From 71d8678c9ab1cc183b48d8db985b5f12ded5bde9 Mon Sep 17 00:00:00 2001 From: youngyangyang04 <826123027@qq.com> Date: Fri, 9 Oct 2020 10:24:49 +0800 Subject: [PATCH] Update --- README.md | 11 +- ...ºä¸Žä¸­åºé历åºåˆ—构造二å‰æ ‘.png | Bin 0 -> 9196 bytes ...与åŽåºé历åºåˆ—构造二å‰æ ‘1.png | Bin 0 -> 9422 bytes ...与åŽåºé历åºåˆ—构造二å‰æ ‘2.png | Bin 0 -> 62243 bytes ...åºä¸ŽåŽåºé历åºåˆ—构造二å‰æ ‘.md | 149 +++++++++++++----- problems/0111.二å‰æ ‘的最å°æ·±åº¦.md | 7 +- problems/0141.环形链表.md | 45 ++++++ 7 files changed, 169 insertions(+), 43 deletions(-) create mode 100644 pics/105. 从å‰åºä¸Žä¸­åºé历åºåˆ—构造二å‰æ ‘.png create mode 100644 pics/106. 从中åºä¸ŽåŽåºé历åºåˆ—构造二å‰æ ‘1.png create mode 100644 pics/106.从中åºä¸ŽåŽåºé历åºåˆ—构造二å‰æ ‘2.png create mode 100644 problems/0141.环形链表.md diff --git a/README.md b/README.md index bc3927d1..89bceef7 100644 --- a/README.md +++ b/README.md @@ -67,7 +67,16 @@ * [字符串：å‰ç¼€è¡¨ä¸å³ç§»ï¼Œéš¾é“就写ä¸å‡ºKMP了？](https://mp.weixin.qq.com/s/p3hXynQM2RRROK5c6X7xfw) * [字符串：总结篇ï¼](https://mp.weixin.qq.com/s/gtycjyDtblmytvBRFlCZJg) -* [åŒæŒ‡é’ˆæ³•ï¼šæ€»ç»“篇ï¼](https://mp.weixin.qq.com/s/_p7grwjISfMh0U65uOyCjA) +* åŒæŒ‡é’ˆæ³• + * [数组：就移除个元素很难么？](https://mp.weixin.qq.com/s/wj0T-Xs88_FHJFwayElQlA) + * [字符串：这é“题目，使用库函数一行代ç æžå®š](https://mp.weixin.qq.com/s/X02S61WCYiCEhaik6VUpFA) + * [字符串：替æ¢ç©ºæ ¼](https://mp.weixin.qq.com/s/t0A9C44zgM-RysAQV3GZpg) + * [字符串：花å¼å转还ä¸å¤Ÿï¼](https://mp.weixin.qq.com/s/X3qpi2v5RSp08mO-W5Vicw) + * [链表：å¬è¯´è¿‡ä¸¤å¤©å转链表åˆå†™ä¸å‡ºæ¥äº†ï¼Ÿ](https://mp.weixin.qq.com/s/pnvVP-0ZM7epB8y3w_Njwg) + * [链表：环找到了，那入å£å‘¢ï¼Ÿ](https://mp.weixin.qq.com/s/_QVP3IkRZWx9zIpQRgajzA) + * [哈希表：解决了两数之和，那么能解决三数之和么？](https://mp.weixin.qq.com/s/r5cgZFu0tv4grBAexdcd8A) + * [åŒæŒ‡é’ˆæ³•ï¼šä¸€æ ·çš„é“ç†ï¼Œèƒ½è§£å†³å››æ•°ä¹‹å’Œ](https://mp.weixin.qq.com/s/nQrcco8AZJV1pAOVjeIU_g) + * [åŒæŒ‡é’ˆæ³•ï¼šæ€»ç»“篇ï¼](https://mp.weixin.qq.com/s/_p7grwjISfMh0U65uOyCjA) * 栈与队列 * 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zcFpbs()Cr*P|1NXkh3~*VPhb0#J(b$XCdJyDP9&u`m)#gLJs&qik~7Bw>0PmOOLZE z92`;v$S-}`DB;5tkTaOz7^w?nq&*J&dQ05T~o;Qzwg-y^lPQOj) 给出两个åºåˆ— + +# 106.从中åºä¸ŽåŽåºé历åºåˆ—构造二å‰æ ‘ + +æ ¹æ®ä¸€æ£µæ ‘的中åºé历与åŽåºé历构造二å‰æ ‘。 + +注æ„: +ä½ å¯ä»¥å‡è®¾æ ‘中没有é‡å¤çš„元素。 + +例如，给出 + +中åºé历 inorder = [9,3,15,20,7] +åŽåºé历 postorder = [9,15,7,20,3] +返回如下的二å‰æ ‘： + + + ## æ€è·¯ -首先回忆一下如何根æ®ä¸¤ä¸ªé¡ºåºæž„造一个唯一的二å‰æ ‘，相信ç†è®ºçŸ¥è¯†å¤§å®¶åº”该都清楚，就是以åŽåºæ•°ç»„最åŽä¸€ä¸ªå…ƒç´ ä¸ºåˆ‡å‰²ç‚¹ï¼Œå…ˆåˆ‡ä¸­åºæ•°ç»„，根æ®ä¸­åºæ•°ç»„，å过æ¥åœ¨åˆ‡åŽåºæ•°ç»„。一层一层切下去，æ¯æ¬¡åŽåºæ•°ç»„最åŽä¸€ä¸ªå…ƒç´ å°±æ˜¯èŠ‚点元素。 +首先回忆一下如何根æ®ä¸¤ä¸ªé¡ºåºæž„造一个唯一的二å‰æ ‘，相信ç†è®ºçŸ¥è¯†å¤§å®¶åº”该都清楚，就是以 åŽåºæ•°ç»„的最åŽä¸€ä¸ªå…ƒç´ ä¸ºåˆ‡å‰²ç‚¹ï¼Œå…ˆåˆ‡ä¸­åºæ•°ç»„，根æ®ä¸­åºæ•°ç»„，å过æ¥åœ¨åˆ‡åŽåºæ•°ç»„。一层一层切下去，æ¯æ¬¡åŽåºæ•°ç»„最åŽä¸€ä¸ªå…ƒç´ å°±æ˜¯èŠ‚点元素。 如果让我们肉眼看两个åºåˆ—，画一颗二å‰æ ‘çš„è¯ï¼Œåº”该分分钟都å¯ä»¥ç”»å‡ºæ¥ã€‚ æµç¨‹å¦‚图： - 那么代ç åº”该怎么写呢？ -说é“一层一层切割，就应该想到了递归。 +说到一层一层切割，就应该想到了递归。 æ¥çœ‹ä¸€ä¸‹ä¸€å…±åˆ†å‡ æ­¥ï¼š @@ -22,7 +38,7 @@ https://leetcode-cn.com/problems/construct-binary-tree-from-inorder-and-postorde * 第二步：如果ä¸ä¸ºç©ºï¼Œé‚£ä¹ˆå–åŽåºæ•°ç»„最åŽä¸€ä¸ªå…ƒç´ ä½œä¸ºèŠ‚点元素。 -* 第三步：找到åŽåºæ•°ç»„最åŽä¸€ä¸ªå…ƒç´ åœ¨åŽåºæ•°ç»„çš„ä½ç½®ï¼Œä½œä¸ºåˆ‡å‰²ç‚¹ +* 第三步：找到åŽåºæ•°ç»„最åŽä¸€ä¸ªå…ƒç´ åœ¨ä¸­åºæ•°ç»„çš„ä½ç½®ï¼Œä½œä¸ºåˆ‡å‰²ç‚¹ * 第四步：切割中åºæ•°ç»„，切æˆä¸­åºå·¦æ•°ç»„和中åºå³æ•°ç»„ （顺åºåˆ«æžå了，一定是先切中åºæ•°ç»„） @@ -35,24 +51,26 @@ https://leetcode-cn.com/problems/construct-binary-tree-from-inorder-and-postorde ``` TreeNode* traversal (vector& inorder, vector& postorder) { + // 第一步 if (postorder.size() == 0) return NULL; - // åŽåºé历数组最åŽä¸€ä¸ªå…ƒç´ ï¼Œå°±æ˜¯å½“å‰çš„中间节点 + // 第二步：åŽåºé历数组最åŽä¸€ä¸ªå…ƒç´ ï¼Œå°±æ˜¯å½“å‰çš„中间节点 int rootValue = postorder[postorder.size() - 1]; TreeNode* root = new TreeNode(rootValue); // å¶å­èŠ‚点 if (postorder.size() == 1) return root; - 找切割点 + // 第三步：找切割点 int delimiterIndex; for (delimiterIndex = 0; delimiterIndex < inorder.size(); delimiterIndex++) { if (inorder[delimiterIndex] == rootValue) break; } - 切割中åºæ•°ç»„，得到 中åºå·¦æ•°ç»„和中åºå³æ•°ç»„ - 切割åŽåºæ•°ç»„，得到 åŽåºå·¦æ•°ç»„å’ŒåŽåºå³æ•°ç»„ + // 第四步：切割中åºæ•°ç»„，得到 中åºå·¦æ•°ç»„和中åºå³æ•°ç»„ + // 第五步：切割åŽåºæ•°ç»„，得到 åŽåºå·¦æ•°ç»„å’ŒåŽåºå³æ•°ç»„ + // 第六步 root->left = traversal(中åºå·¦æ•°ç»„, åŽåºå·¦æ•°ç»„); root->right = traversal(中åºå³æ•°ç»„, åŽåºå³æ•°ç»„); @@ -60,11 +78,11 @@ https://leetcode-cn.com/problems/construct-binary-tree-from-inorder-and-postorde } ``` -难点大家应该å‘现了，如何切割呢，边界值找ä¸å¥½å¾ˆå®¹æ˜“乱套。 +**难点大家应该å‘现了，就是如何切割，以åŠè¾¹ç•Œå€¼æ‰¾ä¸å¥½å¾ˆå®¹æ˜“乱套。** 此时应该注æ„确定切割的标准，是左闭å³å¼€ï¼Œè¿˜æœ‰å·¦å¼€åˆé—­ï¼Œè¿˜æ˜¯å·¦é—­åˆé—­ï¼Œè¿™ä¸ªå°±æ˜¯ä¸å˜é‡ï¼Œè¦åœ¨é€’归中ä¿æŒè¿™ä¸ªä¸å˜é‡ã€‚ -在切割的过程中会产生四个区间，把æ¡ä¸å¥½ä¸å˜é‡çš„è¯ï¼Œä¸€ä¼šå·¦é—­å³å¼€ï¼Œä¸€ä¼šå·¦é—­åˆé—­ï¼Œå¿…è¦ä¹±å¥—ï¼ +**在切割的过程中会产生四个区间，把æ¡ä¸å¥½ä¸å˜é‡çš„è¯ï¼Œä¸€ä¼šå·¦é—­å³å¼€ï¼Œä¸€ä¼šå·¦é—­åˆé—­ï¼Œå¿…然乱套ï¼** 我在[数组：æ¯æ¬¡é‡åˆ°äºŒåˆ†æ³•ï¼Œéƒ½æ˜¯ä¸€çœ‹å°±ä¼šï¼Œä¸€å†™å°±åºŸ](https://mp.weixin.qq.com/s/fCf5QbPDtE6SSlZ1yh_q8Q)å’Œ[数组：这个循环å¯ä»¥è½¬æ‡µå¾ˆå¤šäººï¼](https://mp.weixin.qq.com/s/KTPhaeqxbMK9CxHUUgFDmg)中都强调过循环ä¸å˜é‡çš„é‡è¦æ€§ï¼Œåœ¨äºŒåˆ†æŸ¥æ‰¾ä»¥åŠèžºæ—‹çŸ©é˜µçš„求解中，åšæŒå¾ªçŽ¯ä¸å˜é‡éžå¸¸é‡è¦ï¼Œæœ¬é¢˜ä¹Ÿæ˜¯ã€‚ @@ -77,17 +95,16 @@ https://leetcode-cn.com/problems/construct-binary-tree-from-inorder-and-postorde ``` - // 找到中åºé历的切割点 - int delimiterIndex; - for (delimiterIndex = 0; delimiterIndex < inorder.size(); delimiterIndex++) { - if (inorder[delimiterIndex] == rootValue) break; - } +// 找到中åºé历的切割点 +int delimiterIndex; +for (delimiterIndex = 0; delimiterIndex < inorder.size(); delimiterIndex++) { + if (inorder[delimiterIndex] == rootValue) break; +} - // 左闭å³å¼€åŒºé—´ - // [0, delimiterIndex) - vector leftInorder(inorder.begin(), inorder.begin() + delimiterIndex); - // [delimiterIndex + 1, end) - vector rightInorder(inorder.begin() + delimiterIndex + 1, inorder.end() ); +// 左闭å³å¼€åŒºé—´ï¼š[0, delimiterIndex) +vector leftInorder(inorder.begin(), inorder.begin() + delimiterIndex); +// [delimiterIndex + 1, end) +vector rightInorder(inorder.begin() + delimiterIndex + 1, inorder.end() ); ``` 接下æ¥å°±è¦åˆ‡å‰²åŽåºæ•°ç»„了。 @@ -96,7 +113,7 @@ https://leetcode-cn.com/problems/construct-binary-tree-from-inorder-and-postorde åŽåºæ•°ç»„的切割点怎么找？ -åŽåºæ•°ç»„没有明确的切割元素æ¥è¿›è¡Œå·¦å³åˆ‡å‰²ï¼Œä¸æƒ³ä¸­åºæ•°ç»„有明确的切割左å³ï¼Œå·¦å³åˆ†å¼€å°±å¯ä»¥äº†ã€‚ +åŽåºæ•°ç»„没有明确的切割元素æ¥è¿›è¡Œå·¦å³åˆ‡å‰²ï¼Œä¸åƒä¸­åºæ•°ç»„有明确的切割点，切割点左å³åˆ†å¼€å°±å¯ä»¥äº†ã€‚ **此时有一个很é‡çš„点，就是中åºæ•°ç»„大å°ä¸€å®šæ˜¯å’ŒåŽåºæ•°ç»„的大å°ç›¸åŒçš„（这是必然）。** @@ -105,28 +122,27 @@ https://leetcode-cn.com/problems/construct-binary-tree-from-inorder-and-postorde 代ç å¦‚下： ``` - // postorder èˆå¼ƒæœ«å°¾å…ƒç´  - postorder.resize(postorder.size() - 1); +// postorder èˆå¼ƒæœ«å°¾å…ƒç´ ï¼Œå› ä¸ºè¿™ä¸ªå…ƒç´ å°±æ˜¯ä¸­é—´èŠ‚点，已ç»ç”¨è¿‡äº† +postorder.resize(postorder.size() - 1); - // ä¾ç„¶å·¦é—­å³å¼€ï¼Œæ³¨æ„这里使用了左中åºæ•°ç»„大å°ä½œä¸ºåˆ‡å‰²ç‚¹ - // [0, leftInorder.size) - vector leftPostorder(postorder.begin(), postorder.begin() + leftInorder.size()); - // [leftInorder.size(), end) - vector rightPostorder(postorder.begin() + leftInorder.size(), postorder.end()); +// 左闭å³å¼€ï¼Œæ³¨æ„这里使用了左中åºæ•°ç»„大å°ä½œä¸ºåˆ‡å‰²ç‚¹ï¼š[0, leftInorder.size) +vector leftPostorder(postorder.begin(), postorder.begin() + leftInorder.size()); +// [leftInorder.size(), end) +vector rightPostorder(postorder.begin() + leftInorder.size(), postorder.end()); ``` -此时，中åºæ•°ç»„切æˆäº†å·¦ä¸­åºæ•°ç»„å’Œå³ä¸­åºæ•°ç»„，åŽåºæ•°ç»„切割æˆåºæ•°ç»„å’Œå³åŽåºæ•°ç»„。 +此时，中åºæ•°ç»„切æˆäº†å·¦ä¸­åºæ•°ç»„å’Œå³ä¸­åºæ•°ç»„，åŽåºæ•°ç»„切割æˆå·¦åŽåºæ•°ç»„å’Œå³åŽåºæ•°ç»„。 接下æ¥å¯ä»¥é€’归了，代ç å¦‚下： ``` - root->left = traversal(leftInorder, leftPostorder); - root->right = traversal(rightInorder, rightPostorder); +root->left = traversal(leftInorder, leftPostorder); +root->right = traversal(rightInorder, rightPostorder); ``` 完整代ç å¦‚下： -## C++ å®Œæ•´ä»£ç  +### C++å®Œæ•´ä»£ç  ``` class Solution { @@ -206,6 +222,7 @@ private: vector leftPostorder(postorder.begin(), postorder.begin() + leftInorder.size()); vector rightPostorder(postorder.begin() + leftInorder.size(), postorder.end()); + // 一下为日志 cout << "----------" << endl; cout << "leftInorder :"; @@ -244,11 +261,11 @@ public: }; ``` -**此时应该å‘现了，如上的代ç æ€§èƒ½å¹¶ä¸å¥½ï¼Œåº”为æ¯å±‚递归定定义了新的vector，既耗时åˆè€—空间，但是上é¢çš„代ç æ˜¯æœ€å¥½ç†è§£çš„，为了方便读者ç†è§£ï¼Œæ‰€ä»¥ç”¨å¦‚上的代ç æ¥è®²è§£ã€‚** +**此时应该å‘现了，如上的代ç æ€§èƒ½å¹¶ä¸å¥½ï¼Œåº”为æ¯å±‚递归定定义了新的vector（就是数组），既耗时åˆè€—空间，但上é¢çš„代ç æ˜¯æœ€å¥½ç†è§£çš„，为了方便读者ç†è§£ï¼Œæ‰€ä»¥ç”¨å¦‚上的代ç æ¥è®²è§£ã€‚** 下é¢ç»™å‡ºç”¨ä¸‹è¡¨ç´¢å¼•å†™å‡ºçš„代ç ç‰ˆæœ¬ï¼šï¼ˆæ€è·¯æ˜¯ä¸€æ ·çš„，åªä¸è¿‡ä¸ç”¨é‡å¤å®šä¹‰vector了，æ¯æ¬¡ç”¨ä¸‹è¡¨ç´¢å¼•æ¥åˆ†å‰²ï¼‰ -## C++最终优化版本 +### C++优化版本 ``` class Solution { private: @@ -368,7 +385,24 @@ public: # 105. 从å‰åºä¸Žä¸­åºé历åºåˆ—构造二å‰æ ‘ -åŒæ ·çš„é“ç† +æ ¹æ®ä¸€æ£µæ ‘çš„å‰åºé历与中åºé历构造二å‰æ ‘。 + +注æ„: +ä½ å¯ä»¥å‡è®¾æ ‘中没有é‡å¤çš„元素。 + +例如，给出 + +å‰åºé历 preorder = [3,9,20,15,7] +中åºé历 inorder = [9,3,15,20,7] +返回如下的二å‰æ ‘： + + + +## æ€è·¯ + +本题和106是一样的é“ç†ã€‚ + +我就直接给出代ç äº†ã€‚ 带日志的版本C++代ç å¦‚下： （**带日志的版本仅用于调试，ä¸è¦åœ¨leetcode上æ交，会超时**） @@ -444,9 +478,8 @@ public: }; ``` -105. 从å‰åºä¸Žä¸­åºé历åºåˆ—构造二å‰æ ‘，最åŽç‰ˆæœ¬ï¼š +105.从å‰åºä¸Žä¸­åºé历åºåˆ—构造二å‰æ ‘，最åŽç‰ˆæœ¬ï¼ŒC++代ç ï¼š -C++代ç ï¼š ``` class Solution { private: @@ -493,3 +526,45 @@ public: } }; ``` + +# æ€è€ƒé¢˜ + +å‰åºå’Œä¸­åºå¯ä»¥å”¯ä¸€ç¡®å®šä¸€é¢—二å‰æ ‘。 + +åŽåºå’Œä¸­åºå¯ä»¥å”¯ä¸€ç¡®å®šä¸€é¢—二å‰æ ‘。 + +那么å‰åºå’ŒåŽåºå¯ä¸å¯ä»¥å”¯ä¸€ç¡®å®šä¸€é¢—二å‰æ ‘呢？ + +**å‰åºå’ŒåŽåºä¸èƒ½å”¯ä¸€ç¡®å®šä¸€é¢—二å‰æ ‘ï¼**，因为没有中åºé历无法确定左å³éƒ¨åˆ†ï¼Œä¹Ÿå°±æ˜¯æ— æ³•åˆ†å‰²ã€‚ + +举一个例å­ï¼š + + + +tree1 çš„å‰åºé历是[1 2 3]， åŽåºé历是[3 2 1]。 + +tree2 çš„å‰åºé历是[1 2 3]， åŽåºé历是[3 2 1]。 + +那么tree1 å’Œ tree2 çš„å‰åºå’ŒåŽåºå®Œå…¨ç›¸åŒï¼Œè¿™æ˜¯ä¸€æ£µæ ‘ä¹ˆï¼Œå¾ˆæ˜Žæ˜¾æ˜¯ä¸¤æ£µæ ‘ï¼ + +所以å‰åºå’ŒåŽåºä¸èƒ½å”¯ä¸€ç¡®å®šä¸€é¢—二å‰æ ‘ï¼ + +# 总结 + +之å‰æˆ‘们讲的二å‰æ ‘题目都是å„ç§é历二å‰æ ‘，这次开始构造二å‰æ ‘了，æ€è·¯å…¶å®žæ¯”较简å•ï¼Œä½†æ˜¯çœŸæ­£ä»£ç å®žçŽ°å‡ºæ¥å¹¶ä¸å®¹æ˜“。 + +所以è¦é¿å…眼高手低，è¸å®žçš„把代ç å†™å‡ºæ¥ã€‚ + +我åŒæ—¶ç»™å‡ºäº†æ·»åŠ æ—¥å¿—的代ç ç‰ˆæœ¬ï¼Œå› ä¸ºè¿™ç§é¢˜ç›®æ˜¯ä¸å¤ªå®¹æ˜“写出æ¥è°ƒä¸€è°ƒå°±èƒ½è¿‡çš„，所以一定è¦æŠŠæµç¨‹æ—¥å¿—打出æ¥ï¼Œçœ‹çœ‹ç¬¦ä¸ç¬¦åˆè‡ªå·±çš„æ€è·¯ã€‚ + +大家é‡åˆ°è¿™ç§é¢˜ç›®çš„时候，也è¦å­¦ä¼šæ‰“日志æ¥è°ƒè¯•ï¼ˆå¦‚何打日志有时候也是个技术活），ä¸è¦è„‘动模拟，脑动模拟很容易越想越乱。 + +最åŽæˆ‘还给出了为什么å‰åºå’Œä¸­åºå¯ä»¥å”¯ä¸€ç¡®å®šä¸€é¢—二å‰æ ‘，åŽåºå’Œä¸­åºå¯ä»¥å”¯ä¸€ç¡®å®šä¸€é¢—二å‰æ ‘，而å‰åºå’ŒåŽåºå´ä¸è¡Œã€‚ + +认真研究完本篇，相信大家对二å‰æ ‘的构造会清晰很多。 + +如果学到了，就赶紧转å‘给身边需è¦çš„åŒå­¦å§ï¼ + +åŠ ä¸ªæ²¹ï¼ + + diff --git a/problems/0111.二å‰æ ‘的最å°æ·±åº¦.md b/problems/0111.二å‰æ ‘的最å°æ·±åº¦.md index a4edce23..eebfd76e 100644 --- a/problems/0111.二å‰æ ‘的最å°æ·±åº¦.md +++ b/problems/0111.二å‰æ ‘的最å°æ·±åº¦.md @@ -165,20 +165,17 @@ public: queue que; que.push(root); while(!que.empty()) { - int size = que.size(); + int size = que.size(); depth++; // 记录最å°æ·±åº¦ - int flag = 0; for (int i = 0; i < size; i++) { TreeNode* node = que.front(); que.pop(); if (node->left) que.push(node->left); if (node->right) que.push(node->right); if (!node->left && !node->right) { // 当左å³å­©å­éƒ½ä¸ºç©ºçš„时候，说明是最低点的一层了，退出 - flag = 1; - break; + return depth; } } - if (flag == 1) break; } return depth; } diff --git a/problems/0141.环形链表.md b/problems/0141.环形链表.md new file mode 100644 index 00000000..4198ba4a --- /dev/null +++ b/problems/0141.环形链表.md @@ -0,0 +1,45 @@ + +## æ€è·¯ + +å¯ä»¥ä½¿ç”¨å¿«æ…¢æŒ‡é’ˆæ³•ï¼Œ 分别定义 fast å’Œ slow指针，从头结点出å‘，fast指针æ¯æ¬¡ç§»åŠ¨ä¸¤ä¸ªèŠ‚点，slow指针æ¯æ¬¡ç§»åŠ¨ä¸€ä¸ªèŠ‚点，如果 fast å’Œ slowæŒ‡é’ˆåœ¨é€”ä¸­ç›¸é‡ ï¼Œè¯´æ˜Žè¿™ä¸ªé“¾è¡¨æœ‰çŽ¯ã€‚ + +为什么fast 走两个节点，slow走一个节点，有环的è¯ï¼Œä¸€å®šä¼šåœ¨çŽ¯å†…相é‡å‘¢ï¼Œè€Œä¸æ˜¯æ°¸è¿œçš„错开呢？ + +首先第一点： **fast指针一定先进入环中，如果fast 指针和slow指针相é‡çš„è¯ï¼Œä¸€å®šæ˜¯åœ¨çŽ¯ä¸­ç›¸é‡ï¼Œè¿™æ˜¯æ¯‹åº¸ç½®ç–‘的。** + +那么æ¥çœ‹ä¸€ä¸‹ï¼Œ**为什么fast指针和slow指针一定会相é‡å‘¢ï¼Ÿ** + +å¯ä»¥ç”»ä¸€ä¸ªçŽ¯ï¼Œç„¶åŽè®© fast指针在任æ„一个节点开始追赶slow指针。 + +会å‘现最终都是这ç§æƒ…况， 如下图： + + + +fastå’Œslowå„自å†èµ°ä¸€æ­¥ï¼Œ fastå’Œslow就相é‡äº† + +这是因为fast是走两步，slow是走一步，**其实相对于slowæ¥è¯´ï¼Œfast是一个节点一个节点的é è¿‘slowçš„**，所以fast一定å¯ä»¥å’Œslowé‡åˆã€‚ + + +## C++代ç å¦‚下 + +``` +class Solution { +public: + bool hasCycle(ListNode *head) { + ListNode* fast = head; + ListNode* slow = head; + while(fast != NULL && fast->next != NULL) { + slow = slow->next; + fast = fast->next->next; + // 快慢指针相é‡ï¼Œè¯´æ˜Žæœ‰çŽ¯ + if (slow == fast) return true; + } + return false; + } +}; +``` +## 扩展 + +åšå®Œè¿™é“题目，å¯ä»¥åœ¨åšåš142.环形链表II，ä¸ä»…ä»…è¦æ‰¾çŽ¯ï¼Œè¿˜è¦æ‰¾çŽ¯çš„å…¥å£ã€‚ + +142.环形链表II题解：[链表：环找到了，那入å£å‘¢ï¼Ÿ](https://mp.weixin.qq.com/s/_QVP3IkRZWx9zIpQRgajzA)