孩å­ï¼ˆå¦‚æžœroot的左孩å­ä¸åœ¨èŒƒå›´å†…çš„è¯ï¼‰ã€‚ + +**因为`trimBST(root->left, int low, int high)` 将返回当å‰root左孿 ‘(以root->leftä¸ºæ ¹èŠ‚ç‚¹çš„äºŒå‰æ ‘)修剪完之åŽçš„æ–°çš„æ ¹èŠ‚ç‚¹ã€‚** + +代ç å¦‚下: + +``` +TreeNode* trimBST(TreeNode* root, int low, int high) +``` + +* 确定终止æ¡ä»¶ + +修剪的æ“ä½œå¹¶ä¸æ˜¯åœ¨ç»ˆæ­¢æ¡ä»¶ä¸Šè¿›è¡Œçš„,所以就是é‡åˆ°ç©ºèŠ‚ç‚¹è¿”å›žå°±å¯ä»¥äº†ã€‚ + +``` +if (root == nullptr ) return nullptr; +``` + +* 确定å•层递归的逻辑 + +如果root(当å‰èŠ‚ç‚¹ï¼‰çš„å…ƒç´ å°äºŽlow的数值,那么应该递归å³å­æ ‘,并返回å³å­æ ‘的头结点。 + +代ç å¦‚下: + +``` +if (root->val < low) { + TreeNode* right = trimBST(root->right, low, high); // 寻找符åˆåŒºé—´[low, high]的节点 + return right; +} +``` + +如果root(当å‰èŠ‚ç‚¹)的元素å°äºŽhighçš„ï¼Œé‚£ä¹ˆåº”è¯¥é€’å½’å·¦å­æ ‘ï¼Œå¹¶è¿”å›žå·¦å­æ ‘的头结点。 + +代ç å¦‚下: + +``` +if (root->val > high) { + TreeNode* left = trimBST(root->left, low, high); // 寻找符åˆåŒºé—´[low, high]的节点 + return left; +} +``` + +接下æ¥è¦å°†å¤„ç†å®Œå·¦å­æ ‘的结果赋给root->left,处ç†å®Œå³å­æ ‘的结果赋给root->right。 + +最åŽè¿”回root节点,代ç å¦‚下: + + +``` +root->left = trimBST(root->left, low, high); // root->leftæŽ¥å…¥ç¬¦åˆæ¡ä»¶çš„å·¦å­©å­ +root->right = trimBST(root->right, low, high); // root->rightæŽ¥å…¥ç¬¦åˆæ¡ä»¶çš„å³å­©å­ +return root; +``` + +æ­¤æ—¶å¤§å®¶æ˜¯ä¸æ˜¯è¿˜æ²¡å‘现这个 多余的节点究竟是如何删除的? + +其实就是通过,这两个语å¥åˆ é™¤çš„。 +``` +root->left = trimBST(root->left, low, high); +root->right = trimBST(root->right, low, high); +``` + +root釿–°è§„划root的左å³å­©å­ç©¶ç«Ÿæ˜¯è°ï¼Œæ‹¿å›¾ä¸­ç¤ºä¾‹ä¸ºä¾‹ï¼Œæ­¤æ—¶root为节点3,那么trimBST(root->left, low, high)返回的就是节点2,`root->left = trimBST(root->left, low, high);` 相当于把节点0删除了。 + +æœ€åŽæ•´ä½“代ç å¦‚下: + +``` +class Solution { +public: + // 注æ„这里是返回该树的头结点 + TreeNode* trimBST(TreeNode* root, int low, int high) { + if (root == nullptr ) return nullptr; + if (root->val < low) { + TreeNode* right = trimBST(root->right, low, high); // 寻找符åˆåŒºé—´[low, high]的节点 + return right; + } + if (root->val > high) { + TreeNode* left = trimBST(root->left, low, high); // 寻找符åˆåŒºé—´[low, high]的节点 + return left; + } + root->left = trimBST(root->left, low, high); // root->leftæŽ¥å…¥ç¬¦åˆæ¡ä»¶çš„å·¦å­©å­ + root->right = trimBST(root->right, low, high); // root->rightæŽ¥å…¥ç¬¦åˆæ¡ä»¶çš„å³å­©å­ + return root; + } +}; +``` + +精简之åŽä»£ç å¦‚下: + +``` +class Solution { +public: + TreeNode* trimBST(TreeNode* root, int low, int high) { + if (root == nullptr) return nullptr; + if (root->val < low) return trimBST(root->right, low, high); + if (root->val > high) return trimBST(root->left, low, high); + root->left = trimBST(root->left, low, high); + root->right = trimBST(root->right, low, high); + return root; + } +}; +``` + +## 迭代法 + +å› ä¸ºäºŒå‰æœç´¢æ ‘çš„æœ‰åºæ€§ï¼Œä¸éœ€è¦ä½¿ç”¨æ ˆæ¨¡æ‹Ÿé€’归的过程。 + +在剪æžçš„æ—¶å€™ï¼Œå¯ä»¥åˆ†ä¸ºä¸‰æ­¥ï¼š + +* å°†root移动到[L, R] èŒƒå›´å†…ï¼Œæ³¨æ„æ˜¯å·¦é—­å³é—­åŒºé—´ +* 剪æžå·¦å­æ ‘ +* 剪æžå³å­æ ‘ + +代ç å¦‚下: + +``` +class Solution { +public: + TreeNode* trimBST(TreeNode* root, int L, int R) { + if (!root) return nullptr; + + // 处ç†å¤´ç»“点,让root移动到[L, R] èŒƒå›´å†…ï¼Œæ³¨æ„æ˜¯å·¦é—­å³é—­ + while (root->val < L || root->val > R) { + if (root->val < L) root = root->right; // å°äºŽLå¾€å³èµ° + else root = root->left; // 大于R往左走 + } + TreeNode *cur = root; + // 此时rootå·²ç»åœ¨[L, R] 范围内,处ç†å·¦å­©å­å…ƒç´ å°äºŽL的情况 + while (cur != nullptr) { + while (cur->left && cur->left->val < L) { + cur->left = cur->left->right; + } + cur = cur->left; + } + cur = root; + + // 此时rootå·²ç»åœ¨[L, R] 范围内,处ç†å³å­©å­å¤§äºŽR的情况 + while (cur != nullptr) { + while (cur->right && cur->right->val > R) { + cur->right = cur->right->left; + } + cur = cur->right; + } + return root; + } +}; +``` + +# 总结 + +ä¿®å‰ªäºŒå‰æœç´¢æ ‘其实并ä¸éš¾ï¼Œä½†åœ¨é€’归法中大家å¯çœ‹å‡ºæˆ‘费了很大的功夫æ¥è®²è§£å¦‚何删除节点的,这个æ€è·¯å…¶å®žæ˜¯æ¯”较绕的。 + +最终的代ç å€’是很简æ´ã€‚ + +**如果ä¸å¯¹é€’归有深刻的ç†è§£ï¼Œè¿™é“题目还是有难度的ï¼** + +本题我ä¾ç„¶ç»™å‡ºé€’归法和迭代法,大家åªè¦æŽŒæ¡é€’归其实就å¯ä»¥äº†ï¼Œå¦‚果想进一步学习,就把迭代法也写一写。 + +**就酱,如果学到了,就转å‘给身边需è¦çš„åŒå­¦å§ï¼**