From 60fa8d03eaaa6aabfb4d4f2671c51568c609fe7c Mon Sep 17 00:00:00 2001 From: youngyangyang04 <826123027@qq.com> Date: Fri, 30 Oct 2020 10:26:02 +0800 Subject: [PATCH] Update --- README.md | 3 + pics/17. 电话号码的字母组合.png | Bin 60700 -> 128255 bytes pics/463.岛屿的周长.png | Bin 0 -> 31992 bytes pics/463.岛屿的周长1.png | Bin 0 -> 51043 bytes pics/55.跳跃游戏.png | Bin 0 -> 63937 bytes problems/0017.电话号码的字母组合.md | 205 ++++++++++++++---- problems/0055.跳跃游戏.md | 41 ++++ problems/0077.组合优化.md | 2 +- .../0129.求根到叶子节点数字之和.md | 21 +- problems/0216.组合总和III.md | 8 +- problems/0463.岛屿的周长.md | 78 +++++++ 11 files changed, 308 insertions(+), 50 deletions(-) create mode 100644 pics/463.岛屿的周长.png create mode 100644 pics/463.岛屿的周长1.png create mode 100644 pics/55.跳跃游戏.png create mode 100644 problems/0055.跳跃游戏.md create mode 100644 problems/0463.岛屿的周长.md diff --git a/README.md b/README.md index dfe008a2..40c975dc 100644 --- a/README.md +++ b/README.md @@ -132,6 +132,7 @@ * [关于回溯算法,你该了解这些!](https://mp.weixin.qq.com/s/gjSgJbNbd1eAA5WkA-HeWw) * [回溯算法:求组合问题!](https://mp.weixin.qq.com/s/OnBjbLzuipWz_u4QfmgcqQ) * [回溯算法:组合问题再剪剪枝](https://mp.weixin.qq.com/s/Ri7spcJMUmph4c6XjPWXQA) + * [回溯算法:求组合总和!](https://mp.weixin.qq.com/s/HX7WW6ixbFZJASkRnCTC3w) (持续更新中....) @@ -305,6 +306,7 @@ |[0051.N皇后](https://github.com/youngyangyang04/leetcode/blob/master/problems/0051.N皇后.md) |回溯|困难| **回溯**| |[0052.N皇后II](https://github.com/youngyangyang04/leetcode/blob/master/problems/0052.N皇后II.md) |回溯|困难| **回溯**| |[0053.最大子序和](https://github.com/youngyangyang04/leetcode/blob/master/problems/0053.最大子序和.md) |数组 |简单|**暴力** **贪心** 动态规划 分治| +|[0055.跳跃游戏](https://github.com/youngyangyang04/leetcode/blob/master/problems/0053.最大子序和.md) |数组 |中等| **贪心** 经典题目| |[0059.螺旋矩阵II](https://github.com/youngyangyang04/leetcode/blob/master/problems/0059.螺旋矩阵II.md) |数组 |中等|**模拟**| |[0077.组合](https://github.com/youngyangyang04/leetcode/blob/master/problems/0077.组合.md) |回溯 |中等|**回溯**| |[0078.子集](https://github.com/youngyangyang04/leetcode/blob/master/problems/0078.子集.md) |回溯/数组 |中等|**回溯**| @@ -328,6 +330,7 @@ |[0113.路径总和II](https://github.com/youngyangyang04/leetcode/blob/master/problems/0113.路径总和II.md) |二叉树树 |简单|**深度优先搜索/递归** **回溯** **栈**| |[0116.填充每个节点的下一个右侧节点指针](https://github.com/youngyangyang04/leetcode/blob/master/problems/0116.填充每个节点的下一个右侧节点指针.md) |二叉树 |中等|**递归** **迭代/广度优先搜索**| |[0117.填充每个节点的下一个右侧节点指针II](https://github.com/youngyangyang04/leetcode/blob/master/problems/0117.填充每个节点的下一个右侧节点指针II.md) |二叉树 |中等|**递归** **迭代/广度优先搜索**| +|[0129.求根到叶子节点数字之和](https://github.com/youngyangyang04/leetcode/blob/master/problems/0129.求根到叶子节点数字之和.md) |二叉树 |中等|**递归/回溯** 递归里隐藏着回溯,和113.路径总和II类似| |[0131.分割回文串](https://github.com/youngyangyang04/leetcode/blob/master/problems/0131.分割回文串.md) |回溯 |中等|**回溯**| |[0141.环形链表](https://github.com/youngyangyang04/leetcode/blob/master/problems/0141.环形链表.md) |链表 |简单|**快慢指针/双指针**| |[0142.环形链表II](https://github.com/youngyangyang04/leetcode/blob/master/problems/0142.环形链表II.md) |链表 |中等|**快慢指针/双指针**| diff --git a/pics/17. 电话号码的字母组合.png b/pics/17. 电话号码的字母组合.png index fc076d97e6afdbafe4b2c7bb1a559f5c8a126c98..b11f7114f56ddb2439efaf63613d9795a4a5a847 100644 GIT binary patch literal 128255 zcmeFZWmr^g+cvDoMJPy#bf+TS-JL2aB_RzXQbU7;po9uYr-FoZcXvtmPy*6D^zfc@ z#eMnQ_w!uepZEK=@5i%k!^QxMS!{eb)a0>mlit2@;|8{(g3OZ}H+~zq zaRX%%0}cE}R@dYK_;%CjiM-T}f&ub%@Po_?T}2C3)f*4NdyE@5-&o&3MIHjaNWs^Q z8@JMK-na$6-$ec{4dt)D{x*#z4HlgI;)>*o${+>p4TC?lx}y}6Z)Ijc2t-l=nJ zk*jg`H01rhQt*!iC7CSRaIP1hlsnyb(_1xp3v;|)p3z9m!Q(mYMw zeKld-c(LU)Aa*FYdnTGXc#+}_HyS|{)SpaURHj^gv+(O?M_Gw=hRXNSB%AE>04cA{7j21zoZft+W5}3T!D!>gJP&&iW@*ffONqus-l5JK zq=kU9KRie%1ss#yDC9dLB1>SwQhAvD|M+M9uEWaL$!Zf_o6c^ZxF4{@@Lis*r4D)M z4aCOi*Kf>UlIsNt{eDUVT;|bz1Bc^{%l`HuGJT8m2$o}ro$(LT@N<45O|#xd_tvDw z@(%go#9i&A#}Kycj!$~b13|gq>b5xFzvJDQH_!-YE!9Z6qg6OCKWRoyWZP5h%c8M8 zQm&P!O_FBvXss7_v;J5+Pn(rpD;9b3TyKLM-?7H(s+XVsb*tci`!IiA=1;GEIM=yK 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zVY2G7kjp>P=_W*LRbGIvk&B_J?z1#X5KjhF?(a_YNcU##lj43O-azAIU`X&?M#z2} zXpk?p5-APczMW%`{ie*(G_`;Kuj&2&dnr@@k0fKp4=Xrc4leb&4KDO2Y`>; MTDrfLYT8EqA5)-G5C8xG literal 0 HcmV?d00001 diff --git a/problems/0017.电话号码的字母组合.md b/problems/0017.电话号码的字母组合.md index e5e3dac9..53da5572 100644 --- a/problems/0017.电话号码的字母组合.md +++ b/problems/0017.电话号码的字母组合.md @@ -1,64 +1,140 @@ - ## 题目地址 https://leetcode-cn.com/problems/letter-combinations-of-a-phone-number/ -## 思路 +> 多个集合求组合问题。 -本题要解决如下问题: +# 17.电话号码的字母组合 + +题目链接:https://leetcode-cn.com/problems/letter-combinations-of-a-phone-number/ + +给定一个仅包含数字 2-9 的字符串,返回所有它能表示的字母组合。 + +给出数字到字母的映射如下(与电话按键相同)。注意 1 不对应任何字母。 + +![17.电话号码的字母组合](https://img-blog.csdnimg.cn/2020102916424043.png) + +示例: +输入:"23" +输出:["ad", "ae", "af", "bd", "be", "bf", "cd", "ce", "cf"]. + +说明:尽管上面的答案是按字典序排列的,但是你可以任意选择答案输出的顺序。 + +# 思路 + +从示例上来说,输入"23",最直接的想法就是两层for循环遍历了吧,正好把组合的情况都输出了。 + +如果输入"233"呢,那么就三层for循环,如果"2333"呢,就四层for循环....... + +大家应该感觉出和[回溯算法:求组合问题!](https://mp.weixin.qq.com/s/OnBjbLzuipWz_u4QfmgcqQ)遇到的一样的问题,就是这for循环的层数如何写出来,此时又是回溯法登场的时候了。 + +理解本题后,要解决如下三个问题: 1. 数字和字母如何映射 -2. 两个字母我就两个for循环,三个字符我就三个for循环,以此类推,然后发现代码根本写不出来 +2. 两个字母就两个for循环,三个字符我就三个for循环,以此类推,然后发现代码根本写不出来 3. 输入1 * #按键等等异常情况 -接下来一一解决这几个问题。 +## 数字和字母如何映射 + +可以使用map或者定义一个二位数组,例如:string letterMap[10],来做映射,我这里定义一个二维数组,代码如下: + +``` +const string letterMap[10] = { + "", // 0 + "", // 1 + "abc", // 2 + "def", // 3 + "ghi", // 4 + "jkl", // 5 + "mno", // 6 + "pqrs", // 7 + "tuv", // 8 + "wxyz", // 9 +}; +``` + +## 回溯法来解决n个for循环的问题 + +对于回溯法还不了解的同学看这篇:[关于回溯算法,你该了解这些!](https://mp.weixin.qq.com/s/gjSgJbNbd1eAA5WkA-HeWw) -1. 数字和字母如何映射 - -定义一个二位数组,例如:string letterMap[10],来做映射 - -2. 两个字母我就两个for循环,三个字符我就三个for循环,以此类推,然后发现代码根本写不出来。 - -**遇到这种情况,就应该想到回溯了。** - -这是一个回溯法的经典题目,**不要以为回溯是一个性能很高的算法,回溯其实就是暴力枚举,纯暴力,搜出所有的可能性。** - -回溯一般都伴随着递归,而这种组合问题,都可以画成一个树形结构。 - -例如:输入:"23",如图所示: +例如:输入:"23",抽象为树形结构,如图所示: -可以想成遍历这棵树,然后把叶子节点都保存下来,输出["ad", "ae", "af", "bd", "be", "bf", "cd", "ce", "cf"]。 +图中可以看出遍历的深度,就是输入"23"的长度,而叶子节点就是我们要收集的结果,输出["ad", "ae", "af", "bd", "be", "bf", "cd", "ce", "cf"]。 +回溯三部曲: -3. 输入1 * #按键等等异常情况 +* 确定回溯函数参数 -题目的测试数据中应该没有异常情况的数据,可以不考虑,但是要知道会有这些异常。 +首先需要一个字符串s来收集叶子节点的结果,然后用一个字符串数组result保存起来,这两个变量我依然定义为全局。 +再来看参数,参数指定是有题目中给的string digits,然后还要有一个参数就是int型的index。 -**那么在来讲一讲回溯法,回溯法的模板如下:** +注意这个index可不是 [回溯算法:求组合问题!](https://mp.weixin.qq.com/s/OnBjbLzuipWz_u4QfmgcqQ)和[回溯算法:求组合总和!](https://mp.weixin.qq.com/s/HX7WW6ixbFZJASkRnCTC3w)中的startIndex了。 + +这个index是记录遍历第几个数字了,就是用来遍历digits的(题目中给出数字字符串),同时index也表示树的深度。 + +代码如下: ``` -backtracking() { - if (终止条件) { - 存放结果; - } +vector result; +string s; +void backtracking(const string& digits, int index) +``` - for (枚举同一个位置的所有可能性,可以想成节点孩子的数量) { - 递归,处理节点; - backtracking(); - 回溯,撤销处理结果 - } +* 确定终止条件 + +例如输入用例"23",两个数字,那么根节点往下递归两层就可以了,叶子节点就是要收集的结果集。 + +那么终止条件就是如果index 等于 输入的数字个数(digits.size)了(本来index就是用来遍历digits的)。 + +然后收集结果,结束本层递归。 + +代码如下: + +``` +if (index == digits.size()) { + result.push_back(s); + return; } ``` -按照这个模板,不难写出如下代码: +* 确定单层遍历逻辑 -## C++代码 +首先要取index指向的数字,并找到对应的字符集(手机键盘的字符集)。 + +然后for循环来处理这个字符集,代码如下: ``` +int digit = digits[index] - '0'; // 将index指向的数字转为int +string letters = letterMap[digit]; // 取数字对应的字符集 +for (int i = 0; i < letters.size(); i++) { + s.push_back(letters[i]); // 处理 + backtracking(digits, index + 1); // 递归,注意index+1,一下层要处理下一个数字了 + s.pop_back(); // 回溯 +} +``` + +**注意这里for循环,可不像是在[回溯算法:求组合问题!](https://mp.weixin.qq.com/s/OnBjbLzuipWz_u4QfmgcqQ)和[回溯算法:求组合总和!](https://mp.weixin.qq.com/s/HX7WW6ixbFZJASkRnCTC3w)中从startIndex开始遍历的**。 + +**因为本题每一个数字代表的是不同集合,也就是求不同集合之间的组合,而[77. 组合](https://mp.weixin.qq.com/s/OnBjbLzuipWz_u4QfmgcqQ)和[216.组合总和III](https://mp.weixin.qq.com/s/HX7WW6ixbFZJASkRnCTC3w)都是是求同一个集合中的组合!** + + +## 输入1 * #按键等等异常情况 + +代码中最好考虑这些异常情况,但题目的测试数据中应该没有异常情况的数据,所以我就没有加了。 + +**但是要知道会有这些异常,如果是现场面试中,一定要考虑到!** + + +# C++代码 +关键地方都讲完了,按照[关于回溯算法,你该了解这些!](https://mp.weixin.qq.com/s/gjSgJbNbd1eAA5WkA-HeWw)中的回溯法模板,不难写出如下C++代码: + + +``` +// 版本一 class Solution { private: const string letterMap[10] = { @@ -75,7 +151,53 @@ private: }; public: vector result; - void getCombinations(const string& digits, int index, const string& s) { + string s; + void backtracking(const string& digits, int index) { + if (index == digits.size()) { + result.push_back(s); + return; + } + int digit = digits[index] - '0'; // 将index指向的数字转为int + string letters = letterMap[digit]; // 取数字对应的字符集 + for (int i = 0; i < letters.size(); i++) { + s.push_back(letters[i]); // 处理 + backtracking(digits, index + 1); // 递归,注意index+1,一下层要处理下一个数字了 + s.pop_back(); // 回溯 + } + } + vector letterCombinations(string digits) { + s.clear(); + result.clear(); + if (digits.size() == 0) { + return result; + } + backtracking(digits, 0); + return result; + } +}; +``` + +一些写法,是把回溯的过程放在递归函数里了,例如如下代码,我可以写成这样:(注意注释中不一样的地方) + +``` +// 版本二 +class Solution { +private: + const string letterMap[10] = { + "", // 0 + "", // 1 + "abc", // 2 + "def", // 3 + "ghi", // 4 + "jkl", // 5 + "mno", // 6 + "pqrs", // 7 + "tuv", // 8 + "wxyz", // 9 + }; +public: + vector result; + void getCombinations(const string& digits, int index, const string& s) { // 注意参数的不同 if (index == digits.size()) { result.push_back(s); return; @@ -83,10 +205,11 @@ public: int digit = digits[index] - '0'; string letters = letterMap[digit]; for (int i = 0; i < letters.size(); i++) { - getCombinations(digits, index + 1, s + letters[i]); + getCombinations(digits, index + 1, s + letters[i]); // 注意这里的不同 } } vector letterCombinations(string digits) { + result.clear(); if (digits.size() == 0) { return result; } @@ -97,8 +220,16 @@ public: }; ``` -# 拓展 +我不建议把回溯藏在递归的参数里这种写法,很不直观,我在[二叉树:以为使用了递归,其实还隐藏着回溯](https://mp.weixin.qq.com/s/ivLkHzWdhjQQD1rQWe6zWA)这篇文章中也深度分析了,回溯隐藏在了哪里。 -请问为什么 getCombinations(const string& digits, int index, const string& s)函数里的string& s 前要加const,不加的报错 +所以大家可以按照版本一来写就可以了。 + +# 总结 + +本篇将题目的三个要点一一列出,并重点强调了和前面讲解过的[77. 组合](https://mp.weixin.qq.com/s/OnBjbLzuipWz_u4QfmgcqQ)和[216.组合总和III](https://mp.weixin.qq.com/s/HX7WW6ixbFZJASkRnCTC3w)的区别,本题是多个集合求组合,所以在回溯的搜索过程中,都有一些细节需要注意的。 + +其实本题不算难,但也处处是细节,大家还要自己亲自动手写一写。 + +**就酱,如果学到了,就帮Carl转发一波吧,让更多小伙伴知道这里!** > 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/0055.跳跃游戏.md b/problems/0055.跳跃游戏.md new file mode 100644 index 00000000..acf2f953 --- /dev/null +++ b/problems/0055.跳跃游戏.md @@ -0,0 +1,41 @@ +## 链接 +https://leetcode-cn.com/problems/jump-game/ + +## 思路 + +其实贪心和动态规划很容易混在一起,在面试中,我们应该本着能用贪心就用贪心,贪心解决不了再考虑用动态规划。 毕竟贪心更容易理解,并快速写出代码。 + +刚看到本题一开始可能想:当前位置元素如果是3,我究竟是跳一步呢,还是两步呢,还是三步呢,究竟跳几步才是最优呢? + +其实如果本题是要求只能跳元素数值大小的个数,不能多也不能少,问是否达到终点,那么一定要用动态规划了。 + +但本题其实我们就看跳到的范围能否覆盖终点,就可以了。 + +那么我们每次取最大的覆盖范围,看最后能否覆盖终点。 + +如图: + + + +那么i每次移动只能在cover的范围内移动,每移动一个元素,cover得到该元素数值的补充,让i继续移动下去。 + +而cover每次只取 得到该元素数值补充后的范围 和 cover本身范围 的最大值。 + +如果cover大于等于了终点下表,直接return true就可以了。 + +C++代码如下: + +``` +class Solution { +public: + bool canJump(vector& nums) { + int cover = 0; + if (nums.size() == 1) return true; // 只有一个元素,就是能达到 + for (int i = 0; i <= cover; i++) { // 注意这里是小于等于cover + cover = max(i + nums[i], cover); + if (cover >= nums.size() - 1) return true; // 说明可以覆盖到终点了 + } + return false; + } +}; +``` diff --git a/problems/0077.组合优化.md b/problems/0077.组合优化.md index 6525a9c7..6f12abd0 100644 --- a/problems/0077.组合优化.md +++ b/problems/0077.组合优化.md @@ -77,7 +77,7 @@ for (int i = startIndex; i <= n; i++) { 2. 还需要的元素个数为: k - path.size(); -3. 在集合n中至少要从该起始位置 : n - (k - path.size()) + 1,开始遍历 +3. 在集合n中至多要从该起始位置 : n - (k - path.size()) + 1,开始遍历 为什么有个+1呢,因为包括起始位置,我们要是一个左闭的集合。 diff --git a/problems/0129.求根到叶子节点数字之和.md b/problems/0129.求根到叶子节点数字之和.md index edd5f423..7d061a43 100644 --- a/problems/0129.求根到叶子节点数字之和.md +++ b/problems/0129.求根到叶子节点数字之和.md @@ -1,3 +1,5 @@ +## 链接 +https://leetcode-cn.com/problems/sum-root-to-leaf-numbers/ ## 思路 @@ -122,7 +124,6 @@ private: } return sum; } - // 递归函数不需要返回值,因为我们要遍历整个树 void traversal(TreeNode* cur) { if (!cur->left && !cur->right) { // 遇到了叶子节点 result += vectorToInt(path); @@ -130,14 +131,14 @@ private: } if (cur->left) { // 左 (空节点不遍历) - path.push_back(cur->left->val); - traversal(cur->left); // 递归 - path.pop_back(); // 回溯 + path.push_back(cur->left->val); // 处理节点 + traversal(cur->left); // 递归 + path.pop_back(); // 回溯,撤销 } if (cur->right) { // 右 (空节点不遍历) - path.push_back(cur->right->val); - traversal(cur->right); // 递归 - path.pop_back(); // 回溯 + path.push_back(cur->right->val); // 处理节点 + traversal(cur->right); // 递归 + path.pop_back(); // 回溯,撤销 } return ; } @@ -151,3 +152,9 @@ public: } }; ``` + +# 总结 + +过于简洁的代码,很容易让初学者忽视了本题中回溯的精髓,甚至作者本身都没有想清楚自己用了回溯。 + +**我这里提供的代码把整个回溯过程充分体现出来,希望可以帮助大家看的明明白白!** diff --git a/problems/0216.组合总和III.md b/problems/0216.组合总和III.md index d2e3762e..99e82100 100644 --- a/problems/0216.组合总和III.md +++ b/problems/0216.组合总和III.md @@ -168,6 +168,8 @@ if (sum > targetSum) { // 剪枝操作 } ``` +和[回溯算法:组合问题再剪剪枝](https://mp.weixin.qq.com/s/Ri7spcJMUmph4c6XjPWXQA) 一样,for循环的范围也可以剪枝,i <= 9 - (k - path.size()) + 1就可以了。 + 最后C++代码如下: ``` @@ -175,10 +177,6 @@ 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 @@ -187,7 +185,7 @@ private: if (sum == targetSum) result.push_back(path); return; } - for (int i = startIndex; i <= 9; i++) { + for (int i = startIndex; i <= 9 - (k - path.size()) + 1; i++) { // 剪枝 sum += i; // 处理 path.push_back(i); // 处理 backtracking(targetSum, k, sum, i + 1); // 注意i+1调整startIndex diff --git a/problems/0463.岛屿的周长.md b/problems/0463.岛屿的周长.md new file mode 100644 index 00000000..35ec0013 --- /dev/null +++ b/problems/0463.岛屿的周长.md @@ -0,0 +1,78 @@ +## 思路 + +岛屿问题最容易让人想到BFS或者DFS,但是这道题还真的没有必要,别把简单问题搞复杂了。 + +### 解法一: + +遍历每一个空格,遇到岛屿,计算其上下左右的情况,遇到水域或者出界的情况,就可以计算边了。 + +如图: + + + +代码如下:(详细注释) + +``` +class Solution { +public: + int direction[4][2] = {0, 1, 1, 0, -1, 0, 0, -1}; + int islandPerimeter(vector>& grid) { + int result = 0; + for (int i = 0; i < grid.size(); i++) { + for (int j = 0; j < grid[0].size(); j++) { + if (grid[i][j] == 1) { + for (int k = 0; k < 4; k++) { // 上下左右四个方向 + int x = i + direction[k][0]; + int y = j + direction[k][1]; // 计算周边坐标x,y + if (x < 0 // i在边界上 + || x >= grid.size() // i在边界上 + || y < 0 // j在边界上 + || y >= grid[0].size() // j在边界上 + || grid[x][y] == 0) { // x,y位置是水域 + result++; + } + } + } + } + } + return result; + } +}; +``` + +### 解法二: + +计算出总的岛屿数量,因为有一对相邻两个陆地,边的总数就减2,那么在计算出相邻岛屿的数量就可以了。 + +result = 岛屿数量 * 4 - cover * 2; + +如图: + + + +代码如下:(详细注释) + +``` +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 + for (int i = 0; i < grid.size(); i++) { + for (int j = 0; j < grid[0].size(); j++) { + if (grid[i][j] == 1) { + sum++; + // 统计上边相邻陆地 + if(i - 1 >= 0 && grid[i - 1][j] == 1) cover++; + // 统计左边相邻陆地 + if(j - 1 >= 0 && grid[i][j - 1] == 1) cover++; + // 为什么没统计下边和右边? 因为避免重复计算 + } + } + } + return sum * 4 - cover * 2; + } +}; +``` +