From 8f5b6cfad3e0221f370d6f7c1eb8ed69e702769c Mon Sep 17 00:00:00 2001 From: youngyangyang04 <826123027@qq.com> Date: Fri, 25 Sep 2020 16:59:24 +0800 Subject: [PATCH] Update --- README.md | 5 +- pics/102.二叉树的层序遍历.png | Bin 0 -> 31965 bytes ...与后序遍历序列构造二叉树.png | Bin 0 -> 111608 bytes pics/107.二叉树的层次遍历II.png | Bin 0 -> 33751 bytes pics/199.二叉树的右视图.png | Bin 0 -> 22450 bytes pics/429. N叉树的层序遍历.png | Bin 0 -> 30744 bytes pics/637.二叉树的层平均值.png | Bin 0 -> 36834 bytes pics/我要打十个.gif | Bin 0 -> 1146235 bytes problems/0102.二叉树的层序遍历.md | 217 +++++++- ...序与中序遍历序列构造二叉树.md | 8 + ...序与后序遍历序列构造二叉树.md | 495 ++++++++++++++++++ problems/0429.N叉树的层序遍历.md | 35 ++ problems/0589.N叉树的前序遍历.md | 56 ++ problems/0590.N叉树的后序遍历.md | 54 ++ 14 files changed, 859 insertions(+), 11 deletions(-) create mode 100644 pics/102.二叉树的层序遍历.png create mode 100644 pics/106.从中序与后序遍历序列构造二叉树.png create mode 100644 pics/107.二叉树的层次遍历II.png create mode 100644 pics/199.二叉树的右视图.png create mode 100644 pics/429. N叉树的层序遍历.png create mode 100644 pics/637.二叉树的层平均值.png create mode 100644 pics/我要打十个.gif create mode 100644 problems/0105.从前序与中序遍历序列构造二叉树.md create mode 100644 problems/0106.从中序与后序遍历序列构造二叉树.md create mode 100644 problems/0429.N叉树的层序遍历.md create mode 100644 problems/0589.N叉树的前序遍历.md create mode 100644 problems/0590.N叉树的后序遍历.md diff --git a/README.md b/README.md index 113f0cb5..06802c9e 100644 --- a/README.md +++ b/README.md @@ -231,6 +231,8 @@ |[0101.对称二叉树](https://github.com/youngyangyang04/leetcode/blob/master/problems/0101.对称二叉树.md) |树 |简单|**递归** **迭代/队列/栈**| |[0102.二叉树的层序遍历](https://github.com/youngyangyang04/leetcode/blob/master/problems/0102.二叉树的层序遍历.md) |树 |中等|**广度优先搜索/队列**| |[0104.二叉树的最大深度](https://github.com/youngyangyang04/leetcode/blob/master/problems/0104.二叉树的最大深度.md) |树 |简单|**递归** **迭代/队列/BFS**| +|[0105.从前序与中序遍历序列构造二叉树](https://github.com/youngyangyang04/leetcode/blob/master/problems/0105.从前序与中序遍历序列构造二叉树.md) |树 |中等|**递归**| +|[0106.从中序与后序遍历序列构造二叉树](https://github.com/youngyangyang04/leetcode/blob/master/problems/0106.从中序与后序遍历序列构造二叉树.md) |树 |中等|**递归**| |[0107.二叉树的层次遍历II](https://github.com/youngyangyang04/leetcode/blob/master/problems/0107.二叉树的层次遍历II.md) |树 |简单|**广度优先搜索/队列/BFS**| |[0110.平衡二叉树](https://github.com/youngyangyang04/leetcode/blob/master/problems/0110.平衡二叉树.md) |树 |简单|**递归**| |[0111.二叉树的最小深度](https://github.com/youngyangyang04/leetcode/blob/master/problems/0111.二叉树的最小深度.md) |树 |简单|**递归** **队列/BFS**| @@ -273,7 +275,8 @@ |[0538.把二叉搜索树转换为累加树](https://github.com/youngyangyang04/leetcode/blob/master/problems/0538.把二叉搜索树转换为累加树.md) |二叉树 |简单|**递归** **迭代**| |[0541.反转字符串II](https://github.com/youngyangyang04/leetcode/blob/master/problems/0541.反转字符串II.md) |字符串 |简单| **模拟**| |[0575.分糖果](https://github.com/youngyangyang04/leetcode/blob/master/problems/0575.分糖果.md) |哈希表 |简单|**哈希**| -|[0589.N叉树的前序遍历](https://github.com/youngyangyang04/leetcode/blob/master/problems/0589.N叉树的前序遍历.md) |树 |简单|**递归****栈/迭代**| +|[0589.N叉树的前序遍历](https://github.com/youngyangyang04/leetcode/blob/master/problems/0589.N叉树的前序遍历.md) |树 |简单|**递归** **栈/迭代**| +|[0590.N叉树的后序遍历](https://github.com/youngyangyang04/leetcode/blob/master/problems/0590.N叉树的后序遍历.md) |树 |简单|**递归** **栈/迭代**| |[0617.合并二叉树](https://github.com/youngyangyang04/leetcode/blob/master/problems/0617.合并二叉树.md) |树 |简单|**递归** **迭代**| |[0637.二叉树的层平均值](https://github.com/youngyangyang04/leetcode/blob/master/problems/0637.二叉树的层平均值.md) |树 |简单|**广度优先搜索/队列**| |[0654.最大二叉树](https://github.com/youngyangyang04/leetcode/blob/master/problems/0654.最大二叉树.md) |树 |中等|**递归**| diff --git a/pics/102.二叉树的层序遍历.png b/pics/102.二叉树的层序遍历.png new file mode 100644 index 0000000000000000000000000000000000000000..dcfcf9722ae184e0819175f746982e5b1620bc54 GIT binary patch literal 31965 zcmeFZcTiK|*EI?Vq9|YiR8T?bAYcQegGviMB=lxMq<4@ms31x&A{`-=By_2vBT}UZ zgx-{10!r`P=Lr1Xnfu4R^UmD4-^};Df1n-`PkGATYp=ET@mE!rrKF&zAR;27l$U!9 zCn6$|0Y7o4PC~zV<;V*DBDROiJ|xO+yE+RF9vf@Pzfe*l;sXCZMMUgpN<<2M1^m#1 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zh{C&zqlHxKJ#k2@T47xArh+$dB{sl%5wR}xvmbJLkyq6R&1kF&rvKc<4)8ZToB(tW z86=14dAyic#cEK??H}dQ&SL*v`Wzl*>YSadn}cX0MrBd9zO75|NX^-we2JT+o9vkh z`s0`*Y^jF+kmIGhzF+4S)TD&}5sWnm06%oFH)i>Pgzg9mUu_up1aU2=(i>%ATn-^I z?`%}RzLvxWIs8)+FVpK24bV2bDJM|ZKTM6IY$=f2gOm@_fz#ku(xwuJJc1z%Z|i@Qj=-n|sX>l%yU-l?9h`^O%h8A5y- z7t$^F2D&wE=c=Db(F(OPA@NUJcyvAR_bYY&Sc2ZPA4G6Tb5|dx>wnz6%m1r1tHOeE zlrm;iHk_!pc~=PPke2p_DP>yW>o!(l+Us2q^gkhb^2-9ON6s2x-l$c^#VH^iVUHT5t+O z(c3Hw!LT_XX2$D7H-$J?S54fLy#v{I*96%7o{|HMKH!~}0k=3Nj!9zcM)=`fWHhdN zHyKjsM|V_k&@nS~?OMc;uF?*}QW_bAGJN6p$Ylj3!hMLwf$d9B7099GeeUjl6oR4T z;2Ovc%tEhHO7?g>^bc1dFelQu1RamgitggJ}6F!b(!sYYi)fPdPhUEAQJ!(VJ%xY&X|WkGUvohERY@!CZ-&!2$cW)LfqQ0o*10{ zlZm{4^-7kjS9%62IVzF_-%`WDMT>zZ%Pfwybojt~5zP6gMguam30KU968A|?+m>*2 z{KcNA5&$Bk4T%1&cxa4c2pp`siz{B&Thrc_u^0_HuZ9J-i}PS0pQ#l$2e2;|zz>Tz zS~_ev$wvE3Li20V9mxQ4kcrFE^@0u{hCqg~Wx4+sTLh&06r~%@0LB^^fg#r{s4@&O z!#B)ufkHi!Ue0q3`YJMwC0ueM1(L`BPjoO6fv+hidPG@5Vvt9i4=Elpm{JVJzlzAB zO1o@>{f2m^O&Q3bN&CbOOvb-(m5yxnR z97@0rY_xzIGN?xu*06>#-~k(rH~}zP6$)jv;0sv@kN|SgU3XZc3hGb?HzMbb5b%Nu zFenNlash+%`XCp}7={nr(ExRvfE-mwK^4R>g>o<;7}(fA4o(o@6<{GBgeb=y44?pT zY^f2=NJcdPSedJui4Nbmz=j>^$b{tUU=}G#zy_vCS$yLg$!kc(*w?{T!3@LcUH4gCwY8(R;;_v_#-r)|E&O;u&2*4EJF;jAApc|K?0xP-^ zics0W2k5;V3^u@mUWFhT2Z#qAjsXlcmV*tzh{qvfaEV|5;|k?qfd|wviUo|L4o~LC z8ZuD>M9Si-L}R4DcFW 我要打十个! + +看完这篇文章虽然不能打十个,但是可以迅速打五个!而且够快! + + +# 102.二叉树的层序遍历 + +给你一个二叉树,请你返回其按 层序遍历 得到的节点值。 (即逐层地,从左到右访问所有节点)。 + + + ## 思路 -我们之前讲过了,二叉树的深度优先遍历:[一文学通二叉树前中后序递归法与迭代法](https://github.com/youngyangyang04/leetcode/blob/master/problems/0144.二叉树的前序遍历.md)里面有前中后序遍历的方式,前中后序分辨可以使用递归和迭代的方法来实现,接下来我们再来介绍二叉树的另一种遍历方式,也就是层序遍历。 +我们之前讲过了三篇关于二叉树的深度优先遍历的文章: -相似题目: -* [0102.二叉树的层序遍历](https://github.com/youngyangyang04/leetcode/blob/master/problems/0102.二叉树的层序遍历.md) -* [0107.二叉树的层次遍历II](https://github.com/youngyangyang04/leetcode/blob/master/problems/0107.二叉树的层次遍历II.md) -* [0199.二叉树的右视图](https://github.com/youngyangyang04/leetcode/blob/master/problems/0199.二叉树的右视图.md) -* [0637.二叉树的层平均值](https://github.com/youngyangyang04/leetcode/blob/master/problems/0637.二叉树的层平均值.md) +* [二叉树:前中后序递归法](https://mp.weixin.qq.com/s/PwVIfxDlT3kRgMASWAMGhA) +* [二叉树:前中后序迭代法](https://mp.weixin.qq.com/s/c_zCrGHIVlBjUH_hJtghCg) +* [二叉树:前中后序迭代方式统一写法](https://mp.weixin.qq.com/s/WKg0Ty1_3SZkztpHubZPRg) + +接下来我们再来介绍二叉树的另一种遍历方式:层序遍历。 层序遍历一个二叉树。就是从左到右一层一层的去遍历二叉树。这种遍历的方式和我们之前讲过的都不太一样。 -需要借用一个辅助数据结构队列来实现,**队列先进先出,符合一层一层遍历的逻辑,而是用栈先进后出适合模拟深度优先遍历也就是递归的逻辑。** +需要借用一个辅助数据结构即队列来实现,**队列先进先出,符合一层一层遍历的逻辑,而是用栈先进后出适合模拟深度优先遍历也就是递归的逻辑。** -使用队列实现广度优先遍历,动画如下: +**而这种层序遍历方式就是图论中的广度优先遍历,只不过我们应用在二叉树上。** +使用队列实现二叉树广度优先遍历,动画如下: + +![102二叉树的层序遍历.mp4](ad3d58a5-b8ee-42a5-bc89-6ad4d9e3cbf2) 这样就实现了层序从左到右遍历二叉树。 -代码如下:这份代码也可以作为二叉树层序遍历的模板。 +代码如下:**这份代码也可以作为二叉树层序遍历的模板,以后在打四个就靠它了**。 ## C++代码 @@ -35,7 +49,8 @@ public: while (!que.empty()) { int size = que.size(); vector vec; - for (int i = 0; i < size; i++) {// 这里一定要使用固定大小size,不要使用que.size() + // 这里一定要使用固定大小size,不要使用que.size(),因为que.size是不断变化的 + for (int i = 0; i < size; i++) { TreeNode* node = que.front(); que.pop(); vec.push_back(node->val); @@ -49,4 +64,186 @@ public: }; ``` +**此时我们就掌握了二叉树的层序遍历了,那么如下四道leetcode上的题目,只需要修改模板的一两行代码(不能再多了),便可打倒!** + +# 107.二叉树的层次遍历 II + +给定一个二叉树,返回其节点值自底向上的层次遍历。 (即按从叶子节点所在层到根节点所在的层,逐层从左向右遍历) + + + +## 思路 + +相对于102.二叉树的层序遍历,就是最后把result数组反转一下就可以了。 + +## C++代码 + +``` +class Solution { +public: + vector> levelOrderBottom(TreeNode* root) { + queue que; + if (root != NULL) que.push(root); + vector> result; + while (!que.empty()) { + int size = que.size(); + vector vec; + for (int i = 0; i < size; i++) { + TreeNode* node = que.front(); + que.pop(); + vec.push_back(node->val); + if (node->left) que.push(node->left); + if (node->right) que.push(node->right); + } + result.push_back(vec); + } + reverse(result.begin(), result.end()); // 在这里反转一下数组即可 + return result; + + } +}; +``` + + +# 199.二叉树的右视图 + +给定一棵二叉树,想象自己站在它的右侧,按照从顶部到底部的顺序,返回从右侧所能看到的节点值。 + + + +## 思路 + +层序遍历的时候,判断是否遍历到单层的最后面的元素,如果是,就放进result数组中,随后返回result就可以了。 + +## C++代码 + +``` +class Solution { +public: + vector rightSideView(TreeNode* root) { + queue que; + if (root != NULL) que.push(root); + vector result; + while (!que.empty()) { + int size = que.size(); + for (int i = 0; i < size; i++) { + TreeNode* node = que.front(); + que.pop(); + if (i == (size - 1)) result.push_back(node->val); // 将每一层的最后元素放入result数组中 + if (node->left) que.push(node->left); + if (node->right) que.push(node->right); + } + } + return result; + } +}; +``` + +# 637.二叉树的层平均值 + +给定一个非空二叉树, 返回一个由每层节点平均值组成的数组。 + + + +## 思路 + +本题就是层序遍历的时候把一层求个总和在取一个均值。 + +## C++代码 + +``` +class Solution { +public: + vector averageOfLevels(TreeNode* root) { + queue que; + if (root != NULL) que.push(root); + vector result; + while (!que.empty()) { + int size = que.size(); + double sum = 0; // 统计每一层的和 + for (int i = 0; i < size; i++) { + TreeNode* node = que.front(); + que.pop(); + sum += node->val; + if (node->left) que.push(node->left); + if (node->right) que.push(node->right); + } + result.push_back(sum / size); // 将每一层均值放进结果集 + } + return result; + } +}; + +``` + +# 429.N叉树的层序遍历 + +给定一个 N 叉树,返回其节点值的层序遍历。 (即从左到右,逐层遍历)。 + +例如,给定一个 3叉树 : + + + + +返回其层序遍历: + +[ + [1], + [3,2,4], + [5,6] +] + + +## 思路 + +这道题依旧是模板题,只不过一个节点有多个孩子了 + +## C++代码 + +``` +class Solution { +public: + vector> levelOrder(Node* root) { + queue que; + if (root != NULL) que.push(root); + vector> result; + while (!que.empty()) { + int size = que.size(); + vector vec; + for (int i = 0; i < size; i++) { + Node* node = que.front(); + que.pop(); + vec.push_back(node->val); + for (int i = 0; i < node->children.size(); i++) { // 将节点孩子加入队列 + if (node->children[i]) que.push(node->children[i]); + } + } + result.push_back(vec); + } + return result; + + } +}; +``` + +# 总结 + +二叉树的层序遍历,就是图论中的广度优先搜索在二叉树中的应用,需要借助队列来实现(此时是不是又发现队列的应用了)。 + +学会二叉树的层序遍历,可以一口气撸完leetcode上五道题目: + +* 102.二叉树的层序遍历 +* 107.二叉树的层次遍历II +* 199.二叉树的右视图 +* 637.二叉树的层平均值 +* 589.N叉树的前序遍历 + +虽然不能一口气打十个,打五个也还行。 + +如果非要打十个,还得找叶师傅! + + + + + > 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/0105.从前序与中序遍历序列构造二叉树.md b/problems/0105.从前序与中序遍历序列构造二叉树.md new file mode 100644 index 00000000..eb39b313 --- /dev/null +++ b/problems/0105.从前序与中序遍历序列构造二叉树.md @@ -0,0 +1,8 @@ +# 链接 + +https://leetcode-cn.com/problems/construct-binary-tree-from-preorder-and-inorder-traversal/ + +# 思路: + +详细见 +[0106.从中序与后序遍历序列构造二叉树](https://github.com/youngyangyang04/leetcode/blob/master/problems/0106.从中序与后序遍历序列构造二叉树.md) diff --git a/problems/0106.从中序与后序遍历序列构造二叉树.md b/problems/0106.从中序与后序遍历序列构造二叉树.md new file mode 100644 index 00000000..6af49fd6 --- /dev/null +++ b/problems/0106.从中序与后序遍历序列构造二叉树.md @@ -0,0 +1,495 @@ +## 题目地址 +https://leetcode-cn.com/problems/construct-binary-tree-from-inorder-and-postorder-traversal/ + +## 思路 + +首先回忆一下如何根据两个顺序构造一个唯一的二叉树,相信理论知识大家应该都清楚,就是以后序数组最后一个元素为切割点,先切中序数组,根据中序数组,反过来在切后序数组。一层一层切下去,每次后序数组最后一个元素就是节点元素。 + +如果让我们肉眼看两个序列,画一颗二叉树的话,应该分分钟都可以画出来。 + +流程如图: + + + + +那么代码应该怎么写呢? + +说道一层一层切割,就应该想到了递归。 + +来看一下一共分几步: + +* 第一步:如果数组大小为零的话,说明是空节点了。 + +* 第二步:如果不为空,那么取后序数组最后一个元素作为节点元素。 + +* 第三步:找到后序数组最后一个元素在后序数组的位置,作为切割点 + +* 第四步:切割中序数组,切成中序左数组和中序右数组 (顺序别搞反了,一定是先切中序数组) + +* 第五步:切割后序数组,切成后序左数组和后序右数组 + +* 第六步:递归处理左区间和右区间 + +不难写出如下代码:(先把框架写出来) + +``` + TreeNode* traversal (vector& inorder, vector& postorder) { + + if (postorder.size() == 0) return NULL; + + // 后序遍历数组最后一个元素,就是当前的中间节点 + int rootValue = postorder[postorder.size() - 1]; + TreeNode* root = new TreeNode(rootValue); + + // 叶子节点 + if (postorder.size() == 1) return root; + + 找切割点 + int delimiterIndex; + for (delimiterIndex = 0; delimiterIndex < inorder.size(); delimiterIndex++) { + if (inorder[delimiterIndex] == rootValue) break; + } + + 切割中序数组,得到 中序左数组和中序右数组 + 切割后序数组,得到 后序左数组和后序右数组 + + root->left = traversal(中序左数组, 后序左数组); + root->right = traversal(中序右数组, 后序右数组); + + return root; + } +``` + +难点大家应该发现了,如何切割呢,边界值找不好很容易乱套。 + +此时应该注意确定切割的标准,是左闭右开,还有左开又闭,还是左闭又闭,这个就是不变量,要在递归中保持这个不变量。 + +在切割的过程中会产生四个区间,把握不好不变量的话,一会左闭右开,一会左闭又闭,必要乱套! + +我在[数组:每次遇到二分法,都是一看就会,一写就废](https://mp.weixin.qq.com/s/fCf5QbPDtE6SSlZ1yh_q8Q)和[数组:这个循环可以转懵很多人!](https://mp.weixin.qq.com/s/KTPhaeqxbMK9CxHUUgFDmg)中都强调过循环不变量的重要性,在二分查找以及螺旋矩阵的求解中,坚持循环不变量非常重要,本题也是。 + + +首先要切割中序数组,为什么先切割中序数组呢? + +切割点在后序数组的最后一个元素,就是用这个元素来切割中序数组的,所以必要先切割中序数组。 + +中序数组相对比较好切,找到切割点(后序数组的最后一个元素)在中序数组的位置,然后切割,如下代码中我坚持左闭右开的原则: + + +``` + // 找到中序遍历的切割点 + int delimiterIndex; + for (delimiterIndex = 0; delimiterIndex < inorder.size(); delimiterIndex++) { + if (inorder[delimiterIndex] == rootValue) break; + } + + // 左闭右开区间 + // [0, delimiterIndex) + vector leftInorder(inorder.begin(), inorder.begin() + delimiterIndex); + // [delimiterIndex + 1, end) + vector rightInorder(inorder.begin() + delimiterIndex + 1, inorder.end() ); +``` + +接下来就要切割后序数组了。 + +首先后序数组的最后一个元素指定不能要了,这是切割点 也是 当前二叉树中间节点的元素,已经用了。 + +后序数组的切割点怎么找? + +后序数组没有明确的切割元素来进行左右切割,不想中序数组有明确的切割左右,左右分开就可以了。 + +**此时有一个很重的点,就是中序数组大小一定是和后序数组的大小相同的(这是必然)。** + +中序数组我们都切成了左中序数组和右中序数组了,那么后序数组就可以按照左中序数组的大小来切割,切成左后序数组和右后序数组。 + +代码如下: + +``` + // postorder 舍弃末尾元素 + postorder.resize(postorder.size() - 1); + + // 依然左闭右开,注意这里使用了左中序数组大小作为切割点 + // [0, leftInorder.size) + vector leftPostorder(postorder.begin(), postorder.begin() + leftInorder.size()); + // [leftInorder.size(), end) + vector rightPostorder(postorder.begin() + leftInorder.size(), postorder.end()); +``` + +此时,中序数组切成了左中序数组和右中序数组,后序数组切割成序数组和右后序数组。 + +接下来可以递归了,代码如下: + +``` + root->left = traversal(leftInorder, leftPostorder); + root->right = traversal(rightInorder, rightPostorder); +``` + +完整代码如下: + +## C++ 完整代码 + +``` +class Solution { +private: + TreeNode* traversal (vector& inorder, vector& postorder) { + if (postorder.size() == 0) return NULL; + + // 后序遍历数组最后一个元素,就是当前的中间节点 + int rootValue = postorder[postorder.size() - 1]; + TreeNode* root = new TreeNode(rootValue); + + // 叶子节点 + if (postorder.size() == 1) return root; + + // 找到中序遍历的切割点 + int delimiterIndex; + for (delimiterIndex = 0; delimiterIndex < inorder.size(); delimiterIndex++) { + if (inorder[delimiterIndex] == rootValue) break; + } + + // 切割中序数组 + // 左闭右开区间:[0, delimiterIndex) + vector leftInorder(inorder.begin(), inorder.begin() + delimiterIndex); + // [delimiterIndex + 1, end) + vector rightInorder(inorder.begin() + delimiterIndex + 1, inorder.end() ); + + // postorder 舍弃末尾元素 + postorder.resize(postorder.size() - 1); + + // 切割后序数组 + // 依然左闭右开,注意这里使用了左中序数组大小作为切割点 + // [0, leftInorder.size) + vector leftPostorder(postorder.begin(), postorder.begin() + leftInorder.size()); + // [leftInorder.size(), end) + vector rightPostorder(postorder.begin() + leftInorder.size(), postorder.end()); + + root->left = traversal(leftInorder, leftPostorder); + root->right = traversal(rightInorder, rightPostorder); + + return root; + } +public: + TreeNode* buildTree(vector& inorder, vector& postorder) { + if (inorder.size() == 0 || postorder.size() == 0) return NULL; + return traversal(inorder, postorder); + } +}; + +``` + +相信大家自己就算是思路清晰, 代码写出来一定是各种问题,所以一定要加日志来调试,看看是不是按照自己思路来切割的,不要大脑模拟,那样越想越糊涂。 + +加了日志的代码如下:(加了日志的代码不要在leetcode上提交,容易超时) + + +``` +class Solution { +private: + TreeNode* traversal (vector& inorder, vector& postorder) { + if (postorder.size() == 0) return NULL; + + int rootValue = postorder[postorder.size() - 1]; + TreeNode* root = new TreeNode(rootValue); + + if (postorder.size() == 1) return root; + + int delimiterIndex; + for (delimiterIndex = 0; delimiterIndex < inorder.size(); delimiterIndex++) { + if (inorder[delimiterIndex] == rootValue) break; + } + + vector leftInorder(inorder.begin(), inorder.begin() + delimiterIndex); + vector rightInorder(inorder.begin() + delimiterIndex + 1, inorder.end() ); + + postorder.resize(postorder.size() - 1); + + vector leftPostorder(postorder.begin(), postorder.begin() + leftInorder.size()); + vector rightPostorder(postorder.begin() + leftInorder.size(), postorder.end()); + + cout << "----------" << endl; + + cout << "leftInorder :"; + for (int i : leftInorder) { + cout << i << " "; + } + cout << endl; + + cout << "rightInorder :"; + for (int i : rightInorder) { + cout << i << " "; + } + cout << endl; + + cout << "leftPostorder :"; + for (int i : leftPostorder) { + cout << i << " "; + } + cout << endl; + cout << "rightPostorder :"; + for (int i : rightPostorder) { + cout << i << " "; + } + cout << endl; + + root->left = traversal(leftInorder, leftPostorder); + root->right = traversal(rightInorder, rightPostorder); + + return root; + } +public: + TreeNode* buildTree(vector& inorder, vector& postorder) { + if (inorder.size() == 0 || postorder.size() == 0) return NULL; + return traversal(inorder, postorder); + } +}; +``` + +**此时应该发现了,如上的代码性能并不好,应为每层递归定定义了新的vector,既耗时又耗空间,但是上面的代码是最好理解的,为了方便读者理解,所以用如上的代码来讲解。** + +下面给出用下表索引写出的代码版本:(思路是一样的,只不过不用重复定义vector了,每次用下表索引来分割) + +## C++最终优化版本 +``` +class Solution { +private: + // 中序区间:[inorderBegin, inorderEnd),后序区间[postorderBegin, postorderEnd) + TreeNode* traversal (vector& inorder, int inorderBegin, int inorderEnd, vector& postorder, int postorderBegin, int postorderEnd) { + if (postorderBegin == postorderEnd) return NULL; + + int rootValue = postorder[postorderEnd - 1]; + TreeNode* root = new TreeNode(rootValue); + + if (postorderEnd - postorderBegin == 1) return root; + + int delimiterIndex; + for (delimiterIndex = inorderBegin; delimiterIndex < inorderEnd; delimiterIndex++) { + if (inorder[delimiterIndex] == rootValue) break; + } + // 切割中序数组 + // 左中序区间,左闭右开[leftInorderBegin, leftInorderEnd) + int leftInorderBegin = inorderBegin; + int leftInorderEnd = delimiterIndex; + // 右中序区间,左闭右开[rightInorderBegin, rightInorderEnd) + int rightInorderBegin = delimiterIndex + 1; + int rightInorderEnd = inorderEnd; + + // 切割后序数组 + // 左后序区间,左闭右开[leftPostorderBegin, leftPostorderEnd) + int leftPostorderBegin = postorderBegin; + int leftPostorderEnd = postorderBegin + delimiterIndex - inorderBegin; // 终止位置是 需要加上 中序区间的大小size + // 右后序区间,左闭右开[rightPostorderBegin, rightPostorderEnd) + int rightPostorderBegin = postorderBegin + (delimiterIndex - inorderBegin); + int rightPostorderEnd = postorderEnd - 1; // 排除最后一个元素,已经作为节点了 + + root->left = traversal(inorder, leftInorderBegin, leftInorderEnd, postorder, leftPostorderBegin, leftPostorderEnd); + root->right = traversal(inorder, rightInorderBegin, rightInorderEnd, postorder, rightPostorderBegin, rightPostorderEnd); + + return root; + } +public: + TreeNode* buildTree(vector& inorder, vector& postorder) { + if (inorder.size() == 0 || postorder.size() == 0) return NULL; + // 左闭右开的原则 + return traversal(inorder, 0, inorder.size(), postorder, 0, postorder.size()); + } +}; +``` + +那么这个版本写出来依然要打日志进行调试,打日志的版本如下:(**该版本不要在leetcode上提交,容易超时**) + +``` +class Solution { +private: + TreeNode* traversal (vector& inorder, int inorderBegin, int inorderEnd, vector& postorder, int postorderBegin, int postorderEnd) { + if (postorderBegin == postorderEnd) return NULL; + + int rootValue = postorder[postorderEnd - 1]; + TreeNode* root = new TreeNode(rootValue); + + if (postorderEnd - postorderBegin == 1) return root; + + int delimiterIndex; + for (delimiterIndex = inorderBegin; delimiterIndex < inorderEnd; delimiterIndex++) { + if (inorder[delimiterIndex] == rootValue) break; + } + // 切割中序数组 + // 左中序区间,左闭右开[leftInorderBegin, leftInorderEnd) + int leftInorderBegin = inorderBegin; + int leftInorderEnd = delimiterIndex; + // 右中序区间,左闭右开[rightInorderBegin, rightInorderEnd) + int rightInorderBegin = delimiterIndex + 1; + int rightInorderEnd = inorderEnd; + + // 切割后序数组 + // 左后序区间,左闭右开[leftPostorderBegin, leftPostorderEnd) + int leftPostorderBegin = postorderBegin; + int leftPostorderEnd = postorderBegin + delimiterIndex - inorderBegin; // 终止位置是 需要加上 中序区间的大小size + // 右后序区间,左闭右开[rightPostorderBegin, rightPostorderEnd) + int rightPostorderBegin = postorderBegin + (delimiterIndex - inorderBegin); + int rightPostorderEnd = postorderEnd - 1; // 排除最后一个元素,已经作为节点了 + + cout << "----------" << endl; + cout << "leftInorder :"; + for (int i = leftInorderBegin; i < leftInorderEnd; i++) { + cout << inorder[i] << " "; + } + cout << endl; + + cout << "rightInorder :"; + for (int i = rightInorderBegin; i < rightInorderEnd; i++) { + cout << inorder[i] << " "; + } + cout << endl; + + cout << "leftpostorder :"; + for (int i = leftPostorderBegin; i < leftPostorderEnd; i++) { + cout << postorder[i] << " "; + } + cout << endl; + + cout << "rightpostorder :"; + for (int i = rightPostorderBegin; i < rightPostorderEnd; i++) { + cout << postorder[i] << " "; + } + cout << endl; + + root->left = traversal(inorder, leftInorderBegin, leftInorderEnd, postorder, leftPostorderBegin, leftPostorderEnd); + root->right = traversal(inorder, rightInorderBegin, rightInorderEnd, postorder, rightPostorderBegin, rightPostorderEnd); + + return root; + } +public: + TreeNode* buildTree(vector& inorder, vector& postorder) { + if (inorder.size() == 0 || postorder.size() == 0) return NULL; + return traversal(inorder, 0, inorder.size(), postorder, 0, postorder.size()); + } +}; +``` + +# 105. 从前序与中序遍历序列构造二叉树 + +同样的道理 + +带日志的版本C++代码如下: (**带日志的版本仅用于调试,不要在leetcode上提交,会超时**) + +``` +class Solution { +private: + TreeNode* traversal (vector& inorder, int inorderBegin, int inorderEnd, vector& preorder, int preorderBegin, int preorderEnd) { + if (preorderBegin == preorderEnd) return NULL; + + int rootValue = preorder[preorderBegin]; // 注意用preorderBegin 不要用0 + TreeNode* root = new TreeNode(rootValue); + + if (preorderEnd - preorderBegin == 1) return root; + + int delimiterIndex; + for (delimiterIndex = inorderBegin; delimiterIndex < inorderEnd; delimiterIndex++) { + if (inorder[delimiterIndex] == rootValue) break; + } + // 切割中序数组 + // 中序左区间,左闭右开[leftInorderBegin, leftInorderEnd) + int leftInorderBegin = inorderBegin; + int leftInorderEnd = delimiterIndex; + // 中序右区间,左闭右开[rightInorderBegin, rightInorderEnd) + int rightInorderBegin = delimiterIndex + 1; + int rightInorderEnd = inorderEnd; + + // 切割前序数组 + // 前序左区间,左闭右开[leftPreorderBegin, leftPreorderEnd) + int leftPreorderBegin = preorderBegin + 1; + int leftPreorderEnd = preorderBegin + 1 + delimiterIndex - inorderBegin; // 终止位置是起始位置加上中序左区间的大小size + // 前序右区间, 左闭右开[rightPreorderBegin, rightPreorderEnd) + int rightPreorderBegin = preorderBegin + 1 + (delimiterIndex - inorderBegin); + int rightPreorderEnd = preorderEnd; + + cout << "----------" << endl; + cout << "leftInorder :"; + for (int i = leftInorderBegin; i < leftInorderEnd; i++) { + cout << inorder[i] << " "; + } + cout << endl; + + cout << "rightInorder :"; + for (int i = rightInorderBegin; i < rightInorderEnd; i++) { + cout << inorder[i] << " "; + } + cout << endl; + + cout << "leftPreorder :"; + for (int i = leftPreorderBegin; i < leftPreorderEnd; i++) { + cout << preorder[i] << " "; + } + cout << endl; + + cout << "rightPreorder :"; + for (int i = rightPreorderBegin; i < rightPreorderEnd; i++) { + cout << preorder[i] << " "; + } + cout << endl; + + + root->left = traversal(inorder, leftInorderBegin, leftInorderEnd, preorder, leftPreorderBegin, leftPreorderEnd); + root->right = traversal(inorder, rightInorderBegin, rightInorderEnd, preorder, rightPreorderBegin, rightPreorderEnd); + + return root; + } + +public: + TreeNode* buildTree(vector& preorder, vector& inorder) { + if (inorder.size() == 0 || preorder.size() == 0) return NULL; + return traversal(inorder, 0, inorder.size(), preorder, 0, preorder.size()); + + } +}; +``` + +105. 从前序与中序遍历序列构造二叉树,最后版本: + +C++代码: +``` +class Solution { +private: + TreeNode* traversal (vector& inorder, int inorderBegin, int inorderEnd, vector& preorder, int preorderBegin, int preorderEnd) { + if (preorderBegin == preorderEnd) return NULL; + + int rootValue = preorder[preorderBegin]; // 注意用preorderBegin 不要用0 + TreeNode* root = new TreeNode(rootValue); + + if (preorderEnd - preorderBegin == 1) return root; + + int delimiterIndex; + for (delimiterIndex = inorderBegin; delimiterIndex < inorderEnd; delimiterIndex++) { + if (inorder[delimiterIndex] == rootValue) break; + } + // 切割中序数组 + // 中序左区间,左闭右开[leftInorderBegin, leftInorderEnd) + int leftInorderBegin = inorderBegin; + int leftInorderEnd = delimiterIndex; + // 中序右区间,左闭右开[rightInorderBegin, rightInorderEnd) + int rightInorderBegin = delimiterIndex + 1; + int rightInorderEnd = inorderEnd; + + // 切割前序数组 + // 前序左区间,左闭右开[leftPreorderBegin, leftPreorderEnd) + int leftPreorderBegin = preorderBegin + 1; + int leftPreorderEnd = preorderBegin + 1 + delimiterIndex - inorderBegin; // 终止位置是起始位置加上中序左区间的大小size + // 前序右区间, 左闭右开[rightPreorderBegin, rightPreorderEnd) + int rightPreorderBegin = preorderBegin + 1 + (delimiterIndex - inorderBegin); + int rightPreorderEnd = preorderEnd; + + root->left = traversal(inorder, leftInorderBegin, leftInorderEnd, preorder, leftPreorderBegin, leftPreorderEnd); + root->right = traversal(inorder, rightInorderBegin, rightInorderEnd, preorder, rightPreorderBegin, rightPreorderEnd); + + return root; + } + +public: + TreeNode* buildTree(vector& preorder, vector& inorder) { + if (inorder.size() == 0 || preorder.size() == 0) return NULL; + + // 参数坚持左闭右开的原则 + return traversal(inorder, 0, inorder.size(), preorder, 0, preorder.size()); + } +}; +``` diff --git a/problems/0429.N叉树的层序遍历.md b/problems/0429.N叉树的层序遍历.md new file mode 100644 index 00000000..7dc76d1b --- /dev/null +++ b/problems/0429.N叉树的层序遍历.md @@ -0,0 +1,35 @@ + +## 题目地址 +https://leetcode-cn.com/problems/sum-of-left-leaves/ + +## 思路 + +层序遍历,和 102题目一个套路 + +## C++代码 + +``` +class Solution { +public: + vector> levelOrder(Node* root) { + queue que; + if (root != NULL) que.push(root); + vector> result; + while (!que.empty()) { + int size = que.size(); + vector vec; + for (int i = 0; i < size; i++) { // 这里一定要使用固定大小size,不要使用que.size() + Node* node = que.front(); + que.pop(); + vec.push_back(node->val); + for (int i = 0; i < node->children.size(); i++) { + if (node->children[i]) que.push(node->children[i]); + } + } + result.push_back(vec); + } + return result; + + } +}; +``` diff --git a/problems/0589.N叉树的前序遍历.md b/problems/0589.N叉树的前序遍历.md new file mode 100644 index 00000000..dfb7cf78 --- /dev/null +++ b/problems/0589.N叉树的前序遍历.md @@ -0,0 +1,56 @@ +## 题目地址 +https://leetcode-cn.com/problems/n-ary-tree-preorder-traversal/ + +## 思路 + + + +## 递归C++代码 + +``` +class Solution { +private: + vector result; + void traversal (Node* root) { + if (root == NULL) return; + result.push_back(root->val); + for (int i = 0; i < root->children.size(); i++) { + traversal(root->children[i]); + } + } + +public: + vector preorder(Node* root) { + result.clear(); + traversal(root); + return result; + } +}; +``` + +## 迭代法C++代码 + +``` +class Solution { + +public: + vector preorder(Node* root) { + vector result; + if (root == NULL) return result; + stack st; + st.push(root); + while (!st.empty()) { + Node* node = st.top(); + st.pop(); + result.push_back(node->val); + // 注意要倒叙,这样才能达到前序(中左右)的效果 + for (int i = node->children.size() - 1; i >= 0; i--) { + if (node->children[i] != NULL) { + st.push(node->children[i]); + } + } + } + return result; + } +}; +``` diff --git a/problems/0590.N叉树的后序遍历.md b/problems/0590.N叉树的后序遍历.md new file mode 100644 index 00000000..36c98fef --- /dev/null +++ b/problems/0590.N叉树的后序遍历.md @@ -0,0 +1,54 @@ +## 题目地址 +https://leetcode-cn.com/problems/n-ary-tree-postorder-traversal/ +## 思路 + +## 递归C++代码 + +``` +class Solution { +private: + vector result; + void traversal (Node* root) { + if (root == NULL) return; + for (int i = 0; i < root->children.size(); i++) { // 子孩子 + traversal(root->children[i]); + } + result.push_back(root->val); // 中 + + } + +public: + vector postorder(Node* root) { + result.clear(); + traversal(root); + return result; + + } +}; +``` + +## 迭代法C++代码 + +``` +class Solution { +public: + vector postorder(Node* root) { + vector result; + if (root == NULL) return result; + stack st; + st.push(root); + while (!st.empty()) { + Node* node = st.top(); + st.pop(); + result.push_back(node->val); + for (int i = 0; i < node->children.size(); i++) { // 相对于前序遍历,这里反过来 + if (node->children[i] != NULL) { + st.push(node->children[i]); + } + } + } + reverse(result.begin(), result.end()); // 反转数组 + return result; + } +}; +```