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z-XD1kmIx?=v))oc$Uh7Gy%zd)&|tbjyIh77igNz^lzTb&_wrL2ARnJDw1c@o%+2QS zXi$xSS+(H? -代码如下:(详细注释) +C++代码如下:(详细注释) -``` +```C++ class Solution { public: int direction[4][2] = {0, 1, 1, 0, -1, 0, 0, -1}; @@ -50,12 +53,11 @@ result = 岛屿数量 * 4 - cover * 2; -代码如下:(详细注释) +C++代码如下:(详细注释) -``` +```C++ class Solution { public: - int direction[4][2] = {0, 1, 1, 0, -1, 0, 0, -1}; int islandPerimeter(vector>& grid) { int sum = 0; // 陆地数量 int cover = 0; // 相邻数量 diff --git a/problems/链表总结篇.md b/problems/链表总结篇.md index 8632463e..16954683 100644 --- a/problems/链表总结篇.md +++ b/problems/链表总结篇.md @@ -1,9 +1,131 @@ +> 之前链表篇没有做总结,所以是时候总结一波 -> 链表理论基础 +# 链表的理论基础 + +在这篇文章[关于链表,你该了解这些!](https://mp.weixin.qq.com/s/ntlZbEdKgnFQKZkSUAOSpQ)中,介绍了如下几点: + +* 链表的种类主要为:单链表,双链表,循环链表 +* 链表的存储方式:链表的节点在内存中是分散存储的,通过指针连在一起。 +* 链表是如何进行增删改查的。 +* 数组和链表在不同场景下的性能分析。 + +**可以说把链表基础的知识都概括了,但又不像教科书那样的繁琐**。 + +# 链表经典题目 + +## 虚拟头结点 + +在[链表:听说用虚拟头节点会方便很多?](https://mp.weixin.qq.com/s/slM1CH5Ew9XzK93YOQYSjA)中,我们讲解了链表操作中一个非常总要的技巧:虚拟头节点。 + +链表的一大问题就是操作当前节点必须要找前一个节点才能操作。这就造成了,头结点的尴尬,因为头结点没有前一个节点了。 + +**每次对应头结点的情况都要单独处理,所以使用虚拟头结点的技巧,就可以解决这个问题**。 + +在[链表:听说用虚拟头节点会方便很多?](https://mp.weixin.qq.com/s/slM1CH5Ew9XzK93YOQYSjA)中,我给出了用虚拟头结点和没用虚拟头结点的代码,大家对比一下就会发现,使用虚拟头结点的好处。 + +## 链表的基本操作 + +在[链表:一道题目考察了常见的五个操作!](https://mp.weixin.qq.com/s/Cf95Lc6brKL4g2j8YyF3Mg)中,我们通设计链表把链表常见的五个操作练习了一遍。 + +这是练习链表基础操作的非常好的一道题目,考察了: + +* 获取链表第index个节点的数值 +* 在链表的最前面插入一个节点 +* 在链表的最后面插入一个节点 +* 在链表第index个节点前面插入一个节点 +* 删除链表的第index个节点的数值 + +**可以说把这道题目做了,链表基本操作就OK了,再也不用担心链表增删改查整不明白了**。 + +这里我依然使用了虚拟头结点的技巧,大家复习的时候,可以去看一下代码。 + +## 反转链表 + +在[链表:听说过两天反转链表又写不出来了?](https://mp.weixin.qq.com/s/pnvVP-0ZM7epB8y3w_Njwg)中,讲解了如何反转链表。 + +因为反转链表的代码相对简单,有的同学可能直接背下来了,但一写还是容易出问题。 + +反转链表是面试中高频题目,很考察面试者对链表操作的熟练程度。 + +我在[文章](https://mp.weixin.qq.com/s/pnvVP-0ZM7epB8y3w_Njwg)中,给出了两种反转的方式,迭代法和递归法。 + +建议大家先学透迭代法,然后再看递归法,因为递归法比较绕,如果迭代还写不明白,递归基本也写不明白了。 + +**可以先通过迭代法,彻底弄清楚链表反转的过程!** + +## 环形链表 + +在[链表:环找到了,那入口呢?](https://mp.weixin.qq.com/s/_QVP3IkRZWx9zIpQRgajzA)中,讲解了在链表如何找环,以及如何找环的入口位置。 + +这道题目可以说是链表的比较难的题目了。 + +很多同学关注的问题是:为什么一定会相遇,快指针就不能跳过慢指针么? + +可以确定如下两点: + +* fast指针一定先进入环中,如果fast 指针和slow指针相遇的话,一定是在环中相遇,这是毋庸置疑的。 +* fast和slow都进入环里之后,fast相对于slow来说,fast是一个节点一个节点的靠近slow的,**注意是相对运动,所以fast一定可以和slow重合**。 + +如果fast是一次走三个节点,那么可能会跳过slow,因为相对于slow来说,fast是两个节点移动的。 + +确定有否有环比较容易,但是找到环的入口就不太容易了,需要点数学推理。 + +我在[链表:环找到了,那入口呢?](https://mp.weixin.qq.com/s/_QVP3IkRZWx9zIpQRgajzA)中给出了详细的推理,兼顾易懂和简洁了。 + +这是一位录友在评论区有一个疑问,感觉这个问题很不错,但评论区根本说不清楚,我就趁着总结篇,补充一下这个证明。 + +在推理过程中,**为什么第一次在环中相遇,slow的 步数 是 x+y 而不是 x + 若干环的长度 + y 呢?** + +了解这个问题一定要先把文章[链表:环找到了,那入口呢?](https://mp.weixin.qq.com/s/_QVP3IkRZWx9zIpQRgajzA)看了,即文章中如下的地方: + + -* [关于链表,你该了解这些!](https://mp.weixin.qq.com/s/ntlZbEdKgnFQKZkSUAOSpQ) - * [链表:听说用虚拟头节点会方便很多?](https://mp.weixin.qq.com/s/slM1CH5Ew9XzK93YOQYSjA) - * [链表:一道题目考察了常见的五个操作!](https://mp.weixin.qq.com/s/Cf95Lc6brKL4g2j8YyF3Mg) - * [链表:听说过两天反转链表又写不出来了?](https://mp.weixin.qq.com/s/pnvVP-0ZM7epB8y3w_Njwg) - * [链表:环找到了,那入口呢?](https://mp.weixin.qq.com/s/_QVP3IkRZWx9zIpQRgajzA) +首先slow进环的时候,fast一定是先进环来了。 + +如果slow进环入口,fast也在环入口,那么把这个环展开成直线,就是如下图的样子: + + + +可以看出如果slow 和 fast同时在环入口开始走,一定会在环入口3相遇,slow走了一圈,fast走了两圈。 + +重点来了,slow进环的时候,fast一定是在环的任意一个位置,如图: + + + +那么fast指针走到环入口3的时候,已经走了k + n 个节点,slow相应的应该走了(k + n) / 2 个节点。 + +因为k是小于n的(图中可以看出),所以(k + n) / 2 一定小于n。 + +**也就是说slow一定没有走到环入口3,而fast已经到环入口3了**。 + +这说明什么呢? + +**在slow开始走的那一环已经和fast相遇了**。 + +那有同学又说了,为什么fast不能跳过去呢? 在刚刚已经说过一次了,**fast相对于slow是一次移动一个节点,所以不可能跳过去**。 + +好了,这次把为什么第一次在环中相遇,slow的 步数 是 x+y 而不是 x + 若干环的长度 + y ,用数学推理了一下,算是对[链表:环找到了,那入口呢?](https://mp.weixin.qq.com/s/_QVP3IkRZWx9zIpQRgajzA)的补充。 + +这次可以说把环形链表这道题目的各个细节,完完整整的证明了一遍,说这是全网最详细讲解不为过吧,哈哈。 + +# 总结 + +考察链表的操作其实就是考察指针的操作,是面试中的常见类型。 + +链表篇中开头介绍[链表理论知识](https://mp.weixin.qq.com/s/slM1CH5Ew9XzK93YOQYSjA),然后分别通过经典题目介绍了如下知识点: + +* [虚拟头结点的技巧](https://mp.weixin.qq.com/s/slM1CH5Ew9XzK93YOQYSjA) +* [链表的增删改查](https://mp.weixin.qq.com/s/Cf95Lc6brKL4g2j8YyF3Mg) +* [反转一个链表](https://mp.weixin.qq.com/s/pnvVP-0ZM7epB8y3w_Njwg) +* [有否环形,以及环的入口](https://mp.weixin.qq.com/s/_QVP3IkRZWx9zIpQRgajzA) + +虽然这几篇文章都是几个月前发的了,但在在文章留言区,可以看到很多录友都在从头打卡! + +如果希望从基础学起来的同学,也可以从头学起来,从头开始打卡,打卡的同时也总结自己的所学所思,一定进步飞快! + +**在公众号左下方,「算法汇总」可以找到历史文章,都是按系列排好顺序的,快去通关学习吧!** + +![](https://img-blog.csdnimg.cn/20201030210901823.jpg) + +**「代码随想录」这么用心的公众号,不分享给身边的同学朋友啥的,是不是可惜了? 哈哈**