From baf55b429aef2e10b3b92c2821f0ae9cbff34b08 Mon Sep 17 00:00:00 2001 From: youngyangyang04 <826123027@qq.com> Date: Wed, 21 Oct 2020 09:02:35 +0800 Subject: [PATCH] Update --- README.md | 4 + problems/0084.柱状图中最大的矩形.md | 74 ++++++ problems/0143.重排链表.md | 17 +- .../0450.删除二叉搜索树中的节点.md | 227 ++++++++++++++++-- .../0701.二叉搜索树中的插入操作.md | 2 +- .../450.删除二叉搜索树中的节点.gif | Bin 0 -> 503260 bytes 6 files changed, 294 insertions(+), 30 deletions(-) create mode 100644 video/450.删除二叉搜索树中的节点.gif diff --git a/README.md b/README.md index b7f926fe..ccfa84bd 100644 --- a/README.md +++ b/README.md @@ -118,6 +118,9 @@ * [二叉树:搜索树的最小绝对差](https://mp.weixin.qq.com/s/Hwzml6698uP3qQCC1ctUQQ) * [二叉树:我的众数是多少?](https://mp.weixin.qq.com/s/KSAr6OVQIMC-uZ8MEAnGHg) * [二叉树:公共祖先问题](https://mp.weixin.qq.com/s/n6Rk3nc_X3TSkhXHrVmBTQ) + * [本周小结!(二叉树系列四)](https://mp.weixin.qq.com/s/CbdtOTP0N-HIP7DR203tSg) + * [二叉树:搜索树的公共祖先问题](https://mp.weixin.qq.com/s/Ja9dVw2QhBcg_vV-1fkiCg) + * [二叉树:搜索树中的插入操作](https://mp.weixin.qq.com/s/lwKkLQcfbCNX2W-5SOeZEA) @@ -262,6 +265,7 @@ |[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**| |[0083.删除排序链表中的重复元素](https://github.com/youngyangyang04/leetcode/blob/master/problems/0083.删除排序链表中的重复元素.md) |链表 |简单|**模拟**| +|[0084.柱状图中最大的矩形](https://github.com/youngyangyang04/leetcode/blob/master/problems/0084.柱状图中最大的矩形.md) |数组 |困难|**单调栈**| |[0090.子集II](https://github.com/youngyangyang04/leetcode/blob/master/problems/0090.子集II.md) |回溯/数组 |中等|**回溯**| |[0093.复原IP地址](https://github.com/youngyangyang04/leetcode/blob/master/problems/0093.复原IP地址) |回溯 |中等|**回溯**| |[0094.二叉树的中序遍历](https://github.com/youngyangyang04/leetcode/blob/master/problems/0094.二叉树的中序遍历.md) |树 |中等|**递归** **迭代/栈**| diff --git a/problems/0084.柱状图中最大的矩形.md b/problems/0084.柱状图中最大的矩形.md index 2c0eae97..21dae82a 100644 --- a/problems/0084.柱状图中最大的矩形.md +++ b/problems/0084.柱状图中最大的矩形.md @@ -29,3 +29,77 @@ public: ``` 如上代码并不能通过leetcode,超时了,因为时间复杂度是O(n^2)。 + +## 思考一下动态规划 + +## 单调栈 + +单调栈的思路还是不容易理解的, + +想清楚从大到小,还是从小到大, + +本题是从栈底到栈头 从小到大,和 接雨水正好反过来。 + + + +``` +class Solution { +public: + int largestRectangleArea(vector& heights) { + stack st; + heights.insert(heights.begin(), 0); // 数组头部加入元素0 + heights.push_back(0); // 数组尾部加入元素0 + st.push(0); + int result = 0; + // 第一个元素已经入栈,从下表1开始 + for (int i = 1; i < heights.size(); i++) { + // 注意heights[i] 是和heights[st.top()] 比较 ,st.top()是下表 + if (heights[i] > heights[st.top()]) { + st.push(i); + } else if (heights[i] == heights[st.top()]) { + st.pop(); // 这个可以加,可以不加,效果一样,思路不同 + st.push(i); + } else { + while (heights[i] < heights[st.top()]) { // 注意是while + int mid = st.top(); + st.pop(); + int left = st.top(); + int right = i; + int w = right - left - 1; + int h = heights[mid]; + result = max(result, w * h); + } + st.push(i); + } + } + return result; + } +}; + +``` + +代码精简之后: + +``` +class Solution { +public: + int largestRectangleArea(vector& heights) { + stack st; + heights.insert(heights.begin(), 0); // 数组头部加入元素0 + heights.push_back(0); // 数组尾部加入元素0 + st.push(0); + int result = 0; + for (int i = 1; i < heights.size(); i++) { + while (heights[i] < heights[st.top()]) { + int mid = st.top(); + st.pop(); + int w = i - st.top() - 1; + int h = heights[mid]; + result = max(result, w * h); + } + st.push(i); + } + return result; + } +}; +``` diff --git a/problems/0143.重排链表.md b/problems/0143.重排链表.md index a51f79b3..9011692b 100644 --- a/problems/0143.重排链表.md +++ b/problems/0143.重排链表.md @@ -26,8 +26,8 @@ public: } cur = head; int i = 1; - int j = vec.size() - 1; - int count = 0; // 计数,用来取前面,取后面 + int j = vec.size() - 1; // i j为之前前后的双指针 + int count = 0; // 计数,偶数去后面,奇数取前面 while (i <= j) { if (count % 2 == 0) { cur->next = vec[j]; @@ -39,7 +39,7 @@ public: cur = cur->next; count++; } - if (vec.size() % 2 == 0) { + if (vec.size() % 2 == 0) { // 如果是偶数,还要多处理中间的一个 cur->next = vec[i]; cur = cur->next; } @@ -54,7 +54,7 @@ public: ``` class Solution { public: - void reorderList(ListNode* head) { + void reorderList(ListNode* head) { deque que; ListNode* cur = head; if (cur == nullptr) return; @@ -65,7 +65,7 @@ public: } cur = head; - int count = 0; + int count = 0; // 计数,偶数去后面,奇数取前面 ListNode* node; while(que.size()) { if (count % 2 == 0) { @@ -79,7 +79,7 @@ public: cur->next = node; cur = cur->next; } - cur->next = nullptr; + cur->next = nullptr; // 注意结尾 } }; ``` @@ -99,6 +99,7 @@ public: ``` class Solution { private: + // 反转链表 ListNode* reverseList(ListNode* head) { ListNode* temp; // 保存cur的下一个节点 ListNode* cur = head; @@ -137,7 +138,7 @@ public: ListNode* cur2 = head2; ListNode* cur = head; cur1 = cur1->next; - int count = 0; + int count = 0; // 偶数取head2的元素,奇数取head1的元素 while (cur1 && cur2) { if (count % 2 == 0) { cur->next = cur2; @@ -149,7 +150,7 @@ public: count++; cur = cur->next; } - if (cur2 != nullptr) { + if (cur2 != nullptr) { // 处理结尾 cur->next = cur2; } if (cur1 != nullptr) { diff --git a/problems/0450.删除二叉搜索树中的节点.md b/problems/0450.删除二叉搜索树中的节点.md index 7f024675..0e696e23 100644 --- a/problems/0450.删除二叉搜索树中的节点.md +++ b/problems/0450.删除二叉搜索树中的节点.md @@ -1,55 +1,132 @@ ## 题目地址 https://leetcode-cn.com/problems/delete-node-in-a-bst/ -## 思路 +> 二叉搜索树删除节点就涉及到结构调整了 -平衡二叉树中删除节点一下五种情况: +# 450.删除二叉搜索树中的节点 + +题目链接: https://leetcode-cn.com/problems/delete-node-in-a-bst/ + +给定一个二叉搜索树的根节点 root 和一个值 key,删除二叉搜索树中的 key 对应的节点,并保证二叉搜索树的性质不变。返回二叉搜索树(有可能被更新)的根节点的引用。 + +一般来说,删除节点可分为两个步骤: + +首先找到需要删除的节点; +如果找到了,删除它。 +说明: 要求算法时间复杂度为 O(h),h 为树的高度。 + +示例: + +![450.删除二叉搜索树中的节点](https://img-blog.csdnimg.cn/20201020171048265.png) + +# 思路 + +搜索树的节点删除要比节点增加复杂的多,有很多情况需要考虑,做好心里准备。 + +## 递归 + +递归三部曲: + +* 确定递归函数参数以及返回值 + +说道递归函数的返回值,在[二叉树:搜索树中的插入操作](https://mp.weixin.qq.com/s/lwKkLQcfbCNX2W-5SOeZEA)中通过递归返回值来加入新节点, 这里也可以通过递归返回值删除节点。 + +代码如下: + +``` +TreeNode* deleteNode(TreeNode* root, int key) +``` + +* 确定终止条件 + +遇到空返回,其实这也说明没找到删除的节点,遍历到空节点直接返回了 + +``` +if (root == nullptr) return root; +``` + +* 确定单层递归的逻辑 + +这里就把平衡二叉树中删除节点遇到的情况都搞清楚。 + +有以下五种情况: * 第一种情况:没找到删除的节点,遍历到空节点直接返回了 * 找到删除的节点 * 第二种情况:左右孩子都为空(叶子节点),直接删除节点, 返回NULL为根节点 - * 第三种情况:其左孩子为空,右孩子不为空,删除节点,右孩子补位 ,返回右孩子为根节点 - * 第四种情况:其右孩子为空,左孩子不为空,删除节点,左孩子补位,返回左孩子为根节点 - * 第五种情况:左右孩子节点都不为空,则将删除节点的左孩子放到删除节点的右孩子的最左面节点的左孩子上,返回删除节点右孩子为新的根节点。 + * 第三种情况:删除节点的左孩子为空,右孩子不为空,删除节点,右孩子补位,返回右孩子为根节点 + * 第四种情况:删除节点的右孩子为空,左孩子不为空,删除节点,左孩子补位,返回左孩子为根节点 + * 第五种情况:左右孩子节点都不为空,则将删除节点的左子树头结点(左孩子)放到删除节点的右子树的最左面节点的左孩子上,返回删除节点右孩子为新的根节点。 第五种情况有点难以理解,看下面动画: -动画中颗二叉搜索树中,删除元素7, 那么删除节点(元素7)的左孩子就是5,删除节点(元素7)的右孩子的最左面节点是元素8。 + -将将删除节点(元素7)的左孩子放到删除节点(元素7)的右孩子的最左面节点的左孩子上,就是把5为根节点的子树移到了8的左孩子的位置。 +动画中颗二叉搜索树中,删除元素7, 那么删除节点(元素7)的左孩子就是5,删除节点(元素7)的右子树的最左面节点是元素8。 -接着删除节点(元素7)右孩子为新的根节点。(click)也就是元素7位根节点的树,现在的根节点变成元素9的根节点的树了. +将删除节点(元素7)的左孩子放到删除节点(元素7)的右子树的最左面节点(元素8)的左孩子上,就是把5为根节点的子树移到了8的左孩子的位置。 - +要删除的节点(元素7)的右孩子(元素9)为新的根节点。. +这样就完成删除元素7的逻辑,最好动手画一个图,尝试删除一个节点试试。 +代码如下: -这样就完成删除元素7的逻辑,也可以动手画一个图,尝试删除一个节点试试。 +``` +if (root->val == key) { + // 第二种情况:左右孩子都为空(叶子节点),直接删除节点, 返回NULL为根节点 + // 第三种情况:其左孩子为空,右孩子不为空,删除节点,右孩子补位 ,返回右孩子为根节点 + if (root->left == nullptr) return root->right; + // 第四种情况:其右孩子为空,左孩子不为空,删除节点,左孩子补位,返回左孩子为根节点 + else if (root->right == nullptr) return root->left; + // 第五种情况:左右孩子节点都不为空,则将删除节点的左子树放到删除节点的右子树的最左面节点的左孩子的位置 + // 并返回删除节点右孩子为新的根节点。 + else { + TreeNode* cur = root->right; // 找右子树最左面的节点 + while(cur->left != nullptr) { + cur = cur->left; + } + cur->left = root->left; // 把要删除的节点(root)左子树放在cur的左孩子的位置 + TreeNode* tmp = root; // 把root节点保存一下,下面来删除 + root = root->right; // 返回旧root的右孩子作为新root + delete tmp; // 释放节点内存(这里不写也可以,但C++最好手动释放一下吧) + return root; + } +} +``` -代码如下:(详细注释) +这里相当于把新的节点返回给上一层,上一层就要用 root->left 或者 root->right接住,代码如下: -## C++代码 +``` +if (root->val > key) root->left = deleteNode(root->left, key); +if (root->val < key) root->right = deleteNode(root->right, key); +return root; +``` + +**整体代码如下:(注释中:情况1,2,3,4,5和上面分析严格对应)** ``` class Solution { public: TreeNode* deleteNode(TreeNode* root, int key) { - if (root == NULL) return root; // 第一种情况:没找到删除的节点,遍历到空节点直接返回了 + if (root == nullptr) return root; // 第一种情况:没找到删除的节点,遍历到空节点直接返回了 if (root->val == key) { // 第二种情况:左右孩子都为空(叶子节点),直接删除节点, 返回NULL为根节点 // 第三种情况:其左孩子为空,右孩子不为空,删除节点,右孩子补位 ,返回右孩子为根节点 - if (root->left == NULL) return root->right; + if (root->left == nullptr) return root->right; // 第四种情况:其右孩子为空,左孩子不为空,删除节点,左孩子补位,返回左孩子为根节点 - else if (root->right == NULL) return root->left; - // 第五种情况:左右孩子节点都不为空,则将删除节点的左孩子放到删除节点的右孩子的最左面节点的左孩子的位置 - // 返回删除节点右孩子为新的根节点。 + else if (root->right == nullptr) return root->left; + // 第五种情况:左右孩子节点都不为空,则将删除节点的左子树放到删除节点的右子树的最左面节点的左孩子的位置 + // 并返回删除节点右孩子为新的根节点。 else { - TreeNode* cur = root->right; - while(cur->left != NULL) { + TreeNode* cur = root->right; // 找右子树最左面的节点 + while(cur->left != nullptr) { cur = cur->left; } - cur->left = root->left; - root = root->right; + cur->left = root->left; // 把要删除的节点(root)左子树放在cur的左孩子的位置 + TreeNode* tmp = root; // 把root节点保存一下,下面来删除 + root = root->right; // 返回旧root的右孩子作为新root + delete tmp; // 释放节点内存(这里不写也可以,但C++最好手动释放一下吧) return root; } } @@ -60,5 +137,113 @@ public: }; ``` +这里我在介绍一种通用的删除,普通二叉树的删除方式(没有使用搜索树的特性,遍历整棵树),用交换值的操作来删除目标节点。 + +代码中目标节点(要删除的节点)被操作了两次: + +* 第一次是和目标节点的右子树最左面节点交换。 +* 第二次直接被NULL覆盖了。 + +思路有点绕,感兴趣的同学可以画图自己理解一下。 + +代码如下:(关键部分已经注释) + +``` +class Solution { +public: + TreeNode* deleteNode(TreeNode* root, int key) { + if (root == nullptr) return root; + if (root->val == key) { + if (root->right == nullptr) { // 这里第二次操作目标值:最终删除的作用 + return root->left; + } + TreeNode *cur = root->right; + while (cur->left) { + cur = cur->left; + } + swap(root->val, cur->val); // 这里第一次操作目标值:交换目标值其右子树最左面节点。 + } + root->left = deleteNode(root->left, key); + root->right = deleteNode(root->right, key); + return root; + } +}; +``` + +这个代码是简短一些,思路也巧妙,但是不太好想,实操性不强,推荐第一种写法! + +## 迭代法 + +删除节点的迭代法还是复杂一些的,但其本质我在递归法里都介绍了,最关键就是删除节点的操作(动画模拟的过程) + +代码如下: + +``` +class Solution { +private: + // 将目标节点(删除节点)的左子树放到 目标节点的右子树的最左面节点的左孩子位置上 + // 并返回目标节点右孩子为新的根节点 + // 是动画里模拟的过程 + TreeNode* deleteOneNode(TreeNode* target) { + if (target == nullptr) return target; + if (target->right == nullptr) return target->left; + TreeNode* cur = target->right; + while (cur->left) { + cur = cur->left; + } + cur->left = target->left; + return target->right; + } +public: + TreeNode* deleteNode(TreeNode* root, int key) { + if (root == nullptr) return root; + TreeNode* cur = root; + TreeNode* pre = nullptr; // 记录cur的父节点,用来删除cur + while (cur) { + if (cur->val == key) break; + pre = cur; + if (cur->val > key) cur = cur->left; + else cur = cur->right; + } + if (pre == nullptr) { // 如果搜索树只有头结点 + return deleteOneNode(cur); + } + // pre 要知道是删左孩子还是右孩子 + if (pre->left && pre->left->val == key) { + pre->left = deleteOneNode(cur); + } + if (pre->right && pre->right->val == key) { + pre->right = deleteOneNode(cur); + } + return root; + } +}; +``` + +# 总结 + +读完本篇,大家会发现二叉搜索树删除节点比增加节点复杂的多。 + +**因为二叉搜索树添加节点只需要在叶子上添加就可以的,不涉及到结构的调整,而删除节点操作涉及到结构的调整**。 + +这里我们依然使用递归函数的返回值来完成把节点从二叉树中移除的操作。 + +**这里最关键的逻辑就是第五种情况(删除一个左右孩子都不为空的节点),这种情况一定要想清楚**。 + +而且就算想清楚了,对应的代码也未必可以写出来,所以**这道题目即考察思维逻辑,也考察代码能力**。 + +递归中我给出了两种写法,推荐大家学会第一种(利用搜索树的特性)就可以了,第二种递归写法其实是比较绕的。 + +最后我也给出了相应的迭代法,就是模拟递归法中的逻辑来删除节点,但需要一个pre记录cur的父节点,方便做删除操作。 + +迭代法其实不太容易写出来,所以如果是初学者的话,彻底掌握第一种递归写法就够了。 + +**就酱,又是干货满满的一篇,大家加油!** + + + + + + > 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/0701.二叉搜索树中的插入操作.md b/problems/0701.二叉搜索树中的插入操作.md index 045c7f73..babb3025 100644 --- a/problems/0701.二叉搜索树中的插入操作.md +++ b/problems/0701.二叉搜索树中的插入操作.md @@ -87,7 +87,7 @@ if (root->val < val) root->right = insertIntoBST(root->right, val); return root; ``` -**到这里,大家应该能感受到,如何通过递归函数返回值完成了新加入节点的父子关系赋值操作了,上一层将加入节点返回,本层用root->left或者root->right将其接住**。 +**到这里,大家应该能感受到,如何通过递归函数返回值完成了新加入节点的父子关系赋值操作了,下一层将加入节点返回,本层用root->left或者root->right将其接住**。 整体代码如下: diff --git a/video/450.删除二叉搜索树中的节点.gif 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