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pull merged 18 commits into AlgorithmAndLeetCode:main from itcharge:main
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更新题解列表
itcharge Jul 21, 2022
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更新章节列表
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Update 0035. 搜索插入位置.md
itcharge Jul 21, 2022
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Update 0004. 寻找两个正序数组的中位数.md
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Update 0128. 最长连续序列.md
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Update 0215. 数组中的第K个最大元素.md
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Update 0303. 区域和检索 - 数组不可变.md
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Update 0307. 区域和检索 - 数组可修改.md
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Update 0370. 区间加法.md
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Update 0715. Range 模块.md
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Update 0912. 排序数组.md
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Update 1099. 小于 K 的两数之和.md
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Update 1109. 航班预订统计.md
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Update 1310. 子数组异或查询.md
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Update 剑指 Offer II 119. 最长连续序列.md
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Update 0300. 最长递增子序列.md
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commit 9627f49a8abc9a38ef919cf584c89e4fd684cb4f
16 changes: 8 additions & 8 deletions Assets/Origins/Categories-List.md
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###### 0124. 二叉树中的最大路径和、0543. 二叉树的直径、0337. 打家劫舍 III、0333. 最大 BST 子树

### [数位 DP 题目](../../Contents/10.Dynamic-Programming/07.Number-DP/02.Number-DP-List.md)
### [状态压缩 DP 题目](../../Contents/10.Dynamic-Programming/07.State-DP/02.State-DP-List.md)

###### 0600. 不含连续1的非负整数、0233. 数字 1 的个数、0902. 最大为 N 的数字组合、1015. 可被 K 整除的最小整数
###### 0526. 优美的排列、0464. 我能赢吗、0847. 访问所有节点的最短路径、1994. 好子集的数目、0935. 骑士拨号器、1349. 参加考试的最大学生数

### [状态压缩 DP 题目](../../Contents/10.Dynamic-Programming/08.State-DP/02.State-DP-List.md)
### [计数 DP 题目](../../Contents/10.Dynamic-Programming/08.Count-DP/02.Count-DP-List.md)

###### 0526. 优美的排列、0464. 我能赢吗、0847. 访问所有节点的最短路径、1994. 好子集的数目、0935. 骑士拨号器、1349. 参加考试的最大学生数
###### 0062. 不同路径、0063. 不同路径 II、0096. 不同的二叉搜索树、1259. 不相交的握手

### [概率 DP 题目](../../Contents/10.Dynamic-Programming/09.Probability-DP/02.Probability-DP-List.md)
### [数位 DP 题目](../../Contents/10.Dynamic-Programming/09.Number-DP/02.Number-DP-List.md)

###### 0688. 骑士在棋盘上的概率、0808. 分汤、0837. 新 21 点
###### 0600. 不含连续1的非负整数、0233. 数字 1 的个数、0902. 最大为 N 的数字组合、1015. 可被 K 整除的最小整数

### [计数 DP 题目](../../Contents/10.Dynamic-Programming/10.Count-DP/10.Count-DP-List.md)
### [概率 DP 题目](../../Contents/10.Dynamic-Programming/10.Probability-DP/02.Probability-DP-List.md)

###### 0062. 不同路径、0063. 不同路径 II、0096. 不同的二叉搜索树、1259. 不相交的握手
###### 0688. 骑士在棋盘上的概率、0808. 分汤、0837. 新 21 点

### [动态规划优化题目](../../Contents/10.Dynamic-Programming/11.DP-Optimization/04.DP-Optimization-List.md)
20 changes: 10 additions & 10 deletions Assets/Origins/README-Catalogue-List.md
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- 树形 DP
- [树形 DP 知识](https://github.com/itcharge/LeetCode-Py/blob/main/Contents/10.Dynamic-Programming/06.Tree-DP/01.Tree-DP.md)
- [树形 DP 题目](https://github.com/itcharge/LeetCode-Py/blob/main/Contents/10.Dynamic-Programming/06.Tree-DP/02.Tree-DP-List.md)
- 数位 DP
- [数位 DP 知识](https://github.com/itcharge/LeetCode-Py/blob/main/Contents/10.Dynamic-Programming/07.Number-DP/01.Number-DP.md)
- [数位 DP 题目](https://github.com/itcharge/LeetCode-Py/blob/main/Contents/10.Dynamic-Programming/07.Number-DP/02.Number-DP-List.md)
- 状态压缩 DP
- [状态压缩 DP 知识](https://github.com/itcharge/LeetCode-Py/blob/main/Contents/10.Dynamic-Programming/08.State-DP/01.State-DP.md)
- [状态压缩 DP 题目](https://github.com/itcharge/LeetCode-Py/blob/main/Contents/10.Dynamic-Programming/08.State-DP/02.State-DP-List.md)
- 概率 DP
- [概率 DP 知识](https://github.com/itcharge/LeetCode-Py/blob/main/Contents/10.Dynamic-Programming/09.Probability-DP/01.Probability-DP.md)
- [概率 DP 题目](https://github.com/itcharge/LeetCode-Py/blob/main/Contents/10.Dynamic-Programming/09.Probability-DP/02.Probability-DP-List.md)
- [状态压缩 DP 知识](https://github.com/itcharge/LeetCode-Py/blob/main/Contents/10.Dynamic-Programming/07.State-DP/01.State-DP.md)
- [状态压缩 DP 题目](https://github.com/itcharge/LeetCode-Py/blob/main/Contents/10.Dynamic-Programming/07.State-DP/02.State-DP-List.md)
- 计数 DP
- [计数 DP 知识](https://github.com/itcharge/LeetCode-Py/blob/main/Contents/10.Dynamic-Programming/10.Count-DP/01.Count-DP.md)
- [计数 DP 题目](https://github.com/itcharge/LeetCode-Py/blob/main/Contents/10.Dynamic-Programming/10.Count-DP/10.Count-DP-List.md)
- [计数 DP 知识](https://github.com/itcharge/LeetCode-Py/blob/main/Contents/10.Dynamic-Programming/08.Count-DP/01.Count-DP.md)
- [计数 DP 题目](https://github.com/itcharge/LeetCode-Py/blob/main/Contents/10.Dynamic-Programming/08.Count-DP/02.Count-DP-List.md)
- 数位 DP
- [数位 DP 知识](https://github.com/itcharge/LeetCode-Py/blob/main/Contents/10.Dynamic-Programming/09.Number-DP/01.Number-DP.md)
- [数位 DP 题目](https://github.com/itcharge/LeetCode-Py/blob/main/Contents/10.Dynamic-Programming/09.Number-DP/02.Number-DP-List.md)
- 概率 DP
- [概率 DP 知识](https://github.com/itcharge/LeetCode-Py/blob/main/Contents/10.Dynamic-Programming/10.Probability-DP/01.Probability-DP.md)
- [概率 DP 题目](https://github.com/itcharge/LeetCode-Py/blob/main/Contents/10.Dynamic-Programming/10.Probability-DP/02.Probability-DP-List.md)
- 动态规划优化
- [单调栈 / 优先队列优化](https://github.com/itcharge/LeetCode-Py/blob/main/Contents/10.Dynamic-Programming/11.DP-Optimization/01.Monotone-Stack-Queue-Optimization.md)
- [斜率优化](https://github.com/itcharge/LeetCode-Py/blob/main/Contents/10.Dynamic-Programming/11.DP-Optimization/02.Slope-Optimization.md)
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34 changes: 17 additions & 17 deletions Contents/00.Introduction/05.Categories-List.md
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| 0337 | [打家劫舍 III](https://leetcode.cn/problems/house-robber-iii/) | [Python](https://github.com/itcharge/LeetCode-Py/blob/main/Solutions/0337.%20%E6%89%93%E5%AE%B6%E5%8A%AB%E8%88%8D%20III.md) | 树、深度优先搜索、动态规划、二叉树 | 中等 |
| 0333 | 最大 BST 子树 | | | |

### 数位 DP 题目

| 题号 | 标题 | 题解 | 标签 | 难度 |
| :------ | :------ | :------ | :------ | :------ |
| 0600 | 不含连续1的非负整数 | | | |
| 0233 | 数字 1 的个数 | | | |
| 0902 | 最大为 N 的数字组合 | | | |
| 1015 | 可被 K 整除的最小整数 | | | |

### 状态压缩 DP 题目

| 题号 | 标题 | 题解 | 标签 | 难度 |
Expand All @@ -942,14 +933,6 @@
| 0935 | 骑士拨号器 | | | |
| 1349 | 参加考试的最大学生数 | | | |

### 概率 DP 题目

| 题号 | 标题 | 题解 | 标签 | 难度 |
| :------ | :------ | :------ | :------ | :------ |
| 0688 | 骑士在棋盘上的概率 | | | |
| 0808 | 分汤 | | | |
| 0837 | 新 21 点 | | | |

### 计数 DP 题目

| 题号 | 标题 | 题解 | 标签 | 难度 |
Expand All @@ -959,5 +942,22 @@
| 0096 | [不同的二叉搜索树](https://leetcode.cn/problems/unique-binary-search-trees/) | [Python](https://github.com/itcharge/LeetCode-Py/blob/main/Solutions/0096.%20%E4%B8%8D%E5%90%8C%E7%9A%84%E4%BA%8C%E5%8F%89%E6%90%9C%E7%B4%A2%E6%A0%91.md) | 树、二叉搜索树、数学、动态规划、二叉树 | 中等 |
| 1259 | 不相交的握手 | | | |

### 数位 DP 题目

| 题号 | 标题 | 题解 | 标签 | 难度 |
| :------ | :------ | :------ | :------ | :------ |
| 0600 | 不含连续1的非负整数 | | | |
| 0233 | 数字 1 的个数 | | | |
| 0902 | 最大为 N 的数字组合 | | | |
| 1015 | 可被 K 整除的最小整数 | | | |

### 概率 DP 题目

| 题号 | 标题 | 题解 | 标签 | 难度 |
| :------ | :------ | :------ | :------ | :------ |
| 0688 | 骑士在棋盘上的概率 | | | |
| 0808 | 分汤 | | | |
| 0837 | 新 21 点 | | | |

### 动态规划优化题目

8 changes: 8 additions & 0 deletions Contents/10.Dynamic-Programming/03.Linear-DP/01.Linear-DP.md
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## 1. 线性 DP 简介

> **线性 DP**:具有「线性」阶段划分的动态规划方法统称为线性动态规划(简称为「线性 DP」)。
>
> - 如果状态包含多个维度,则每个维度都是线性划分的阶段,也属于线性 DP。

## 2. 线性 DP 的应用

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## 1. 背包问题简介

> **背包问题**:背包问题是线性 DP 中一类经典而又特殊的模型。背包问题可以描述为:给定一组物品,每种物品都有自己的重量和价格,在限定的总重量内,我们如何选择,才能使得物品的总价格最高。

## 2. 01 背包问题

> **01 背包问题描述**:一共有 `n` 件物品,其中第 `i` 件物品的体积为 `c[i]`,价值为 `w[i]`。现在有一个容量为 `V` 的背包,请问在总容量不超过背包容量上限的情况下,能装入背包的最大价值是多少?

## 3. 完全背包问题

> **完全背包问题**:一共有 `n` 种物品,每种物品有无限多个,其中第 `i` 件物品的体积为 `c[i]`,价值为 `w[i]`。现在有一个容量为 `V` 的背包,请问在总容量不超过背包容量上限的情况下,能装入背包的最大价值是多少?

## 4. 多重背包问题

> **多重背包问题**:一共有 `n` 种物品,其中第 `i` 种物品的件数为 `m[i]`,每件物品的体积为 `c[i]`,价值为 `w[i]`。现在有一个容量为 `V` 的背包,请问在总容量不超过背包容量上限的情况下,能装入背包的最大价值是多少?



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## 1. 区间 DP 简介

> **区间 DP**:线性 DP 的一种,以「区间长度」划分阶段,以两个坐标(区间的左、右端点)作为状态的维度。一个状态通常由被它包含且比它更小的区间状态转移而来。

## 2. 区间 DP 的应用
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## 1. 树形 DP 简介

> **树形 DP**:在树形结构上实现的动态规划方法叫做树形 DP。树形 DP 的求解过程一般以节点从深到浅(子树从小到大)的顺序作为动态规划的「阶段」。将节点编号作为状态的第 1 维,代表以该节点为根的子树。
>
> 通常我们采用递归的方式求解每棵子树,在回溯时从子节点向上进行状态转移。在当前节点的所有子树求解完毕之后,才可以求解当前节点。

## 2. 树形 DP 的应用
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## 1. 状态压缩 DP 简介

> **状态压缩 DP**:如果使用动态规划方法设计的状态是一个大小不超过 `n` 的集合,并且集合中的每个元素都是小于 `k` 的正整数,则我们可以把这个集合看做是一个 `n` 位的 `k` 进制数,以一个 $[0, k^n - 1]$ 之间的十进制整数的形式作为动态规划状态的一维。这种把集合转化为整数记录在动态规划状态中的一类方法,被称为状态压缩动态规划方法。

## 2. 状态压缩 DP 的应用
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## 1. 计数类 DP 简介

> **计数类 DP**:统计可行方案数的一类动态规划,区别于求解最优解,计数类 DP需要统计所有满足条件的可行解数量,这些问题需要满足不重复、不遗漏的条件。

## 2. 计数类 DP 的应用
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## 1. 数位 DP 简介

> **数位 DP**:与数位相关的一类计数类动态规划,即在数位上进行动态规划。这里的数位指的是个位、十位、百位、千位等。
>
> - 数位 DP 一般用来统计区间 `[l, r]` 上满足特定条件的元素个数,或者用于求解满足特定条件的第 `k` 小数。

## 2. 数位 DP 的应用
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## 1. 概率 DP 简介

> **概率 DP**:与概率相关的一类动态规划。由于概率和期望具有线性性质,使得可以在概率和期望之间建立一定的递推关系,从而通过动态规划的方式来解决一些概率问题。

## 2. 概率 DP 的应用
20 changes: 10 additions & 10 deletions Contents/index.md
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- 树形 DP
- [树形 DP 知识](./10.Dynamic-Programming/06.Tree-DP/01.Tree-DP.md)
- [树形 DP 题目](./10.Dynamic-Programming/06.Tree-DP/02.Tree-DP-List.md)
- 数位 DP
- [数位 DP 知识](./10.Dynamic-Programming/07.Number-DP/01.Number-DP.md)
- [数位 DP 题目](./10.Dynamic-Programming/07.Number-DP/02.Number-DP-List.md)
- 状态压缩 DP
- [状态压缩 DP 知识](./10.Dynamic-Programming/08.State-DP/01.State-DP.md)
- [状态压缩 DP 题目](./10.Dynamic-Programming/08.State-DP/02.State-DP-List.md)
- 概率 DP
- [概率 DP 知识](./10.Dynamic-Programming/09.Probability-DP/01.Probability-DP.md)
- [概率 DP 题目](./10.Dynamic-Programming/09.Probability-DP/02.Probability-DP-List.md)
- [状态压缩 DP 知识](./10.Dynamic-Programming/07.State-DP/01.State-DP.md)
- [状态压缩 DP 题目](./10.Dynamic-Programming/07.State-DP/02.State-DP-List.md)
- 计数 DP
- [计数 DP 知识](./10.Dynamic-Programming/10.Count-DP/01.Count-DP.md)
- [计数 DP 题目](./10.Dynamic-Programming/10.Count-DP/10.Count-DP-List.md)
- [计数 DP 知识](./10.Dynamic-Programming/08.Count-DP/01.Count-DP.md)
- [计数 DP 题目](./10.Dynamic-Programming/08.Count-DP/02.Count-DP-List.md)
- 数位 DP
- [数位 DP 知识](./10.Dynamic-Programming/09.Number-DP/01.Number-DP.md)
- [数位 DP 题目](./10.Dynamic-Programming/09.Number-DP/02.Number-DP-List.md)
- 概率 DP
- [概率 DP 知识](./10.Dynamic-Programming/10.Probability-DP/01.Probability-DP.md)
- [概率 DP 题目](./10.Dynamic-Programming/10.Probability-DP/02.Probability-DP-List.md)
- 动态规划优化
- [单调栈 / 优先队列优化](./10.Dynamic-Programming/11.DP-Optimization/01.Monotone-Stack-Queue-Optimization.md)
- [斜率优化](./10.Dynamic-Programming/11.DP-Optimization/02.Slope-Optimization.md)
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- 树形 DP
- [树形 DP 知识](./Contents/10.Dynamic-Programming/06.Tree-DP/01.Tree-DP.md)
- [树形 DP 题目](./Contents/10.Dynamic-Programming/06.Tree-DP/02.Tree-DP-List.md)
- 数位 DP
- [数位 DP 知识](./Contents/10.Dynamic-Programming/07.Number-DP/01.Number-DP.md)
- [数位 DP 题目](./Contents/10.Dynamic-Programming/07.Number-DP/02.Number-DP-List.md)
- 状态压缩 DP
- [状态压缩 DP 知识](./Contents/10.Dynamic-Programming/08.State-DP/01.State-DP.md)
- [状态压缩 DP 题目](./Contents/10.Dynamic-Programming/08.State-DP/02.State-DP-List.md)
- 概率 DP
- [概率 DP 知识](./Contents/10.Dynamic-Programming/09.Probability-DP/01.Probability-DP.md)
- [概率 DP 题目](./Contents/10.Dynamic-Programming/09.Probability-DP/02.Probability-DP-List.md)
- [状态压缩 DP 知识](./Contents/10.Dynamic-Programming/07.State-DP/01.State-DP.md)
- [状态压缩 DP 题目](./Contents/10.Dynamic-Programming/07.State-DP/02.State-DP-List.md)
- 计数 DP
- [计数 DP 知识](./Contents/10.Dynamic-Programming/10.Count-DP/01.Count-DP.md)
- [计数 DP 题目](./Contents/10.Dynamic-Programming/10.Count-DP/10.Count-DP-List.md)
- [计数 DP 知识](./Contents/10.Dynamic-Programming/08.Count-DP/01.Count-DP.md)
- [计数 DP 题目](./Contents/10.Dynamic-Programming/08.Count-DP/02.Count-DP-List.md)
- 数位 DP
- [数位 DP 知识](./Contents/10.Dynamic-Programming/09.Number-DP/01.Number-DP.md)
- [数位 DP 题目](./Contents/10.Dynamic-Programming/09.Number-DP/02.Number-DP-List.md)
- 概率 DP
- [概率 DP 知识](./Contents/10.Dynamic-Programming/10.Probability-DP/01.Probability-DP.md)
- [概率 DP 题目](./Contents/10.Dynamic-Programming/10.Probability-DP/02.Probability-DP-List.md)
- 动态规划优化
- [单调栈 / 优先队列优化](./Contents/10.Dynamic-Programming/11.DP-Optimization/01.Monotone-Stack-Queue-Optimization.md)
- [斜率优化](./Contents/10.Dynamic-Programming/11.DP-Optimization/02.Slope-Optimization.md)
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