From a54fe17338bc06e0e9cfd15d342fe394075e210d Mon Sep 17 00:00:00 2001 From: youngyangyang04 <826123027@qq.com> Date: Thu, 29 Oct 2020 08:35:13 +0800 Subject: [PATCH] Update --- README.md | 9 +- pics/216.组合总和III.png | Bin 88651 -> 223212 bytes pics/216.组合总和III1.png | Bin 0 -> 242374 bytes problems/0077.组合.md | 2 + problems/0216.组合总和III.md | 225 +++++++++++++++---- problems/0901.股票价格跨度.md | 39 ++++ problems/1207.独一无二的出现次数.md | 5 +- 7 files changed, 228 insertions(+), 52 deletions(-) create mode 100644 pics/216.组合总和III1.png create mode 100644 problems/0901.股票价格跨度.md diff --git a/README.md b/README.md index 9677a99f..201a4c44 100644 --- a/README.md +++ b/README.md @@ -14,6 +14,8 @@ # 算法文章精选 +**提示:在电脑端看如下文章的,看不到文章的评论区,建议在手机端「代码随想录」公众号里也翻一下对应的文章,评论区有录友们的打卡总结,相信会和你有不少共鸣!** + * 编程语言 * [C++面试&C++学习指南知识点整理](https://github.com/youngyangyang04/TechCPP) @@ -414,17 +416,16 @@ 大家好,我是程序员Carl,哈工大师兄,ACM 校赛、黑龙江省赛、东北四省赛金牌、亚洲区域赛铜牌获得者,先后在腾讯和百度从事后端技术研发,CSDN博客专家。对算法和C++后端技术有一定的见解,利用工作之余重新刷leetcode。 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zef91fA}5v!$>+3y%^xTLsr1ylEnjPje=7;pZ82a2%FZdr>EpG~6mxXCz=op*iN0%t zhaPn-#*4OY_EZ1?>{w(61q)J!pMi~O2QYF)pI*|9mt@v&CU`7f7Vn<%!~Kp15}i|7 z-%J?4bk>#n<=S92ic6~8llK61e$`avUW~3`yqn30jZi&D9(T#~ok>XNyTq1bgCb`I z+vSPCzK^>u4cHK_VMJJj{bb9S$?&uSqkW2vdbsa4JN)nlA&IT0HKpX{w`LQp76x32 z^-CLBO+*8PZ)hLxxU=|SioRTHK0oj>kkG2dpFyPI*U{^1Y(fuMCYK+&hsQ1uSZCXQ z+O&_af5+q&^fEuu9Ol%eszA;7Sn!5>Cuxi%E3_lQ{FlI1lLH5BQeb(5Z0GLJAdEJ< zHC`hG+2$;N2m^Xy9r)yT!__Hw)`}&L{WC~{kOc{0B8u@y!2_Z0OC=si4L4(!D|k*X$Y#ryZjT<{i*4H!7uhH0F3nv_ip?N+BV2i z_mWAa;1|h|2g?%6(B^w7-#(B(CJ?Q(cfMYod=+bf^Ls_-p`r+%6$OmlVbrv zoV^#}{KZ8796UKK4lw7?ocJci|Lyq|5HK9HwX^oGNAYvb1@N%SD97#_{=Yr{Sq2Ms zyT@PtQsjSpmnA+n+5Jp?pZphi;V%JfP9QLxgV+zZer6l~T$X?LgRP|4*c&fto&9HI z`0M9oG1x#7b%7 literal 0 HcmV?d00001 diff --git a/problems/0077.组合.md b/problems/0077.组合.md index 74b0d95a..35499e68 100644 --- a/problems/0077.组合.md +++ b/problems/0077.组合.md @@ -237,3 +237,5 @@ void backtracking(参数) { **就酱,如果对你有帮助,就帮Carl转发一下吧,让更多的同学发现这里!** + +**[本题剪枝操作文章链接](https://mp.weixin.qq.com/s/Ri7spcJMUmph4c6XjPWXQA)** diff --git a/problems/0216.组合总和III.md b/problems/0216.组合总和III.md index ae18a3fa..d2e3762e 100644 --- a/problems/0216.组合总和III.md +++ b/problems/0216.组合总和III.md @@ -1,84 +1,217 @@ -# 第216题. 组合总和 III +## 链接 +https://leetcode-cn.com/problems/combination-sum-iii/ + +> 别看本篇选的是组合总和III,而不是组合总和,本题和上一篇[回溯算法:求组合问题!](https://mp.weixin.qq.com/s/OnBjbLzuipWz_u4QfmgcqQ)相比难度刚刚好! + +# 第216题.组合总和III + +链接:https://leetcode-cn.com/problems/combination-sum-iii/ + 找出所有相加之和为 n 的 k 个数的组合。组合中只允许含有 1 - 9 的正整数,并且每种组合中不存在重复的数字。 -说明: +说明: +* 所有数字都是正整数。 +* 解集不能包含重复的组合。  -所有数字都是正整数。 -解集不能包含重复的组合。  +示例 1: +输入: k = 3, n = 7 +输出: [[1,2,4]] -示例 1: - -输入: k = 3, n = 7 -输出: [[1,2,4]] -示例 2: - -输入: k = 3, n = 9 -输出: [[1,2,6], [1,3,5], [2,3,4]] +示例 2: +输入: k = 3, n = 9 +输出: [[1,2,6], [1,3,5], [2,3,4]] # 思路 -这道题目注意一下几点: +本题就是在[1,2,3,4,5,6,7,8,9]这个集合中找到和为n的k个数的组合。 -* 解集不能包含重复的组合。 说明不用去重了,难度就小一些。 -* 求的是组合,那么集合没有顺序,for里面依然要从startIndex开始(如果是排列的话,就从0开始) +相对于[回溯算法:求组合问题!](https://mp.weixin.qq.com/s/OnBjbLzuipWz_u4QfmgcqQ),无非就是多了一个限制,本题是要找到和为n的k个数的组合,而整个集合已经是固定的了[1,...,9]。 -本题k相当于限制了树的深度,9就是树的宽度。 +想到这一点了,做过[77. 组合](https://mp.weixin.qq.com/s/OnBjbLzuipWz_u4QfmgcqQ)之后,本题是简单一些了。 + +本题k相当于了树的深度,9(因为整个集合就是9个数)就是树的宽度。 + +例如 k = 2,n = 4的话,就是在集合[1,2,3,4,5,6,7,8,9]中求 k(个数) = 2, n(和) = 4的组合。 选取过程如图: -那么这还是一道标准的模板题,模板: +图中,可以看出,只有最后取到集合(1,3)和为4 符合条件。 + + +## 回溯三部曲 + +* **确定递归函数参数** + +和[回溯算法:求组合问题!](https://mp.weixin.qq.com/s/OnBjbLzuipWz_u4QfmgcqQ)一样,依然需要一维数组path来存放符合条件的结果,二维数组result来存放结果集。 + +这里我依然定义path 和 result为全局变量。 + +至于为什么取名为path?从上面树形结构中,可以看出,结果其实就是一条根节点到叶子节点的路径。 ``` -backtracking() { - if (终止条件) { - 存放结果; - } +vector> result; // 存放结果集 +vector path; // 符合条件的结果 +``` - for (选择:选择列表(可以想成树中节点孩子的数量)) { - 递归,处理节点; - backtracking(); - 回溯,撤销处理结果 - } +接下来还需要如下参数: + +* targetSum(int)目标和,也就是题目中的n。 +* k(int)就是题目中要求k个数的集合。 +* sum(int)为已经收集的元素的总和,也就是path里元素的总和。 +* startIndex(int)为下一层for循环搜索的起始位置。 + +所以代码如下: + +``` +vector> result; +vector path; +void backtracking(int targetSum, int k, int sum, int startIndex) +``` +其实这里sum这个参数也可以省略,每次targetSum减去选取的元素数值,然后判断如果targetSum为0了,说明收集到符合条件的结果了,我这里为了直观便于理解,还是加一个sum参数。 + +还要强调一下,回溯法中递归函数参数很难一次性确定下来,一般先写逻辑,需要啥参数了,填什么参数。 + +* 确定终止条件 + +什么时候终止呢? + +在上面已经说了,k其实就已经限制树的深度,因为就取k个元素,树再往下深了没有意义。 + +所以如果path.size() 和 k相等了,就终止。 + +如果此时path里收集到的元素和(sum) 和targetSum(就是题目描述的n)相同了,就用result收集当前的结果。 + +所以 终止代码如下: + +``` +if (path.size() == k) { + if (sum == targetSum) result.push_back(path); + return; // 如果path.size() == k 但sum != targetSum 直接返回 } ``` +* **单层搜索过程** +本题和[回溯算法:求组合问题!](https://mp.weixin.qq.com/s/OnBjbLzuipWz_u4QfmgcqQ)区别之一就是集合固定的就是9个数[1,...,9],所以for循环固定i<=9 -# C++代码 +如图: + + +处理过程就是 path收集每次选取的元素,相当于树型结构里的边,sum来统计path里元素的总和。 + +代码如下: + +``` +for (int i = startIndex; i <= 9; i++) { + sum += i; + path.push_back(i); + backtracking(targetSum, k, sum, i + 1); // 注意i+1调整startIndex + sum -= i; // 回溯 + path.pop_back(); // 回溯 +} +``` + +**别忘了处理过程 和 回溯过程是一一对应的,处理有加,回溯就要有减!** + +参照[关于回溯算法,你该了解这些!](https://mp.weixin.qq.com/s/gjSgJbNbd1eAA5WkA-HeWw)中的模板,不难写出如下C++代码: ``` class Solution { private: - vector> result; - vector path; - void backtracking(int target, int k, int num, int sum, int startIndex) { - if (sum > target || num > k) { // 剪枝操作,如果sum大于target或者num大于k了没有继续搜索的必要了 - return; + vector> result; // 存放结果集 + vector path; // 符合条件的结果 + // targetSum:目标和,也就是题目中的n。 + // k:题目中要求k个数的集合。 + // sum:已经收集的元素的总和,也就是path里元素的总和。 + // startIndex:下一层for循环搜索的起始位置。 + void backtracking(int targetSum, int k, int sum, int startIndex) { + if (path.size() == k) { + if (sum == targetSum) result.push_back(path); + return; // 如果path.size() == k 但sum != targetSum 直接返回 } - if (num == k && sum == target) { - result.push_back(path); - return; - } - for (int i = startIndex; i <= 9; i++) { - sum += i; - path.push_back(i); - num++; - backtracking(target, k, num, sum, i + 1); - num--; - sum -= i; - path.pop_back(); + sum += i; // 处理 + path.push_back(i); // 处理 + backtracking(targetSum, k, sum, i + 1); // 注意i+1调整startIndex + sum -= i; // 回溯 + path.pop_back(); // 回溯 } } public: vector> combinationSum3(int k, int n) { - backtracking(n, k, 0, 0, 1); + result.clear(); // 可以不加 + path.clear(); // 可以不加 + backtracking(n, k, 0, 1); return result; - } }; ``` + +## 剪枝 + +这道题目,剪枝操作其实是很容易想到了,想必大家看上面的树形图的时候已经想到了。 + +如图: + + +已选元素总和如果已经大于n(图中数值为4)了,那么往后遍历就没有意义了,直接剪掉。 + +那么剪枝的地方一定是在递归终止的地方剪,剪枝代码如下: + +``` +if (sum > targetSum) { // 剪枝操作 + return; +} +``` + +最后C++代码如下: + +``` +class Solution { +private: + vector> result; // 存放结果集 + vector path; // 符合条件的结果 + // targetSum:目标和,也就是题目中的n。 + // k:题目中要求k个数的集合。 + // sum:已经收集的元素的总和,也就是path里元素的总和。 + // startIndex:下一层for循环搜索的起始位置。 + void backtracking(int targetSum, int k, int sum, int startIndex) { + if (sum > targetSum) { // 剪枝操作 + return; // 如果path.size() == k 但sum != targetSum 直接返回 + } + if (path.size() == k) { + if (sum == targetSum) result.push_back(path); + return; + } + for (int i = startIndex; i <= 9; i++) { + sum += i; // 处理 + path.push_back(i); // 处理 + backtracking(targetSum, k, sum, i + 1); // 注意i+1调整startIndex + sum -= i; // 回溯 + path.pop_back(); // 回溯 + } + } + +public: + vector> combinationSum3(int k, int n) { + result.clear(); // 可以不加 + path.clear(); // 可以不加 + backtracking(n, k, 0, 1); + return result; + } +}; +``` + +# 总结 + +开篇就介绍了本题与[回溯算法:求组合问题!](https://mp.weixin.qq.com/s/OnBjbLzuipWz_u4QfmgcqQ)的区别,相对来说加了元素总和的限制,如果做完[回溯算法:求组合问题!](https://mp.weixin.qq.com/s/OnBjbLzuipWz_u4QfmgcqQ)再做本题在合适不过。 + +分析完区别,依然把问题抽象为树形结构,按照回溯三部曲进行讲解,最后给出剪枝的优化。 + +相信做完本题,大家对组合问题应该有初步了解了。 + +**就酱,如果感觉对你有帮助,就帮Carl转发一下吧,让更多小伙伴知道这里!** diff --git a/problems/0901.股票价格跨度.md b/problems/0901.股票价格跨度.md new file mode 100644 index 00000000..e3b546ea --- /dev/null +++ b/problems/0901.股票价格跨度.md @@ -0,0 +1,39 @@ + +这道题也不是单调栈的简单题 + +需要记录 传入的所有price + +注意 股票价格相同的情况 + +需要自己维护一个数组,用stack来记录下表, 因为数组下标从0开始的,注意 栈为空的两种情况(代码中注释)。 + +如果这道题,不用这个应用场景,而是直接给出输入数组的话,会简单一些。 + +这道题目他们都用两个栈来实现,貌似代码简介一些,但我这个最直观。 可以画一个图 + +``` +class StockSpanner { +public: + stack st; + vector prices; + StockSpanner() { + } + + int next(int price) { + prices.push_back(price); + while (!st.empty() && prices[st.top()] <= price) { // 注意这里等于的情况 + st.pop(); + } + int result; + int curPriceIndex = prices.size() - 1; + if (!st.empty()) { // 栈不为空,求差值 + result = curPriceIndex - st.top(); + } else { // 栈为空 + if (prices.size() == 1) result = 1; // 如果是放入第一个元素就是,result是1 + else result = curPriceIndex + 1; // 不是放入的第一个元素了,那么就应该是当前索引+1 + } + st.push(curPriceIndex); + return result; + } +}; +``` diff --git a/problems/1207.独一无二的出现次数.md b/problems/1207.独一无二的出现次数.md index 832a9084..e6488cf1 100644 --- a/problems/1207.独一无二的出现次数.md +++ b/problems/1207.独一无二的出现次数.md @@ -1,4 +1,7 @@ +## 链接 +https://leetcode-cn.com/problems/unique-number-of-occurrences/ + ## 思路 这道题目数组在是哈希法中的经典应用,如果对数组在哈希法中的使用还不熟悉的同学可以看这两篇:[数组在哈希法中的应用](https://mp.weixin.qq.com/s/vM6OszkM6L1Mx2Ralm9Dig)和[哈希法:383. 赎金信](https://mp.weixin.qq.com/s/sYZIR4dFBrw_lr3eJJnteQ) @@ -7,8 +10,6 @@ 回归本题,**本题强调了-1000 <= arr[i] <= 1000**,那么就可以用数组来做哈希,arr[i]作为哈希表(数组)的下标,那么arr[i]可以是负数,怎么办?负数不能做数组下标。 -**PS:本文[leetcode刷题攻略](https://github.com/youngyangyang04/leetcode-master)已经收录,相信可以帮你稳稳的提升算法能力,给star支持一下吧!** - **此时可以定义一个2000大小的数组,例如int count[2002];**,统计的时候,将arr[i]统一加1000,这样就可以统计arr[i]的出现频率了。

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