From 3e39d7f8979ea8ea11f0d1beb75a9fbe1a01a5fd Mon Sep 17 00:00:00 2001 From: youngyangyang04 <826123027@qq.com> Date: Mon, 19 Oct 2020 14:27:31 +0800 Subject: [PATCH] Update --- README.md | 5 + .../19.删除链表的倒数第N个节点.png | Bin 0 -> 46957 bytes ...19.删除链表的倒数第N个节点1.png | Bin 0 -> 49350 bytes ...19.删除链表的倒数第N个节点2.png | Bin 0 -> 48153 bytes ...19.删除链表的倒数第N个节点3.png | Bin 0 -> 59542 bytes ...0019.删除链表的倒数第N个节点.md | 49 +++++ problems/0052.N皇后II.md | 4 +- ...35.二叉搜索树的最近公共祖先.md | 191 +++++++++++++++--- problems/0844.比较含退格的字符串.md | 120 +++++++++++ video/844.比较含退格的字符串.gif | Bin 0 -> 1258577 bytes 10 files changed, 334 insertions(+), 35 deletions(-) create mode 100644 pics/19.删除链表的倒数第N个节点.png create mode 100644 pics/19.删除链表的倒数第N个节点1.png create mode 100644 pics/19.删除链表的倒数第N个节点2.png create mode 100644 pics/19.删除链表的倒数第N个节点3.png create mode 100644 problems/0019.删除链表的倒数第N个节点.md create mode 100644 problems/0844.比较含退格的字符串.md create mode 100644 video/844.比较含退格的字符串.gif diff --git a/README.md b/README.md index ccf76aca..552450dc 100644 --- a/README.md +++ b/README.md @@ -114,7 +114,10 @@ * [本周小结!(二叉树系列三)](https://mp.weixin.qq.com/s/JLLpx3a_8jurXcz6ovgxtg) * [二叉树:合并两个二叉树](https://mp.weixin.qq.com/s/3f5fbjOFaOX_4MXzZ97LsQ) * [二叉树:二叉搜索树登场!](https://mp.weixin.qq.com/s/vsKrWRlETxCVsiRr8v_hHg) + * [二叉树:我是不是一棵二叉搜索树](https://mp.weixin.qq.com/s/8odY9iUX5eSi0eRFSXFD4Q) * [二叉树:搜索树的最小绝对差](https://mp.weixin.qq.com/s/Hwzml6698uP3qQCC1ctUQQ) + * [二叉树:我的众数是多少?](https://mp.weixin.qq.com/s/KSAr6OVQIMC-uZ8MEAnGHg) + * [二叉树:公共祖先问题](https://mp.weixin.qq.com/s/n6Rk3nc_X3TSkhXHrVmBTQ) @@ -172,6 +175,7 @@ * [0015.三数之和](https://mp.weixin.qq.com/s/r5cgZFu0tv4grBAexdcd8A) * [0018.四数之和](https://mp.weixin.qq.com/s/nQrcco8AZJV1pAOVjeIU_g) * [0026.删除排序数组中的重复项](https://github.com/youngyangyang04/leetcode/blob/master/problems/0026.删除排序数组中的重复项.md) + * [19.删除链表的倒数第N个节点](https://github.com/youngyangyang04/leetcode/blob/master/problems/19.删除链表的倒数第N个节点) * [0206.翻转链表](https://mp.weixin.qq.com/s/pnvVP-0ZM7epB8y3w_Njwg) * [0142.环形链表II](https://mp.weixin.qq.com/s/_QVP3IkRZWx9zIpQRgajzA) * [0344.反转字符串](https://mp.weixin.qq.com/s/X02S61WCYiCEhaik6VUpFA) @@ -237,6 +241,7 @@ |[0015.三数之和](https://github.com/youngyangyang04/leetcode/blob/master/problems/0015.三数之和.md) | 数组 |中等|**双指针** **哈希**| |[0017.电话号码的字母组合](https://github.com/youngyangyang04/leetcode/blob/master/problems/0017.电话号码的字母组合.md) | 回溯 |中等|**回溯**| |[0018.四数之和](https://github.com/youngyangyang04/leetcode/blob/master/problems/0018.四数之和.md) | 数组 |中等|**双指针**| +|[0019.删除链表的倒数第N个节点](https://github.com/youngyangyang04/leetcode/blob/master/problems/0019.删除链表的倒数第N个节点.md) | 链表 |中等|**双指针**| |[0020.有效的括号](https://github.com/youngyangyang04/leetcode/blob/master/problems/0020.有效的括号.md) | 栈 |简单|**栈**| |[0021.合并两个有序链表](https://github.com/youngyangyang04/leetcode/blob/master/problems/0021.合并两个有序链表.md) |链表 |简单|**模拟** | |[0024.两两交换链表中的节点](https://github.com/youngyangyang04/leetcode/blob/master/problems/0024.两两交换链表中的节点.md) |链表 |中等|**模拟** | diff --git 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zxbQ8@Tm`vsE5Tfg4>!j9`X1V-6TTp~;CzFxUlMD*omyt}ExcwP*xxansEg^kikf3W z?jnpQINkL%-hs2SU;vlV_Zn+$Ze?d#6}L?P+as}cE}pPnXDz459X+`9>UUpkIIpvc z6{-$BKJ{w?@_o0`O2THPF>XBf$Nl_O9j>rS{BS_^Py3m}8(jafFK-NfXYsdw_9-2% z=vMG$Px$_KfBkbxWN`8>zqb~aPJ%7BSnC>ifbXW4syWg({Jgxt~LH@fDV1qv3Io3)*WOuuqYf7#>6LEk7Gi0QFYd;Bl#`GbJ{O&O=3cY zOo$GZ#IEk$fO-L z+~|5Wc*Ql0Xu0(5K+}+0U_@{pMFpRRLqeIgp zk$+x-x*TMmM@Ro&%X^dGbtkg#ratN)i&|^H8u7)f42*XszR-Oe);b&e0*p@E<|*Zl zdmbL&3^OhzbMr;o#u514A9hYV*YAwH>e$HfKkh0@zN`J4En+7f?`{`-OalL1xvX$0 J + +* fast首先走n + 1步 ,为什么是n+1呢,因为只有这样同时移动的时候slow才能指向删除节点的上一个节点(方便做删除操作),如图: + + +* fast和slow同时移动,之道fast指向末尾,如题: + + +* 删除slow指向的下一个节点,如图: + + +此时不难写出如下C++代码: + +``` +class Solution { +public: + ListNode* removeNthFromEnd(ListNode* head, int n) { + ListNode* dummyHead = new ListNode(0); + dummyHead->next = head; + ListNode* slow = dummyHead; + ListNode* fast = dummyHead; + while(n-- && fast != NULL) { + fast = fast->next; + } + fast = fast->next; // fast再提前走一步,因为需要让slow指向删除节点的上一个节点 + while (fast != NULL) { + fast = fast->next; + slow = slow->next; + } + slow->next = slow->next->next; + return dummyHead->next; + } +}; +``` diff --git a/problems/0052.N皇后II.md b/problems/0052.N皇后II.md index 8d15611b..4fd6482d 100644 --- a/problems/0052.N皇后II.md +++ b/problems/0052.N皇后II.md @@ -43,9 +43,9 @@ void backtracking(int n, int row, vector& chessboard, vector 二叉搜索树的最近公共祖先问题如约而至 + +# 235. 二叉搜索树的最近公共祖先 + +链接:https://leetcode-cn.com/problems/lowest-common-ancestor-of-a-binary-search-tree/ + +给定一个二叉搜索树, 找到该树中两个指定节点的最近公共祖先。 + +百度百科中最近公共祖先的定义为:“对于有根树 T 的两个结点 p、q,最近公共祖先表示为一个结点 x,满足 x 是 p、q 的祖先且 x 的深度尽可能大(一个节点也可以是它自己的祖先)。” + +例如,给定如下二叉搜索树:  root = [6,2,8,0,4,7,9,null,null,3,5] + +![235. 二叉搜索树的最近公共祖先](https://img-blog.csdnimg.cn/20201018172243602.png) + +示例 1: + +输入: root = [6,2,8,0,4,7,9,null,null,3,5], p = 2, q = 8 +输出: 6 +解释: 节点 2 和节点 8 的最近公共祖先是 6。 +示例 2: + +输入: root = [6,2,8,0,4,7,9,null,null,3,5], p = 2, q = 4 +输出: 2 +解释: 节点 2 和节点 4 的最近公共祖先是 2, 因为根据定义最近公共祖先节点可以为节点本身。 +  + +说明: + +* 所有节点的值都是唯一的。 +* p、q 为不同节点且均存在于给定的二叉搜索树中。 + ## 思路 - -遇到这个题目首先想的是要是能自底向上查找就好了,这样就可以找到公共祖先了,可惜二叉树只能自上向低。 - -那么自上相下查找的话,如何记录祖先呢? - -做过[236. 二叉树的最近公共祖先](https://leetcode-cn.com/problems/lowest-common-ancestor-of-a-binary-tree/)题目的同学,应该知道,只要判断一个节点的左子树里有p,右子树里有q,那么当前节点就是最近公共祖先。 +做过[二叉树:公共祖先问题](https://mp.weixin.qq.com/s/n6Rk3nc_X3TSkhXHrVmBTQ)题目的同学应该知道,利用回溯从底向上搜索,遇到一个节点的左子树里有p,右子树里有q,那么当前节点就是最近公共祖先。 那么本题是二叉搜索树,二叉搜索树是有序的,那得好好利用一下这个特点。 在有序树里,如果判断一个节点的左子树里有p,右子树里有q呢? -其实只要从上到下遍历的时候,如果 (p->val <= cur->val && cur->val <= q->val)则说明该节点cur就是最近公共祖先了。 +其实只要从上到下遍历的时候,cur节点是数值在[p, q]区间中则说明该节点cur就是最近公共祖先了。 -理解这一点,本题就很好解了。 +理解这一点,本题就很好解了。 -如图所示 +和[二叉树:公共祖先问题](https://mp.weixin.qq.com/s/n6Rk3nc_X3TSkhXHrVmBTQ)不同,普通二叉树求最近公共祖先需要使用回溯,从底向上来查找,二叉搜索树就不用了,因为搜索树有序(相当于自带方向),那么只要从上向下遍历就可以了。 + +那么我们可以采用前序遍历(其实这里没有中节点的处理逻辑,遍历顺序无所谓了)。 + +如图所示:p为节点3,q为节点5 +可以看出直接按照指定的方向,就可以找到节点4,为最近公共祖先,而且不需要遍历整棵树,找到结果直接返回! + + +递归三部曲如下: + +* 确定递归函数返回值以及参数 + +参数就是当前节点,以及两个结点 p、q。 + +返回值是要返回最近公共祖先,所以是TreeNode * 。 + +代码如下: + +``` +TreeNode* traversal(TreeNode* cur, TreeNode* p, TreeNode* q) +``` + +* 确定终止条件 + +遇到空返回就可以了,代码如下: + +``` +if (cur == NULL) return cur; +``` + +其实都不需要这个终止条件,因为题目中说了p、q 为不同节点且均存在于给定的二叉搜索树中。也就是说一定会找到公共祖先的,所以并不存在遇到空的情况。 + +* 确定单层递归的逻辑 + 在遍历二叉搜索树的时候就是寻找区间[p->val, q->val](注意这里是左闭又闭) -那么如果 cur->val 大于 p->val,同时 cur->val 大于q->val,那么就应该向左遍历。(因为我们此时不知道p和q谁大,所以两个都要判断) +那么如果 cur->val 大于 p->val,同时 cur->val 大于q->val,那么就应该向左遍历(说明目标区间在左子树上)。 + +**需要注意的是此时不知道p和q谁大,所以两个都要判断** 代码如下: ``` - if (cur->val > p->val && cur->val > q->val) { - return traversal(cur->left, p, q); - } +if (cur->val > p->val && cur->val > q->val) { + TreeNode* left = traversal(cur->left, p, q); + if (left != NULL) { + return left; + } +} ``` -如果 cur->val 小于 p->val,同时 cur->val 小于 q->val,那么就应该向右遍历。 +**细心的同学会发现,在这里调用递归函数的地方,把递归函数的返回值left,直接return**。 + + +在[二叉树:公共祖先问题](https://mp.weixin.qq.com/s/n6Rk3nc_X3TSkhXHrVmBTQ)中,如果递归函数有返回值,如何区分要搜索一条边,还是搜索整个树。 + +搜索一条边的写法: ``` - } else if (cur->val < p->val && cur->val < q->val) { - return traversal(cur->right, p, q); - } +if (递归函数(root->left)) return ; + +if (递归函数(root->right)) return ; ``` -剩下的情况,我们就找到了区间使(p->val <= cur->val && cur->val <= q->val)或者是 (q->val <= cur->val && cur->val <= p->val) +搜索整个树写法: + +``` +left = 递归函数(root->left); +right = 递归函数(root->right); +left与right的逻辑处理; +``` + +本题就是标准的搜索一条边的写法,遇到递归函数的返回值,如果不为空,立刻返回。 + + +如果 cur->val 小于 p->val,同时 cur->val 小于 q->val,那么就应该向右遍历(目标区间在右子树)。 + +``` +if (cur->val < p->val && cur->val < q->val) { + TreeNode* right = traversal(cur->right, p, q); + if (right != NULL) { + return right; + } +} +``` + +剩下的情况,就是cur节点在区间(p->val <= cur->val && cur->val <= q->val)或者 (q->val <= cur->val && cur->val <= p->val)中,那么cur就是最近公共祖先了,直接返回cur。 代码如下: ``` - else { - return cur; - } +return cur; ``` 那么整体递归代码如下: -## C++递归代码 - -(我这里特意把递归的过程抽出一个函数traversal,这样代码更清晰,有助于读者理解。) - ``` class Solution { private: TreeNode* traversal(TreeNode* cur, TreeNode* p, TreeNode* q) { - if (cur->val > p->val && cur->val > q->val) { - return traversal(cur->left, p, q); - } else if (cur->val < p->val && cur->val < q->val) { - return traversal(cur->right, p, q); - } else return cur; + if (cur == NULL) return cur; + // 中 + if (cur->val > p->val && cur->val > q->val) { // 左 + TreeNode* left = traversal(cur->left, p, q); + if (left != NULL) { + return left; + } + } + + if (cur->val < p->val && cur->val < q->val) { // 右 + TreeNode* right = traversal(cur->right, p, q); + if (right != NULL) { + return right; + } + } + return cur; } public: TreeNode* lowestCommonAncestor(TreeNode* root, TreeNode* p, TreeNode* q) { - return traversal(root, p, q); } }; ``` +精简后代码如下: -## C++迭代法代码 +``` +class Solution { +public: + TreeNode* lowestCommonAncestor(TreeNode* root, TreeNode* p, TreeNode* q) { + if (root->val > p->val && root->val > q->val) { + return lowestCommonAncestor(root->left, p, q); + } else if (root->val < p->val && root->val < q->val) { + return lowestCommonAncestor(root->right, p, q); + } else return root; + } +}; +``` -同时给出一个迭代的版本,思想是一样的,代码如下: +## 迭代法 + +对于二叉搜索树的迭代法,大家应该在[二叉树:二叉搜索树登场!](https://mp.weixin.qq.com/s/vsKrWRlETxCVsiRr8v_hHg)就了解了。 + +利用其有序性,迭代的方式还是比较简单的,解题思路在递归中已经分析了。 + +迭代代码如下: ``` class Solution { @@ -96,3 +209,15 @@ public: } }; ``` + +灵魂拷问:是不是又被简单的迭代法感动到痛哭流涕? + +# 总结 + +对于二叉搜索树的最近祖先问题,其实要比[普通二叉树公共祖先问题](https://mp.weixin.qq.com/s/n6Rk3nc_X3TSkhXHrVmBTQ)简单的多。 + +不用使用回溯,二叉搜索树自带方向性,可以方便的从上向下查找目标区间,遇到目标区间内的节点,直接返回。 + +最后给出了对应的迭代法,二叉搜索树的迭代法甚至比递归更容易理解,也是因为其有序性(自带方向性),按照目标区间找就行了。 + +**就酱,学到了,就转发给身边需要学习的同学吧!** diff --git a/problems/0844.比较含退格的字符串.md b/problems/0844.比较含退格的字符串.md new file mode 100644 index 00000000..a47bdbb3 --- /dev/null +++ b/problems/0844.比较含退格的字符串.md @@ -0,0 +1,120 @@ +感觉像是使用栈 + +## 思路 + +本文将给出 空间复杂度O(n)的栈模拟方法 以及空间复杂度是O(1)的双指针方法。 + +### 普通方法(使用栈的思路) + +这道题目一看就是要使用栈的节奏,这种匹配(消除)问题也是栈的擅长所在,跟着一起刷题的同学应该知道,在[栈与队列:匹配问题都是栈的强项](https://mp.weixin.qq.com/s/eynAEbUbZoAWrk0ZlEugqg),我就已经提过了一次使用栈来做类似的事情了。 + +**那么本题,确实可以使用栈的思路,但是没有必要使用栈,因为最后比较的时候还要比较栈里的元素,有点麻烦**。 + +这里直接使用字符串string,来作为栈,末尾添加和弹出,string都有相应的接口,最后比较的时候,只要比较两个字符串就可以了,比比较栈里的元素方便一些。 + +代码如下: + +``` +class Solution { +public: + bool backspaceCompare(string S, string T) { + string s; // 当栈来用 + string t; // 当栈来用 + for (int i = 0; i < S.size(); i++) { + if (S[i] != '#') s += S[i]; + else if (!s.empty()) { + s.pop_back(); + + } + for (int i = 0; i < T.size(); i++) { + if (T[i] != '#') t += T[i]; + else if (!t.empty()) { + t.pop_back(); + } + } + if (s == t) return true; // 直接比较两个字符串是否相等,比用栈来比较方便多了 + return false; + } +}; +``` +* 时间复杂度:O(n + m), n为S的长度,m为T的长度 ,也可以理解是O(n)的时间复杂度 +* 空间复杂度:O(n + m) + +当然以上代码,大家可以发现有重复的逻辑处理S,处理T,可以把这块公共逻辑抽离出来,代码精简如下: + +``` +class Solution { +private: +string getString(const string& S) { + string s; + for (int i = 0; i < S.size(); i++) { + if (S[i] != '#') s += S[i]; + else if (!s.empty()) { + s.pop_back(); + } + } + return s; +} +public: + bool backspaceCompare(string S, string T) { + return getString(S) == getString(T); + } +}; +``` +性能依然是: +* 时间复杂度:O(n + m) +* 空间复杂度:O(n + m) + +### 优化方法(从后向前双指针) + +当然还可以有使用 O(1) 的空间复杂度来解决该问题。 + +同时从后向前遍历S和T(i初始为S末尾,j初始为T末尾),记录#的数量,模拟消除的操作,如果#用完了,就开始比较S[i]和S[j]。 + +动画如下: + + + +如果S[i]和S[j]不相同返回false,如果有一个指针(i或者j)先走到的字符串头部位置,也返回false。 + +代码如下: + +``` +class Solution { +public: + bool backspaceCompare(string S, string T) { + int sSkipNum = 0; // 记录S的#数量 + int tSkipNum = 0; // 记录T的#数量 + int i = S.size() - 1; + int j = T.size() - 1; + while (1) { + while (i >= 0) { // 从后向前,消除S的# + if (S[i] == '#') sSkipNum++; + else { + if (sSkipNum > 0) sSkipNum--; + else break; + } + i--; + } + while (j >= 0) { // 从后向前,消除T的# + if (T[j] == '#') tSkipNum++; + else { + if (tSkipNum > 0) tSkipNum--; + else break; + } + j--; + } + // 后半部分#消除完了,接下来比较S[i] != T[j] + if (i < 0 || j < 0) break; // S 或者T 遍历到头了 + if (S[i] != T[j]) return false; + i--;j--; + } + // 说明S和T同时遍历完毕 + if (i == -1 && j == -1) return true; + return false; + } +}; +``` + +* 时间复杂度:O(n + m) +* 空间复杂度:O(1) diff --git a/video/844.比较含退格的字符串.gif b/video/844.比较含退格的字符串.gif 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