From 2d540a964878db0231d3529f9303483a057b44cc Mon Sep 17 00:00:00 2001 From: youngyangyang04 <826123027@qq.com> Date: Wed, 16 Sep 2020 09:23:38 +0800 Subject: [PATCH] Update --- README.md | 4 + pics/93.复原IP地址.png | Bin 0 -> 149340 bytes problems/0093.复原IP地址.md | 117 +++++++++++++++++- problems/0131.分割回文串.md | 44 ++++++- problems/0150.逆波兰表达式求值.md | 93 +++++++++++++- problems/0226.翻转二叉树.md | 2 + ...指Offer59-I.滑动窗口的最大值.md | 45 +++++++ video/150.逆波兰表达式求值.gif | Bin 0 -> 1444756 bytes video/150.逆波兰表达式求值.mp4 | Bin 0 -> 1183964 bytes 9 files changed, 296 insertions(+), 9 deletions(-) create mode 100644 pics/93.复原IP地址.png create mode 100644 problems/剑指Offer59-I.滑动窗口的最大值.md create mode 100644 video/150.逆波兰表达式求值.gif create mode 100644 video/150.逆波兰表达式求值.mp4 diff --git a/README.md b/README.md index e50dc6c3..66ed1706 100644 --- a/README.md +++ b/README.md @@ -59,6 +59,9 @@ * [字符串:总结篇!](https://mp.weixin.qq.com/s/gtycjyDtblmytvBRFlCZJg) * [栈与队列:来看看栈和队列不为人知的一面](https://mp.weixin.qq.com/s/VZRjOccyE09aE-MgLbCMjQ) * [栈与队列:我用栈来实现队列怎么样?](https://mp.weixin.qq.com/s/P6tupDwRFi6Ay-L7DT4NVg) +* [栈与队列:用队列实现栈还有点别扭](https://mp.weixin.qq.com/s/yzn6ktUlL-vRG3-m5a8_Yw) +* [栈与队列:系统中处处都是栈的应用](https://mp.weixin.qq.com/s/nLlmPMsDCIWSqAtr0jbrpQ) +* [栈与队列:匹配问题都是栈的强项](https://mp.weixin.qq.com/s/eynAEbUbZoAWrk0ZlEugqg) (持续更新中....) @@ -475,6 +478,7 @@ backtracking() { |[剑指Offer05.替换空格](https://github.com/youngyangyang04/leetcode/blob/master/problems/剑指Offer05.替换空格.md) |字符串 |简单|**双指针**| |[ 剑指Offer58-I.翻转单词顺序](https://github.com/youngyangyang04/leetcode/blob/master/problems/剑指Offer05.替换空格.md) |字符串 |简单|**模拟/双指针**| |[剑指Offer58-II.左旋转字符串](https://github.com/youngyangyang04/leetcode/blob/master/problems/剑指Offer58-II.左旋转字符串.md) |字符串 |简单|**反转操作**| +|[剑指Offer59-I.滑动窗口的最大值](https://github.com/youngyangyang04/leetcode/blob/master/problems/剑指Offer59-I.滑动窗口的最大值.md) |滑动窗口/队列 |困难|**单调队列**| |[面试题02.07.链表相交](https://github.com/youngyangyang04/leetcode/blob/master/problems/面试题02.07.链表相交.md) |链表 |简单|**模拟**| 持续更新中.... diff --git a/pics/93.复原IP地址.png b/pics/93.复原IP地址.png new file mode 100644 index 0000000000000000000000000000000000000000..63d11f2efb2ec23446d9749f24dc7f3a555c0c1d GIT binary patch literal 149340 zcmeFZWmr~g*ET9FR1j$dLApzjR$98dQ-PZf=>`F%qy%odk?w8~q`Nz$Q9!zDU+7x6 z)_UIe`SzcE>_6WR4-uv}bB=3VW1QnW&ujY2N{b*pzJAO~8vYK9ukjtYn@hkST=3`4oj;Oc z?)(A%hPnA(GVEVJy~mOK$6sH=&fQ$dEin$cbBFJanBYrAN0`lo`_T%cV?Nkef`Tsv z`KY}Dv_2y%D{kJc)xHat?pJ^8b*x@kPeL_O@M=5DkLv7$R&ffIkRYaD0KC_%ha2Y) zNv3dpgI90K_6ycJo%&-W4Ln@(3)|)ig!%5kqQ1QYM|1}U{(t(?6PBz<5~d=C zLg4>!9p9Z4@B1+S{jzzNiqXz$TJ1ujA{HbdcVnO{ge>}fS zziRTj%Vsh{<#K&_oXh#3fDjf+GEnd0U^-FsI{oOi-aoQGc?awq%sK9~*1r-}kr{To z{x~tgrtih*W=^#xJROJUWU1k_l8RRO`u#=tzpnea+4!_E_|`i%rUjO6v-0hvVUk;9 z%Rur=?`1A#)VF*Fu*?QM@U#ZKu~4T!BKiN3GeSZj*Rm`qvH$opYx#;Xp06i+n;nj- zFdTI+pAi*_!qGQg>&D>$N#9R9hRVMpSpP%;op{RRb9BV<84b30;f+w_?-6s 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b/problems/0093.复原IP地址.md index 66ad1ec6..3da5002c 100644 --- a/problems/0093.复原IP地址.md +++ b/problems/0093.复原IP地址.md @@ -1,8 +1,117 @@ ## 题目地址 https://leetcode-cn.com/problems/restore-ip-addresses/ +# 93. 复原IP地址 + +给定一个只包含数字的字符串,复原它并返回所有可能的 IP 地址格式。 + +有效的 IP 地址 正好由四个整数(每个整数位于 0 到 255 之间组成,且不能含有前导 0),整数之间用 '.' 分隔。 + +例如:"0.1.2.201" 和 "192.168.1.1" 是 有效的 IP 地址,但是 "0.011.255.245"、"192.168.1.312" 和 "192.168@1.1" 是 无效的 IP 地址。 + +  + +示例 1: +输入:s = "25525511135" +输出:["255.255.11.135","255.255.111.35"] + +示例 2: +输入:s = "0000" +输出:["0.0.0.0"] + +示例 3: +输入:s = "1111" +输出:["1.1.1.1"] + +示例 4: +输入:s = "010010" +输出:["0.10.0.10","0.100.1.0"] + +示例 5: +输入:s = "101023" +输出:["1.0.10.23","1.0.102.3","10.1.0.23","10.10.2.3","101.0.2.3"] + +提示: +0 <= s.length <= 3000 +s 仅由数字组成 + + ## 思路 +这道题目相信大家刚看时看到的时候,应该会一脸茫然。 + +那么只要意识到这是切割问题,那么切割问题就可以使用回溯搜索法把所有可能性搜出来,和[0131.分割回文串](https://github.com/youngyangyang04/leetcode/blob/master/problems/0131.分割回文串.md) 类似。 + +那么切割问题可以抽象为树型结构,如图: + + + +终止条件: 和[0131.分割回文串](https://github.com/youngyangyang04/leetcode/blob/master/problems/0131.分割回文串.md) 不同,本题明确要求只会分成4段,所以不能用切割线切到最后作为终止条件,而是分割的段数作为终止条件。 + +代码如下: + +``` +if (pointNum == 3) { // 逗点数量为3时,分隔结束 + // 判断第四段子字符串是否合法,如果合法就放进result中 + if (isValid(s, startIndex, s.size() - 1)) { + result.push_back(s); + } + return; +} +``` + +那么再来看循环遍历的过程如何截取子串。 + +在`for (int i = startIndex; i < s.size(); i++)`循环中 [startIndex, i]这个区间就是截取的子串,需要判断这个子串是否合法,如果合法就在字符串后面加上符号`.`表示已经分割。 + +然后就是递归和回溯的过程: + +递归调用时,下一层递归的startIndex要从i+2开始(因为刚刚在字符串中加入了分隔符`.`),同时记录分割符的数量pointNum 要 +1。 + +回溯的时候,就将刚刚加入的分隔符`.` 删掉就可以了,**pointNum其实也要减一,但是 pointNum+1 的逻辑放在递归函数的参数里了,这里相当于隐藏了回溯pointNum的过程**。 + +递归和回溯代码如下: + +``` +// 插入逗点之后下一个子串的起始位置为i+2 +backtracking(s, i + 2, pointNum + 1); +s.erase(s.begin() + i + 1); // 回溯时删掉逗点 +``` + +最后就是在写一个判断段位是否是有效段位了。 + +主要考虑到如下三点: + +* 段位以0为开头的数字不合法 +* 段位里有非正整数字符不合法 +* 段位如果大于255了不合法 + +代码如下: + +``` +// 判断字符串s在左闭又闭区间[start, end]所组成的数字是否合法 +bool isValid(const string& s, int start, int end) { + if (start > end) { + return false; + } + if (s[start] == '0' && start != end) { // 0开头的数字不合法 + return false; + } + int num = 0; + for (int i = start; i <= end; i++) { + if (s[i] > '9' || s[i] < '0') { // 遇到非数字字符不合法 + return false; + } + num = num * 10 + (s[i] - '0'); + if (num > 255) { // 如果大于255了不合法 + return false; + } + } + return true; +} +``` + +关键代码已经讲完,整体代码如下: ## C++代码 @@ -11,7 +120,7 @@ class Solution { private: vector result;// 记录结果 // startIndex: 搜索的起始位置,pointNum:添加逗点的数量 - void search(string& s, int startIndex, int pointNum) { + void backtracking(string& s, int startIndex, int pointNum) { if (pointNum == 3) { // 逗点数量为3时,分隔结束 // 判断第四段子字符串是否合法,如果合法就放进result中 if (isValid(s, startIndex, s.size() - 1)) { @@ -26,7 +135,7 @@ private: // 合法,在i的后面插入一个逗点 s.insert(s.begin() + i + 1 , '.'); // 插入逗点之后下一个子串的起始位置为i+2 - search(s, i + 2, pointNum + 1); + backtracking(s, i + 2, pointNum + 1); s.erase(s.begin() + i + 1); // 回溯时删掉逗点 } else break; } @@ -36,7 +145,7 @@ private: if (start > end) { return false; } - if (s[start] == '0' && start != end) {// 0开头的数字不合法 + if (s[start] == '0' && start != end) { // 0开头的数字不合法 return false; } int num = 0; @@ -54,7 +163,7 @@ private: public: vector restoreIpAddresses(string s) { result.clear(); - search(s, 0, 0); + backtracking(s, 0, 0); return result; } }; diff --git a/problems/0131.分割回文串.md b/problems/0131.分割回文串.md index 17f378e9..1e1244fb 100644 --- a/problems/0131.分割回文串.md +++ b/problems/0131.分割回文串.md @@ -68,9 +68,51 @@ void backtracking (const string& s, int startIndex) { } ``` -在来看看在递归循环,中如何截取子串呢 +在来看看在递归循环,中如何截取子串呢? +在`for (int i = startIndex; i < s.size(); i++)`循环中,我们 定义了起始位置startIndex,那么 [startIndex, i] 就是要截取的子串。 +首先判断这个子串是不是回文,如果是回文,就加入在`vector path`中,path用来记录切割过的回文子串。 + +代码如下: + +``` +for (int i = startIndex; i < s.size(); i++) { + if (isPalindrome(s, startIndex, i)) { // 是回文子串 + // 获取[startIndex,i]在s中的子串 + string str = s.substr(startIndex, i - startIndex + 1); + path.push_back(str); + } else { // 如果不是则直接跳过 + continue; + } +} +``` + +然后就开始递归与回溯的过程,递归的时候,我们要传入i+1 作为下一轮递归的遍历的其实位置(同样也就是切割线)。 大家可以发现在处理组合问题中,也要传入的是i+1,所以 切割问题和组合问题是最像的。 + +代码如下: + +``` +backtracking(s, i + 1, path); // 寻找i+1为起始位置的子串 +path.pop_back(); // 回溯过程,弹出本次已经填在的子串 +``` + +最后我们看一下回文子串要如何判断了,判断一个字符串是否是回文。 + +可以使用双指针法,一个指针从前向后,一个指针从后先前,如果前后指针所指向的元素是相等的,就是回文字符串了。 + +代码如下: +``` + bool isPalindrome(const string& s, int start, int end) { + for (int i = start, j = end; i < j; i++, j--) { + if (s[i] != s[j]) { + return false; + } + } + return true; + } +``` +此时关键代码已经讲解完毕,整体代码如下(详细注释了) ## C++代码 ``` diff --git a/problems/0150.逆波兰表达式求值.md b/problems/0150.逆波兰表达式求值.md index e85f5834..dc85b481 100644 --- a/problems/0150.逆波兰表达式求值.md +++ b/problems/0150.逆波兰表达式求值.md @@ -1,9 +1,73 @@ ## 题目地址 https://leetcode-cn.com/problems/evaluate-reverse-polish-notation/ -## 思路 +> 这不仅仅是一道好题,也展现出计算机的思考方式 -这道题目相当于是二叉树中的后序遍历,也引申出栈与递归之间在某种程度上是可以转换的! +# 150. 逆波兰表达式求值 +根据 逆波兰表示法,求表达式的值。 + +有效的运算符包括 + ,  - ,  * ,  / 。每个运算对象可以是整数,也可以是另一个逆波兰表达式。 + +说明: + +整数除法只保留整数部分。 +给定逆波兰表达式总是有效的。换句话说,表达式总会得出有效数值且不存在除数为 0 的情况。 +  + +示例 1: +输入: ["2", "1", "+", "3", " * "] +输出: 9 +解释: 该算式转化为常见的中缀算术表达式为:((2 + 1) * 3) = 9 + +示例 2: +输入: ["4", "13", "5", "/", "+"] +输出: 6 +解释: 该算式转化为常见的中缀算术表达式为:(4 + (13 / 5)) = 6 + +示例 3: +输入: ["10", "6", "9", "3", "+", "-11", " * ", "/", " * ", "17", "+", "5", "+"] +输出: 22 +解释: +该算式转化为常见的中缀算术表达式为: + ((10 * (6 / ((9 + 3) * -11))) + 17) + 5 += ((10 * (6 / (12 * -11))) + 17) + 5 += ((10 * (6 / -132)) + 17) + 5 += ((10 * 0) + 17) + 5 += (0 + 17) + 5 += 17 + 5 += 22 +  + +逆波兰表达式:是一种后缀表达式,所谓后缀就是指算符写在后面。 + +平常使用的算式则是一种中缀表达式,如 ( 1 + 2 ) * ( 3 + 4 ) 。 + +该算式的逆波兰表达式写法为 ( ( 1 2 + ) ( 3 4 + ) * ) 。 + +逆波兰表达式主要有以下两个优点: + +* 去掉括号后表达式无歧义,上式即便写成 1 2 + 3 4 + * 也可以依据次序计算出正确结果。 + +* 适合用栈操作运算:遇到数字则入栈;遇到算符则取出栈顶两个数字进行计算,并将结果压入栈中。 + +# 思路 + +在上一篇文章中[栈与队列:匹配问题都是栈的强项](https://mp.weixin.qq.com/s/eynAEbUbZoAWrk0ZlEugqg)提到了 递归就是用栈来实现的。 + +所以**栈与递归之间在某种程度上是可以转换的!**这一点我们在后续讲解二叉树的时候,会更详细的讲解到。 + +那么来看一下本题,**其实逆波兰表达式相当于是二叉树中的后序遍历**。 大家可以把运算符作为中间节点,按照后序遍历的规则画出一个二叉树。 + +但我们没有必要从二叉树的角度去解决这个问题,只要知道逆波兰表达式是用后续遍历的方式把二叉树序列化了,就可以了。 + +在进一步看,本题中每一个子表达式要得出一个结果,然后拿这个结果再进行运算,那么**这岂不就是一个相邻字符串消除的过程,和[栈与队列:匹配问题都是栈的强项](https://mp.weixin.qq.com/s/eynAEbUbZoAWrk0ZlEugqg)中的对对碰游戏是不是就非常像了。** + +如动画所示: + + +相信看完动画大家应该知道,这和[1047. 删除字符串中的所有相邻重复项](https://mp.weixin.qq.com/s/eynAEbUbZoAWrk0ZlEugqg)是差不错的,只不过本题不要相邻元素做消除了,而是做运算! + +代码如下: ## C++代码 @@ -26,9 +90,30 @@ public: st.push(stoi(tokens[i])); } } - return st.top(); + int result = st.top(); + st.pop(); // 把栈里最后一个元素弹出(其实不弹出也没事) + return result; } }; ``` -> 更过算法干货文章持续更新,可以微信搜索「代码随想录」第一时间围观,关注后,回复「Java」「C++」 「python」「简历模板」「数据结构与算法」等等,就可以获得我多年整理的学习资料。 + +# 题外话 + +我们习惯看到的表达式都是中缀表达式,因为符合我们的习惯,但是中缀表达式对于计算机来说就不是很友好了。 + +例如:4 + 13 / 5,这就是中缀表达式,计算机从左到右去扫描的话,扫到13,还要判断13后面是什么运算法,还要比较一下优先级,然后13还和后面的5做运算,做完运算之后,还要向前回退到 4 的位置,继续做加法,你说麻不麻烦! + +那么将中缀表达式,转化为后缀表达式之后:["4", "13", "5", "/", "+"] ,就不一样了,计算机可以利用栈里顺序处理,不需要考虑优先级了。也不用回退了, **所以后缀表达式对计算机来说是非常友好的。** + +可以说本题不仅仅是一道好题,也展现出计算机的思考方式。 + +在1970年代和1980年代,惠普在其所有台式和手持式计算器中都使用了RPN(后缀表达式),直到2020年代仍在某些模型中使用了RPN。 + +参考维基百科如下: + +> During the 1970s and 1980s, Hewlett-Packard used RPN in all of their desktop and hand-held calculators, and continued to use it in some models into the 2020s. + + + +> 更多算法干货文章持续更新,可以微信搜索「代码随想录」第一时间围观,关注后,回复「Java」「C++」 「python」「简历模板」「数据结构与算法」等等,就可以获得我多年整理的学习资料。 diff --git a/problems/0226.翻转二叉树.md b/problems/0226.翻转二叉树.md index b8140ff8..9c2f5208 100644 --- a/problems/0226.翻转二叉树.md +++ b/problems/0226.翻转二叉树.md @@ -5,6 +5,8 @@ https://leetcode-cn.com/problems/invert-binary-tree/ ### 递归法 写递归算法的时候,要想一想是采用前中后序哪种遍历方式 +o +如果对递归还不熟,可以看这里[彻底吃透二叉树的前中后序递归法和迭代法!!](https://leetcode-cn.com/problems/binary-tree-inorder-traversal/solution/che-di-chi-tou-er-cha-shu-de-qian-zhong-hou-xu-d-2/) 我们先看看递归算法,对于二叉树的递归方式有三种前中后序,先来看看前序遍历。 diff --git a/problems/剑指Offer59-I.滑动窗口的最大值.md b/problems/剑指Offer59-I.滑动窗口的最大值.md new file mode 100644 index 00000000..ec8fee37 --- /dev/null +++ b/problems/剑指Offer59-I.滑动窗口的最大值.md @@ -0,0 +1,45 @@ + +原理:[0239.滑动窗口最大值](https://github.com/youngyangyang04/leetcode/blob/master/problems/0239.滑动窗口最大值.md) |滑动窗口/队列 |困难| **单调队列**| + +``` +class Solution { +public: + class MyQueue { //单调队列(从大到小) + public: + deque que; // 使用deque来实现单调队列 + void pop(int value) { + if (!que.empty() && value == que.front()) { + que.pop_front(); + } + } + void push(int value) { + while (!que.empty() && value > que.back()) { + que.pop_back(); + } + que.push_back(value); + + } + int front() { + return que.front(); + } + }; + vector maxSlidingWindow(vector& nums, int k) { + MyQueue que; + vector result; + if (nums.empty()) { + return result; + } + for (int i = 0; i < k; i++) { // 先将前k的元素放进队列 + que.push(nums[i]); + } + result.push_back(que.front()); // result 记录前k的元素的最大值 + for (int i = k; i < nums.size(); i++) { + que.pop(nums[i - k]); // 模拟滑动窗口的移动 + que.push(nums[i]); // 模拟滑动窗口的移动 + result.push_back(que.front()); // 记录对应的最大值 + } + return result; + } +}; + +``` diff --git a/video/150.逆波兰表达式求值.gif 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