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Computer-science-is-discrete
- Introduction
Discrete-math
Discrete-math
- Introduction
- Why-we-need-discrete-math
- Book-Discrete-Mathematics-and-Its-Applications
  Book-Discrete-Mathematics-and-Its-Applications
  - Introduction
  - Chapter-2-Basic-Structures
    Chapter-2-Basic-Structures
    
    Chapter-2-Basic-Structures
  - Chapter-5-Induction-and-Recursion
    Chapter-5-Induction-and-Recursion
    
    Chapter-5-Induction-and-Recursion
  - Chapter-6-Counting
    Chapter-6-Counting
    
    Chapter-6-Counting
  - Chpater-9-Relations
    Chpater-9-Relations
    
    Chpater-9-Relations
- Set-theory
  Set-theory
  - Introduction
  - Power-set
- Number-theory
  Number-theory
  - Ordinal-number
  - Prime-number
- Catalan-and-Bell
  Catalan-and-Bell
  - Introduction
  - Partition-of-a-set
    Partition-of-a-set
    
    Introduction
    
    计算机算法设计与分析-习题-2-7&2-8集合划分问题
    计算机算法设计与分析-习题-2-7&2-8集合划分问题
    
    Introduction
  - Catalan-number
    Catalan-number
    
    Introduction
    
    wikipedia-Catalan-number
    wikipedia-Catalan-number
    
    Introduction
Relation-structure-computation
Relation-structure-computation
- Introduction
- Relation
  Relation
  - Introduction
  - Relation
    Relation
    
    Introduction
    
    Representation-of-relation
    Representation-of-relation
    
    Introduction
    
    Closures-of-relation
    Closures-of-relation
    
    Introduction
  - Entity–relationship-model
    Entity–relationship-model
    
    Introduction
  - Order-theory
    Order-theory
    
    Introduction
    
    Partially-order
    Partially-order
    
    Introduction
    
    Total-order
    Total-order
    
    Introduction
    
    Well-order
    Well-order
    
    Introduction
    
    Preorder
    
    Greatest-and-least-elements
    Greatest-and-least-elements
    
    Introduction
- Structure
  Structure
  - Introduction
- Computation
  Computation
  - Introduction
  - Make-it-computational
    Make-it-computational
    
    Introduction
    
    Structuralization-and-formalization
    Structuralization-and-formalization
    
    Introduction
    
    Ordering
    Ordering
    
    Introduction
  - Computation-direction
    Computation-direction
    
    Introduction
    
    Top-down-and-bottom-up
    Top-down-and-bottom-up
    
    Introduction
    
    FIFO-and-FILO
    FIFO-and-FILO
    
    Introduction
  - Relation-based-algorithm-model
    Relation-based-algorithm-model
    
    Introduction
  - Repetition
    Repetition
    
    Introduction
    
    Iteration
    Iteration
    
    Introduction
    
    Iteration
    
    Iterator
    Iterator
    
    Introduction
    
    Induction-and-Recursion
    Induction-and-Recursion
    
    Introduction
    
    Induction-and-deduction
    Induction-and-deduction
    
    Introduction
    
    Induction-and-deduction
    
    Induction
    
    Coinduction
    
    Recursion
    Recursion
    
    Introduction
    
    Recursive-Definition
    Recursive-Definition
    
    Introduction
    
    Recursion
    Recursion
    
    Introduction
    
    Double-recursion
    Double-recursion
    
    Introduction
    
    Recurrence-relation
    Recurrence-relation
    
    Introduction
    
    Recursion-in-computer-science
    Recursion-in-computer-science
    
    Recursive-data-type
    Recursive-data-type
    
    Introduction
    
    Recursion(computer-science)
    Recursion(computer-science)
    
    Introduction
    
    Recursive-programs
    Recursive-programs
    
    Introduction
    
    Structural-and-generative-recursion
    Structural-and-generative-recursion
    
    Introduction
    
    Term-with-recursion-in-computer-science
    
    Corecursion
    
    Summary
  - Computation-on-structure
    Computation-on-structure
    
    Introduction
  - Computer-algebra
    Computer-algebra
    
    Introduction
  - Theory-of-computation
    Theory-of-computation
    
    index
    
    Great-Theoretical-Ideas-in-Computer-Science
    Great-Theoretical-Ideas-in-Computer-Science
    
    Introduction
    
    Theory-of-computation
    
    Model-of-computation
    Model-of-computation
    
    Model-of-computation
    
    Lambda-calculus
    Lambda-calculus
    
    Introduction
    
    Computability-theory
    Computability-theory
    
    Computability-theory
    
    Automata-theory
    Automata-theory
    
    Introduction
    
    Abstract-machine
    
    Turinig-machine
    Turinig-machine
    
    Introduction
    
    cl.cam.uk-What-is-a-Turing-machine
    
    wikipedia-Turing-machine
    
    Finite-state-machine
    Finite-state-machine
    
    Introduction
    
    Event-driven-finite-state-machine
    
    Automata-software
    
    Computational-complexity-theory
    Computational-complexity-theory
    
    TODO-Computational-complexity-theory
    
    TODO-NP-completeness
    
    TODO-NP-hardness
- Model
  Model
  - Introduction
  - Hierarchy-relation-model
    Hierarchy-relation-model
    
    Introduction
  - Nesting-relation-model
    Nesting-relation-model
    
    Introduction
  - Dependency-relation
    Dependency-relation
    
    Introduction
  - Chain
    Chain
    
    Introduction
  - Chain-VS-hierarchy
    Chain-VS-hierarchy
    
    Introduction
  - Stream-model
    Stream-model
    
    Introduction
    
    Programming-model
    Programming-model
    
    Introduction
  - Circular
    Circular
    
    Introduction
- Function-recursion-tree-stack
  Function-recursion-tree-stack
  - Introduction
  - Analysis-and-representation-of-recursion
    Analysis-and-representation-of-recursion
    
    Introduction
Algorithm
Algorithm
- Introduction
- 算法思维
  算法思维
  - Introduction
  - 穷举State-solution-space
    穷举State-solution-space
    
    Introduction
    
    Combinatorial-explosion
    Combinatorial-explosion
    
    Introduction
  - Divide-and-Conquer
    Divide-and-Conquer
    
    Introduction
    
    wikipedia-Divide-and-conquer-algorithm
    wikipedia-Divide-and-conquer-algorithm
    
    Introduction
    
    Divide-and-conquer-and-merge-framework
    Divide-and-conquer-and-merge-framework
    
    Introduction
    
    Complexity-analysis
    Complexity-analysis
    
    Introduction
    
    wikipedia-Master-theorem(analysis-of-algorithms)
    wikipedia-Master-theorem(analysis-of-algorithms)
    
    Introduction
  - Overlapping-subproblem
    Overlapping-subproblem
    
    Introduction
    
    以空间换时间
    以空间换时间
    
    Introduction
  - Recurrence-relation递归状态转移方程
    Recurrence-relation递归状态转移方程
    
    Introduction
- Paradigm
  Paradigm
  - Introduction
  - wikipedia-Algorithmic-paradigm
    wikipedia-Algorithmic-paradigm
    
    Introduction
  - Guide
    Guide
    
    Introduction
    
    Dynamic-programming-VS-search-VS-greedy
    Dynamic-programming-VS-search-VS-greedy
    
    Introduction
  - Brute-force
    Brute-force
    
    Introduction
  - DP&Greedy
    DP&Greedy
    
    Introduction
    
    Optimal-substructure
    Optimal-substructure
    
    Introduction Introduction
    Table of contents
    
    以"结构化思维"来看到substructure
    
    labuladong 动态规划详解 # 二、凑零钱问题
    
    wikipedia Optimal substructure
    
    Problems with optimal substructure
    
    Problems without optimal substructure
    
    Bellman-equation
    Bellman-equation
    
    Introduction
    
    DP
    DP
    
    Introduction
    
    wikipedia-Dynamic-programming
    wikipedia-Dynamic-programming
    
    Introduction
    
    geeksforgeeks-Dynamic-Programming
    geeksforgeeks-Dynamic-Programming
    
    Introduction
    
    CSDN-DP算法分类总结
    CSDN-DP算法分类总结
    
    Introduction
    
    最大子段和
    最大子段和
    
    Introduction
    
    Catalan
    Catalan
    
    Introduction
    
    julyedu-从暴力递归走向动态规划-研究过卡特兰数
    julyedu-从暴力递归走向动态规划-研究过卡特兰数
    
    Introduction
    
    矩阵连乘问题
    矩阵连乘问题
    
    Introduction
    
    wikipedia-Matrix-chain-multiplication
    wikipedia-Matrix-chain-multiplication
    
    Introduction
    
    geeksforgeeks-Matrix-Chain-Multiplication
    geeksforgeeks-Matrix-Chain-Multiplication
    
    Introduction
    
    最优二叉搜索树
    最优二叉搜索树
    
    Introduction
    
    LeetCode-96-不同的二叉搜索树
    LeetCode-96-不同的二叉搜索树
    
    Introduction
    
    凸多边形的最优三角剖分
    凸多边形的最优三角剖分
    
    Introduction
    
    wikipedia-Polygon-triangulation
    wikipedia-Polygon-triangulation
    
    Introduction
    
    LeetCode-1039-多边形三角剖分的最低得分
    LeetCode-1039-多边形三角剖分的最低得分
    
    Introduction
    
    TODO-排队找零问题
    TODO-排队找零问题
    
    Introduction
    
    Greedy
    Greedy
    
    Introduction
    
    Huffman-Coding
    Huffman-Coding
    
    Introduction
    
    Reading-list
  - Heuristic
    Heuristic
    
    Introduction
  - Statistical-algorithms
    Statistical-algorithms
    
    HyperLogLog
- Randomized-algorithm
  Randomized-algorithm
  - Introduction
  - Monte-Carlo-algorithm
    Monte-Carlo-algorithm
    
    Introduction
  - Random-sample
    Random-sample
    
    Introduction
    
    Reservoir-Sample-蓄水池抽样
    Reservoir-Sample-蓄水池抽样
    
    Introduction
  - Fisher–Yates-shuffle
    Fisher–Yates-shuffle
    
    Introduction
- Analysis
  Analysis
  - Introduction
  - wikipedia-Analysis-of-algorithms
    wikipedia-Analysis-of-algorithms
    
    Introduction
- Search
  Search
  - wikipedia-Search-algorithm
    wikipedia-Search-algorithm
    
    Introduction
  - Guide
- Binary-search
  Binary-search
  - Introduction
  - wikipedia-Binary-search-algorithm
    wikipedia-Binary-search-algorithm
    
    Introduction
  - Complexity-analysis
    Complexity-analysis
    
    Introduction
- State-space-search
  State-space-search
  - Introduction
  - Backtracking
    Backtracking
    
    Introduction
    
    计算机算法设计与分析-5-回溯法
    计算机算法设计与分析-5-回溯法
    
    Introduction
    
    wikipedia-Backtracking
    wikipedia-Backtracking
    
    Introduction
    
    Examples
    Examples
    
    Introduction
    
    Sudoku-solving
    Sudoku-solving
    
    Introduction
    
    N-queen
    N-queen
    
    Introduction
    
    LeetCode-51-N-皇后-Hard
    LeetCode-51-N-皇后-Hard
    
    Introduction
    
    LeetCode-52-N-皇后-II-Hard
    LeetCode-52-N-皇后-II-Hard
    
    Introduction
    
    LeetCode-面试题-08.12-八皇后
    LeetCode-面试题-08.12-八皇后
    
    Introduction
    
    Symbol-triangle
    Symbol-triangle
    
    Introduction
    
    M-coloring-of-graph
    M-coloring-of-graph
    
    Introduction
    
    Permutation-of-circle
    Permutation-of-circle
    
    Introduction
  - Branch-and-Bound
    Branch-and-Bound
    
    Introduction
    
    Branch-and-cut
  - Permutation-and-combination
    Permutation-and-combination
    
    Permutation
    Permutation
    
    Introduction
    
    Enum-permutation
    Enum-permutation
    
    Backtrack-enum-all-permutations-of-string
    
    Enum-distinct-permutation-of-with-duplicate
    
    Enum-permutation-reading-list
    
    Reading-list
  - VS-brute-force-search
    VS-brute-force-search
    
    Introduction
- Sorting
  Sorting
  - Introduction
  - Bubble-Sort
    Bubble-Sort
    
    Introduction
  - Insertion-sort
    Insertion-sort
    
    Introduction
  - Quick-sort
    Quick-sort
    
    Introduction
    
    Quicksort&&BST
    Quicksort&&BST
    
    Introduction
  - Merge-sort
    Merge-sort
    
    Introduction
  - Heapsort
    Heapsort
    
    Introduction
  - Shellsort
    Shellsort
    
    Introduction
  - Bucket-sort
    Bucket-sort
    
    Introduction
  - Hybrid
    Hybrid
    
    Introduction
    
    Timsort
    Timsort
    
    Introduction
    
    Introsort
    Introsort
    
    Introduction
  - Lexicographical-order-字典序
    Lexicographical-order-字典序
    
    Introduction
  - LeetCode-912-排序数组
    LeetCode-912-排序数组
    
    Introduction
  - Top-K-rank
    Top-K-rank
    
    Introduction
    
    Selection-algorithm
    Selection-algorithm
    
    Introduction
    
    Quick-select
    Quick-select
    
    Introduction
    
    Median-of-medians
    Median-of-medians
    
    Introduction
    
    最接近
    最接近
    
    Introduction
    
    LeetCode-973-最接近原点的K个点
    LeetCode-973-最接近原点的K个点
    
    Introduction
    
    LeetCode-658-找到K个最接近的元素
    LeetCode-658-找到K个最接近的元素
    
    Introduction
    
    LeetCode-剑指-Offer-40-最小的k个数
    LeetCode-剑指-Offer-40-最小的k个数
    
    Introduction
- Merge-algorithm
  Merge-algorithm
  - Introduction
  - K-way-merge-algorithm
    K-way-merge-algorithm
    
    Introduction
- Classical-algorithm
  Classical-algorithm
  - Tower-of-Hanoi
    Tower-of-Hanoi
    
    Introduction
  - Fibonacci
    Fibonacci
    
    Introduction
- Application
  Application
  - Computational-problem
  - Optimization
    Optimization
    
    Introduction
    
    Mathematical-optimization
    Mathematical-optimization
    
    Loss-function-or-Objective-function
    
    Iterative-optimization-algorithm
    
    Iterative-method
    
    Hill-climbing
    
    Combinatorial-optimization
    Combinatorial-optimization
    
    Introduction
    
    Combinatorics
    Combinatorics
    
    Introduction
    
    Combinatorics
    
    Enumerative-combinatorics
    Enumerative-combinatorics
    
    Introduction
    
    TODO-Linear-programming
    TODO-Linear-programming
    
    wikipedia-Linear-programming
    
    wikipedia-Integer-programming
- 海量数据处理
  海量数据处理
  - Introduction
  - External-sorting
    External-sorting
    
    Introduction
    
    CSDN-外部排序算法总结
    CSDN-外部排序算法总结
    
    Introduction
  - 从大量URL中找出相同URL
    从大量URL中找出相同URL
    
    Introduction
  - 不重复的数字
    不重复的数字
    
    Introduction
  - 从5亿个数中找出中位数
    从5亿个数中找出中位数
    
    Introduction
  - Top-K
    Top-K
    
    Introduction
  - 按照query频率排序
    按照query频率排序
    
    Introduction
Data-structure
Data-structure
- Introduction
- Guide
  Guide
  - Introduction
  - List-of-data-structure
    List-of-data-structure
    
    Introduction
  - Graph&&tree&&list
    Graph&&tree&&list
    
    Introduction
  - Hybrid-data-structure
    Hybrid-data-structure
    
    Introduction
  - Double-linked-list-VS-binary-tree
    Double-linked-list-VS-binary-tree
    
    Introduction
    
    LeetCode
    LeetCode
    
    LeetCode-1367-二叉树中的列表
    LeetCode-1367-二叉树中的列表
    
    Introduction
    
    LeetCode-剑指-Offer-36-二叉搜索树与双向链表
    LeetCode-剑指-Offer-36-二叉搜索树与双向链表
    
    Introduction
    
    LeetCode-114-二叉树展开为链表
    LeetCode-114-二叉树展开为链表
    
    Introduction
    
    LeetCode-109-有序链表转换二叉搜索树
    LeetCode-109-有序链表转换二叉搜索树
    
    Introduction
- ADT&&Impl
  ADT&&Impl
  - Introduction
  - Associative-array&&set
    Associative-array&&set
    
    Introduction
    
    Associative-array
    Associative-array
    
    Introduction
    
    Set
    Set
    
    Introduction
  - Priority-queue
    Priority-queue
    
    Introduction
- Array
  Array
  - Introduction
  - Bit-array
    Bit-array
    
    Introduction
  - Circular-array
    Circular-array
    
    Introduction
    
    spdlog-circular_q
    spdlog-circular_q
    
    Introduction
    
    martinbroadhurst-cirque
    martinbroadhurst-cirque
    
    Introduction
  - Prefix-sum-array-and-difference-array
    Prefix-sum-array-and-difference-array
    
    labuladong-论那些小而美的算法技巧-差分数组前缀和
    labuladong-论那些小而美的算法技巧-差分数组前缀和
    
    Introduction
    
    labuladong-前缀和技巧-解决子数组问题
    labuladong-前缀和技巧-解决子数组问题
    
    Introduction
    
    TODO-Prefix-sum-array-and-difference-array
    TODO-Prefix-sum-array-and-difference-array
    
    Introduction
    
    Difference-array
    Difference-array
    
    Introduction
    
    wikipedia-Prefix-sum
    wikipedia-Prefix-sum
    
    Introduction
  - LeetCode
    LeetCode
    
    Merge-合并
    Merge-合并
    
    geeksforgeeks-Merge-k-sorted-arrays
    geeksforgeeks-Merge-k-sorted-arrays
    
    Introduction
    
    TODO-LeetCode-4-寻找两个正序数组的中位数-Hard
    TODO-LeetCode-4-寻找两个正序数组的中位数-Hard
    
    Introduction
    
    TODO-LeetCode-88-合并两个有序数组
    TODO-LeetCode-88-合并两个有序数组
    
    Introduction
    
    TODO-LeetCode-面试题-10.01-合并排序的数组
    TODO-LeetCode-面试题-10.01-合并排序的数组
    
    Introduction
- Linked-list
  Linked-list
  - Introduction
  - Unrolled-linked-list
    Unrolled-linked-list
    
    Introduction
  - Double-linked-list
    Double-linked-list
    
    Introduction
  - Sentinel-node
    Sentinel-node
    
    Introduction
  - Dummy-node
    Dummy-node
    
    Introduction
  - Algorithm
    Algorithm
    
    Previous-current-next-pointer-三指针
    Previous-current-next-pointer-三指针
    
    Introduction
    
    LeetCode-剑指-Offer-18-删除链表的节点
    LeetCode-剑指-Offer-18-删除链表的节点
    
    Introduction
    
    LeetCode-面试题-02-03-删除中间节点
    LeetCode-面试题-02-03-删除中间节点
    
    Introduction
    
    Fast-slow-double-pointer-快慢双指针
    Fast-slow-double-pointer-快慢双指针
    
    LeetCode-141-环形链表
    LeetCode-141-环形链表
    
    Introduction
    
    LeetCode-142-环形链表-II
    LeetCode-142-环形链表-II
    
    Introduction
    
    LeetCode-面试题-02.02-返回倒数第k个节点
    LeetCode-面试题-02.02-返回倒数第k个节点
    
    Introduction
    
    LeetCode-剑指-Offer-22-链表中倒数第k个节点
    LeetCode-剑指-Offer-22-链表中倒数第k个节点
    
    Introduction
    
    LeetCode-19-删除链表的倒数第N个结点
    LeetCode-19-删除链表的倒数第N个结点
    
    Introduction
    
    LeetCode-876-链表的中间结点
    LeetCode-876-链表的中间结点
    
    Introduction
    
    去重
    去重
    
    LeetCode-83-删除排序链表中的重复元素
    LeetCode-83-删除排序链表中的重复元素
    
    Introduction
    
    LeetCode-82-删除排序链表中的重复元素-II
    LeetCode-82-删除排序链表中的重复元素-II
    
    Introduction
    
    Merge-合并
    Merge-合并
    
    使用链表实现大数加法-求和
    使用链表实现大数加法-求和
    
    LeetCode-2-两数相加
    LeetCode-2-两数相加
    
    Introduction
    
    LeetCode-445-两数相加-II
    LeetCode-445-两数相加-II
    
    Introduction
    
    LeetCode-1669-合并两个链表
    LeetCode-1669-合并两个链表
    
    Introduction
    
    合并有序链表
    合并有序链表
    
    LeetCode-21-合并两个有序链表
    LeetCode-21-合并两个有序链表
    
    Introduction
    
    LeetCode-剑指-Offer-25-合并两个排序的链表
    LeetCode-剑指-Offer-25-合并两个排序的链表
    
    Introduction
    
    LeetCode-23-合并K个升序链表-Hard
    LeetCode-23-合并K个升序链表-Hard
    
    Introduction
    
    公共节点
    公共节点
    
    LeetCode-160-相交链表
    LeetCode-160-相交链表
    
    Introduction
    
    LeetCode-剑指-Offer-52-两个链表的第一个公共节点
    LeetCode-剑指-Offer-52-两个链表的第一个公共节点
    
    Introduction
    
    Reverse-反转
    Reverse-反转
    
    LeetCode-206-反转链表-简单
    LeetCode-206-反转链表-简单
    
    Introduction
    
    LeetCode-92-反转链表-II-中等
    LeetCode-92-反转链表-II-中等
    
    Introduction
    
    LeetCode-剑指-Offer-06-从尾到头打印链表-简单
    LeetCode-剑指-Offer-06-从尾到头打印链表-简单
    
    Introduction
    
    Sort-linked-list
    Sort-linked-list
    
    LeetCode-147-对链表进行插入排序
    LeetCode-147-对链表进行插入排序
    
    Introduction
    
    LeetCode-148-排序链表
    LeetCode-148-排序链表
    
    Introduction
    
    Circle-detection
    Circle-detection
    
    Introduction
    
    TODO-Floyd判环算法
    TODO-Floyd判环算法
    
    Introduction
- Stack
  Stack
  - Introduction
  - wikipedia-Stack(abstract-data-type)
    wikipedia-Stack(abstract-data-type)
    
    Introduction
  - geeksforgeeks-Stack-Data-Structure
  - Monotonic-stack
    Monotonic-stack
    
    Introduction
    
    labuladong-单调栈Monotonic-Stack的使用
    labuladong-单调栈Monotonic-Stack的使用
    
    Introduction
    
    labuladong-单调栈解题模板秒杀三道算法题
    labuladong-单调栈解题模板秒杀三道算法题
    
    Introduction
    
    All-nearest-smaller-values
    All-nearest-smaller-values
    
    Introduction
    
    Stack-sortable-permutation
    Stack-sortable-permutation
    
    Introduction
    
    Monotonic-stack解Max-min-subsequence(子序列)
    Monotonic-stack解Max-min-subsequence(子序列)
    
    Introduction
    
    LeetCode-402-移掉K位数字
    LeetCode-402-移掉K位数字
    
    Introduction
    
    LeetCode-316-去除重复字母
    LeetCode-316-去除重复字母
    
    Introduction
    
    LeetCode-402-移掉K位数字
  - Sort-stack
    Sort-stack
    
    Introduction
  - Stack-and-queue
    Stack-and-queue
    
    Introduction
    
    LeetCode-剑指-Offer-09-用两个栈实现队列
    LeetCode-剑指-Offer-09-用两个栈实现队列
    
    Introduction
  - Reverse-by-stack-反转
    Reverse-by-stack-反转
    
    Reverse-a-string-using-stack
    Reverse-a-string-using-stack
    
    Introduction
    
    Reverse-individual-words
  - Reverse-stack-反转
    Reverse-stack-反转
    
    Introduction
  - Application-of-stack
- Graph
  Graph
  - Introduction
  - Graph-theory
    Graph-theory
    
    Introduction
    
    Directed-graph
    Directed-graph
    
    Introduction
    
    Directed-acyclic-graph
    Directed-acyclic-graph
    
    Introduction
    
    Graph-representations
    Graph-representations
    
    Introduction
    
    Adjacency-list
    Adjacency-list
    
    Introduction
    
    Python-Patterns-Implementing-Graphs
    
    Incidence-matrix
    Incidence-matrix
    
    Introduction
    
    Connectivity(graph theory)
    Connectivity(graph theory)
    
    Introduction
  - Graph-Model
    Graph-Model
    
    Introduction
    
    Dependency-graph
    Dependency-graph
    
    Introduction
    
    Precedence-graph
    Precedence-graph
    
    Introduction
    
    Circular-dependency
    
    Dependency-resolving-algorithm
    Dependency-resolving-algorithm
    
    Introduction
  - Graph-operation
    Graph-operation
    
    Introduction
  - Computational-problems
    Computational-problems
    
    Introduction
    
    Circular
    Circular
    
    Cycle-detection
    Cycle-detection
    
    Introduction
    
    Max-circle
    Max-circle
    
    Introduction
    
    Dominator
    Dominator
    
    Introduction
    
    Closure
    Closure
    
    Introduction
  - Implementation
    Implementation
    
    Introduction
  - Graph-traversal
    Graph-traversal
    
    Introduction
    
    Depth-first search-DFS
    Depth-first search-DFS
    
    Introduction
    
    Breadth-first-search-BFS
    Breadth-first-search-BFS
    
    Introduction
  - Shortest-longest-path
    Shortest-longest-path
    
    Introduction
    
    Dijkstra's-algorithm
    Dijkstra's-algorithm
    
    Introduction
    
    计算机算法设计与分析-4-5-单源最短路径
    计算机算法设计与分析-4-5-单源最短路径
    
    Introduction
    
    LeetCode-787-K站中转内最便宜的航班
    LeetCode-787-K站中转内最便宜的航班
    
    Introduction
    
    Bellman–Ford-algorithm
    Bellman–Ford-algorithm
    
    Introduction
  - Topological-sorting
    Topological-sorting
    
    Introduction
  - Spanning-tree
    Spanning-tree
    
    Introduction
    
    Minimum-spanning-tree
    
    Borůvka's-algorithm
  - Search-algorithm
    Search-algorithm
    
    Guide
    Guide
    
    Introduction
    
    Course-umn-CSci4511w-Class-Notes-on-Search
    Course-umn-CSci4511w-Class-Notes-on-Search
    
    Introduction
    
    Course-washington-Search-Cost&Heuristics
    Course-washington-Search-Cost&Heuristics
    
    Introduction
    
    Property-of-search-algorithm
    Property-of-search-algorithm
    
    Completeness
    Completeness
    
    Introduction
    
    Optimality
    Optimality
    
    Introduction
    
    Iterative-deepening-depth-first-search
    
    Best-first-search
    
    A-star-search-algorithm
    
    B-star-search-algorithm
    
    Beam-search
    
    Uniform-cost-search
    Uniform-cost-search
    
    Introduction
  - Flood-Fill-泛洪算法
    Flood-Fill-泛洪算法
    
    Introduction
    
    LeetCode-733-图像渲染
    LeetCode-733-图像渲染
    
    Introduction
    
    LeetCode-面试题-08.10-颜色填充
    LeetCode-面试题-08.10-颜色填充
    
    Introduction
    
    LeetCode-1034-边框着色
    LeetCode-1034-边框着色
    
    Introduction
    
    LeetCode-面试题-08.10-颜色填充
    LeetCode-面试题-08.10-颜色填充
    
    Introduction
  - LeetCode
    LeetCode
    
    课程表
    课程表
    
    LeetCode-207-课程表
    LeetCode-207-课程表
    
    Introduction
    
    LeetCode-210-课程表-II
    LeetCode-210-课程表-II
    
    Introduction
    
    LeetCode-1462-课程表-IV
    LeetCode-1462-课程表-IV
    
    Introduction
    
    LeetCode-547-省份数量
    LeetCode-547-省份数量
    
    Introduction
- Tree
  Tree
  - Introduction
  - Tree-structure
    Tree-structure
    
    Introduction
    
    Examples
    Examples
    
    Introduction
  - Represent-tree
    Represent-tree
    
    Introduction
  - Tree-data-structure
    Tree-data-structure
    
    Introduction
    
    Binary-tree
    Binary-tree
    
    Introduction
  - Parenthese-and-tree
    Parenthese-and-tree
    
    Introduction
    
    i-programmer-Parentheses-Are-Trees
    i-programmer-Parentheses-Are-Trees
    
    Introduction
    
    Bracket(tournament)
    Bracket(tournament)
    
    Introduction
  - Tree-algorithm
    Tree-algorithm
    
    Introduction
    
    Build-tree
    Build-tree
    
    Introduction
    
    Traversal
    Traversal
    
    Introduction
    
    Implementation
    
    Morris-traversal
    Morris-traversal
    
    Introduction
    
    LeetCode-94-二叉树的中序遍历
    LeetCode-94-二叉树的中序遍历
    
    Introduction
    
    LeetCode-145-二叉树的后序遍历
    LeetCode-145-二叉树的后序遍历
    
    Introduction
    
    LeetCode-173-二叉搜索树迭代器
    LeetCode-173-二叉搜索树迭代器
    
    Introduction
    
    Breadth-first-traverse
    Breadth-first-traverse
    
    LeetCode-剑指-Offer-32-I-从上到下打印二叉树
    LeetCode-剑指-Offer-32-I-从上到下打印二叉树
    
    Introduction
    
    LeetCode-剑指-Offer-32-II-从上到下打印二叉树
    LeetCode-剑指-Offer-32-II-从上到下打印二叉树
    
    Introduction
    
    LeetCode-剑指-Offer-32-III-从上到下打印二叉树
    LeetCode-剑指-Offer-32-III-从上到下打印二叉树
    
    Introduction
    
    Top-K-rank-of-node
    Top-K-rank-of-node
    
    Introduction
    
    Merge-合并
    Merge-合并
    
    LeetCode-617-合并二叉树
    LeetCode-617-合并二叉树
    
    Introduction
    
    Depth
    Depth
    
    Introduction
    
    Sum
    Sum
    
    Introduction
    
    LeetCode-124-二叉树中的最大路径和
    LeetCode-124-二叉树中的最大路径和
    
    Introduction
    
    LeetCode-333-最大BST子树
    LeetCode-333-最大BST子树
    
    Introduction
    
    Serialization-deserialization
    Serialization-deserialization
    
    Introduction
    
    BST
    BST
    
    Introduction
    
    geeksforgeeks-tree-algorithm
    geeksforgeeks-tree-algorithm
    
    Introduction
    
    Maximum-sub-tree-sum-in-Binary-Tree-such-that-sub-tree-is-BST
    Maximum-sub-tree-sum-in-Binary-Tree-such-that-sub-tree-is-BST
    
    Introduction
    
    LeetCode-431-将N叉树编码为二叉树
    LeetCode-431-将N叉树编码为二叉树
    
    Introduction
  - Search-tree
    Search-tree
    
    Introduction
    
    Binary-search-tree
    Binary-search-tree
    
    Introduction
    
    Self-balancing-binary-search-tree
    Self-balancing-binary-search-tree
    
    Introduction
    
    Red-black-tree
    Red-black-tree
    
    Introduction
    
    wisc.edu-Red-Black-Trees
    wisc.edu-Red-Black-Trees
    
    Introduction
    
    Left-leaning-red–black-tree
    Left-leaning-red–black-tree
    
    Introduction
    
    B-tree&&B+tree
    B-tree&&B+tree
    
    Introduction
    
    codinglabs-MySQL索引背后的数据结构及算法原理
    codinglabs-MySQL索引背后的数据结构及算法原理
    
    Introduction
    
    segmentfault-由B-B+树看MySQL索引结构
    segmentfault-由B-B+树看MySQL索引结构
    
    Introduction
    
    B-tree
    B-tree
    
    Introduction
    
    cornell-course-B-Trees
    cornell-course-B-Trees
    
    Introduction
    
    B+tree
    B+tree
    
    Introduction
    
    Trie
    Trie
    
    Introduction
    
    wikipedia-Trie
    wikipedia-Trie
    
    Introduction
    
    geeksforgeeks-trie
  - Disjoint-set
    Disjoint-set
    
    Introduction
  - Implementation
    Implementation
    
    Introduction
    
    Implicit-tree
    Implicit-tree
    
    Introduction
  - Application
    Application
    
    Introduction
- Heap
  Heap
  - Introduction
- Hash
  Hash
  - Introduction
  - Hash-function
    Hash-function
    
    Introduction
    
    Perfect-hash-function
    Perfect-hash-function
    
    Introduction
    
    Rolling-hash
    Rolling-hash
    
    Introduction
    
    Geometric-hashing
    Geometric-hashing
    
    Introduction
    
    SipHash
    
    Cryptographic-hash-functions
    Cryptographic-hash-functions
    
    Introduction
    
    Cipher
    
    Salt(cryptography)
    
    Linear-hash
    Linear-hash
    
    Introduction
    
    Implementation
    Implementation
    
    Introduction
  - Hash-table
    Hash-table
    
    Introduction
    
    wikipedia-Hash-table
    wikipedia-Hash-table
    
    Introduction
    
    geeksforgeeks-hash-table
    geeksforgeeks-hash-table
    
    Introduction
    
    rcoh-Hash-Map-Implementation-in-Popular-Language
    rcoh-Hash-Map-Implementation-in-Popular-Language
    
    Introduction
  - Merkle-tree
    Merkle-tree
    
    Introduction
  - Checksum
    Checksum
    
    Introduction
    
    peterjockisch-Practical-Application-of-Cryptographic-Checksums
    peterjockisch-Practical-Application-of-Cryptographic-Checksums
    
    Introduction
  - Application
    Application
    
    Introduction
    
    去重
    去重
    
    Introduction
    
    Use-checksum-to-find-duplicate-file
    Use-checksum-to-find-duplicate-file
    
    Introduction
  - Error-detection-and-correction
    Error-detection-and-correction
    
    Introduction
    
    Error-correction-code
    Error-correction-code
    
    Introduction
    
    Parity-bit
    Parity-bit
    
    Introduction
- Probabilistic-data-structures
  Probabilistic-data-structures
  - Bloom-filter
    Bloom-filter
    
    Bloom-filter
  - Cuckoo-filter
    Cuckoo-filter
    
    Introduction
  - Skip-list
    Skip-list
    
    Introduction
  - Random-tree
- Judy-array
  Judy-array
  - Introduction
  - sourceforge-library-Judy
    sourceforge-library-Judy
    
    Introduction
  - TODO-nothing-A-Performance-Comparison-of-Judy-to-Hash-Tables
    TODO-nothing-A-Performance-Comparison-of-Judy-to-Hash-Tables
    
    Introduction
  - TODO-rusty.ozlabs-Hashtables-vs-Judy-Arrays
    TODO-rusty.ozlabs-Hashtables-vs-Judy-Arrays
    
    Introduction
- String
  String
  - Introduction
  - wikipedia-String(computer-science)
    wikipedia-String(computer-science)
    
    Introduction
  - Pattern-match
    Pattern-match
    
    Introduction
  - String-search
    String-search
    
    Introduction
    
    Knuth-Morris-Pratt-algorithm
    Knuth-Morris-Pratt-algorithm
    
    Introduction
    
    Rabin-Karp-algorithm
    Rabin-Karp-algorithm
    
    Introduction
  - LeetCode
    LeetCode
    
    Reverse-反转
    Reverse-反转
    
    LeetCode-344-反转字符串
    LeetCode-344-反转字符串
    
    Introduction
    
    LeetCode-541-反转字符串-II
    LeetCode-541-反转字符串-II
    
    Introduction
    
    LeetCode-14-最长公共前缀
    LeetCode-14-最长公共前缀
    
    Introduction
- TODO
LeetCode
LeetCode
- Introduction
- 数学-数字
  数学-数字
  - Introduction
  - LeetCode-7-整数反转
    LeetCode-7-整数反转
    
    Introduction
  - LeetCode-273-整数转换英文表示-困难
    LeetCode-273-整数转换英文表示-困难
    
    Introduction
  - 大整数算术
    大整数算术
    
    Introduction
- Subsequence-Subarray-Substring
  Subsequence-Subarray-Substring
  - Introduction
  - Systematic-method-穷举
    Systematic-method-穷举
    
    Introduction
- LeetCode-16.19-水域大小
  LeetCode-16.19-水域大小
  - Introduction
- Tournament-比赛
  Tournament-比赛
  - Introduction
  - 计算机算法设计与分析-2.11-循环赛日程表
    计算机算法设计与分析-2.11-循环赛日程表
    
    Introduction
Expert-labuladong
Expert-labuladong
- 0-必读系列
  0-必读系列
  - 一文秒杀所有区间相关问题
    一文秒杀所有区间相关问题
    
    Introduction
- 1-动态规划系列
  1-动态规划系列
  - 1.1-动态规划基本技巧
    1.1-动态规划基本技巧
    
    动态规划详解
    动态规划详解
    
    Introduction
  - 1.2-子序列类型问题
    1.2-子序列类型问题
    
    Introduction
    
    子序列解题模板-最长回文子序列
    子序列解题模板-最长回文子序列
    
    Introduction
    
    LeetCode-516-最长回文子序列
    LeetCode-516-最长回文子序列
    
    Introduction
    
    LeetCode-1682-最长回文子序列-II
    LeetCode-1682-最长回文子序列-II
    
    Introduction
    
    LCS-最长公共子序列
    LCS-最长公共子序列
    
    Introduction
    
    详解最长公共子序列问题
    详解最长公共子序列问题
    
    Introduction
    
    LeetCode-1143-最长公共子序列
    LeetCode-1143-最长公共子序列
    
    Introduction
    
    LeetCode-583-两个字符串的删除操作
    LeetCode-583-两个字符串的删除操作
    
    Introduction
    
    LeetCode-712-两个字符串的最小ASCII删除和
    LeetCode-712-两个字符串的最小ASCII删除和
    
    Introduction
    
    LeetCode-115-不同的子序列-困难
    LeetCode-115-不同的子序列-困难
    
    Introduction
    
    LCS-最长公共子序列
    
    最大子数组
    最大子数组
    
    Introduction
    
    动态规划-最大子数组
    动态规划-最大子数组
    
    Introduction
    
    zhihu-经典动态规划-最大子数组问题
    zhihu-经典动态规划-最大子数组问题
    
    Introduction
    
    LeetCode-53-最大子序和
    LeetCode-53-最大子序和
    
    Introduction
    
    LeetCode-剑指-Offer-42-连续子数组的最大和
    LeetCode-剑指-Offer-42-连续子数组的最大和
    
    Introduction
    
    经动态规划-编辑距离
    经动态规划-编辑距离
    
    Introduction
    
    C++source-code
    
    最长递增子序列之信封嵌套问题
    最长递增子序列之信封嵌套问题
    
    Introduction
  - 1.3-背包类型问题
    1.3-背包类型问题
    
    Introduction
    
    经典动态规划-01背包问题
    经典动态规划-01背包问题
    
    Introduction
    
    经典动态规划-01背包问题的变体
    经典动态规划-01背包问题的变体
    
    Introduction
    
    经典动态规划-完全背包问题
    经典动态规划-完全背包问题
    
    Introduction
    
    LeetCode-一篇文章吃透背包问题
    LeetCode-一篇文章吃透背包问题
    
    Introduction
    
    算法设计与分析-3.10-01背包问题
    算法设计与分析-3.10-01背包问题
    
    Introduction
    
    LeetCode-322-零钱兑换
    LeetCode-322-零钱兑换
    
    Introduction
    
    LeetCode-518-零钱兑换-II
    LeetCode-518-零钱兑换-II
    
    Introduction
    
    TODO-LeetCode-279-完全平方数
    TODO-LeetCode-279-完全平方数
    
    Introduction
    
    LeetCode-416-分割等和子集
    LeetCode-416-分割等和子集
    
    Introduction
    
    TODO-LeetCode-494-目标和
    TODO-LeetCode-494-目标和
    
    Introduction
    
    TODO-LeetCode-1046-最后一块石头的重量
    TODO-LeetCode-1046-最后一块石头的重量
    
    Introduction
    
    TODO-LeetCode-1049-最后一块石头的重量-II
    TODO-LeetCode-1049-最后一块石头的重量-II
    
    Introduction
    
    TODO-LeetCode-1155-掷骰子的N种方法
    TODO-LeetCode-1155-掷骰子的N种方法
    
    Introduction
  - 1.4-贪心类型问题
    1.4-贪心类型问题
    
    贪心算法之区间调度问题
    贪心算法之区间调度问题
    
    Introduction
  - 1.5-其他经典问题
    1.5-其他经典问题
    
    LeetCode-股票问题
    LeetCode-股票问题
    
    Introduction
    
    LeetCode股票问题的一种通用解法
    LeetCode股票问题的一种通用解法
    
    Introduction
    
    团灭LeetCode股票买卖问题
    团灭LeetCode股票买卖问题
    
    Introduction
    
    LeetCode-121-买卖股票的最佳时机
    LeetCode-121-买卖股票的最佳时机
    
    Introduction
    
    LeetCode-122-买卖股票的最佳时机-II
    LeetCode-122-买卖股票的最佳时机-II
    
    Introduction
    
    TODO-LeetCode-123-买卖股票的最佳时机-III
    TODO-LeetCode-123-买卖股票的最佳时机-III
    
    Introduction
    
    TODO-LeetCode-188-买卖股票的最佳时机-IV
    TODO-LeetCode-188-买卖股票的最佳时机-IV
    
    Introduction
    
    LeetCode-309-最佳买卖股票时机含冷冻期
    LeetCode-309-最佳买卖股票时机含冷冻期
    
    Introduction
    
    LeetCode-714-买卖股票的最佳时机含手续费
    LeetCode-714-买卖股票的最佳时机含手续费
    
    Introduction
    
    LeetCode-House-robber-打家劫舍
    LeetCode-House-robber-打家劫舍
    
    Introduction
    
    LeetCode-198-打家劫舍
    LeetCode-198-打家劫舍
    
    Introduction
    
    LeetCode-213-打家劫舍-II
    LeetCode-213-打家劫舍-II
    
    Introduction
    
    LeetCode-337-打家劫舍-III
    LeetCode-337-打家劫舍-III
    
    Introduction
- 2.1-整体学习思路
  2.1-整体学习思路
  - 数据结构和算法学习指南
    数据结构和算法学习指南
    
    Introduction
- 2.2-手把手刷链表题目
  2.2-手把手刷链表题目
  - 递归反转链表
    递归反转链表
    
    Introduction
  - 如何k个一组反转链表
    如何k个一组反转链表
    
    Introduction
- 2.3-手把手刷二叉树
  2.3-手把手刷二叉树
  - 刷二叉树-第一期
    刷二叉树-第一期
    
    Introduction
    
    LeetCode-116-填充每个节点的下一个右侧节点指针
    LeetCode-116-填充每个节点的下一个右侧节点指针
    
    Introduction
    
    LeetCode-222-完全二叉树的节点个数
    LeetCode-222-完全二叉树的节点个数
    
    Introduction
    
    LeetCode-226-翻转二叉树
    LeetCode-226-翻转二叉树
    
    Introduction
    
    LeetCode-剑指-Offer-27-二叉树的镜像
    LeetCode-剑指-Offer-27-二叉树的镜像
    
    Introduction
  - 刷二叉树-第二期
    刷二叉树-第二期
    
    Introduction
    
    LeetCode-105-从前序与中序遍历序列构造二叉树
    LeetCode-105-从前序与中序遍历序列构造二叉树
    
    Introduction
    
    LeetCode-105-从前序与中序遍历序列构造二叉树
    
    LeetCode-654-最大二叉树
    LeetCode-654-最大二叉树
    
    Introduction
  - 刷二叉树-第三期
    刷二叉树-第三期
    
    Introduction
  - 刷二叉搜索树-第一期
    刷二叉搜索树-第一期
    
    Introduction
    
    LeetCode-230-二叉搜索树中第K小的元素
    LeetCode-230-二叉搜索树中第K小的元素
    
    Introduction
    
    LeetCode-538-把二叉搜索树转换为累加树
    LeetCode-538-把二叉搜索树转换为累加树
    
    Introduction
  - 刷二叉搜索树-第二期
    刷二叉搜索树-第二期
    
    Introduction
  - 二叉树的序列化-就那几个框架
    二叉树的序列化-就那几个框架
    
    Introduction
    
    LeetCode-297-二叉树的序列化与反序列化-困难
    LeetCode-297-二叉树的序列化与反序列化-困难
    
    Introduction
    
    LeetCode-剑指-Offer-37-序列化二叉树
    LeetCode-剑指-Offer-37-序列化二叉树
    
    Introduction
  - 题目不让我做什么-我就偏要去做什么
    题目不让我做什么-我就偏要去做什么
    
    Introduction
    
    LeetCode-341-扁平化嵌套列表迭代器
    LeetCode-341-扁平化嵌套列表迭代器
    
    Introduction
  - 用Git来讲讲二叉树最近公共祖先
    用Git来讲讲二叉树最近公共祖先
    
    Introduction
    
    LeetCode-试题分析
    
    LeetCode-235-二叉搜索树的最近公共祖先
    LeetCode-235-二叉搜索树的最近公共祖先
    
    Introduction
    
    LeetCode-236-二叉树的最近公共祖先
    LeetCode-236-二叉树的最近公共祖先
    
    Introduction
    
    LeetCode-剑指-Offer-68-I-二叉搜索树的最近公共祖先
    LeetCode-剑指-Offer-68-I-二叉搜索树的最近公共祖先
    
    Introduction
    
    LeetCode-剑指-Offer-68-II-二叉树的最近公共祖先
    LeetCode-剑指-Offer-68-II-二叉树的最近公共祖先
    
    Introduction
    
    LeetCode-1123-最深叶节点的最近公共祖先
    LeetCode-1123-最深叶节点的最近公共祖先
    
    Introduction
  - 完全二叉树的节点数
    完全二叉树的节点数
    
    Introduction
- 2.4-手把手设计数据结构
  2.4-手把手设计数据结构
  - LRU-算法
    LRU-算法
    
    Introduction
    
    LeetCode-146-LRU缓存机制
    LeetCode-146-LRU缓存机制
    
    Introduction
  - LFU-算法
    LFU-算法
    
    Introduction
    
    LeetCode-460-LFU缓存
    LeetCode-460-LFU缓存
    
    Introduction
  - 二叉堆实现优先级队列
    二叉堆实现优先级队列
    
    Introduction
- 2.5-手把手刷数组题目
  2.5-手把手刷数组题目
  - 双指针-滑动窗口-尺取法
    双指针-滑动窗口-尺取法
    
    Introduction
    
    双指针技巧汇总
    双指针技巧汇总
    
    Introduction
    
    二分查找
    二分查找
    
    我作了首诗-保你闭着眼睛也能写对二分查找
    我作了首诗-保你闭着眼睛也能写对二分查找
    
    Introduction
    
    如何运用二分查找算法
    如何运用二分查找算法
    
    Introduction
    
    LeetCode-875-爱吃香蕉的珂珂
    LeetCode-875-爱吃香蕉的珂珂
    
    Introduction
    
    LeetCode-1011-在D天内送达包裹的能力
    LeetCode-1011-在D天内送达包裹的能力
    
    Introduction
    
    二分查找的妙用判定子序列
    二分查找的妙用判定子序列
    
    Introduction
    
    LeetCode-392-判断子序列
    LeetCode-392-判断子序列
    
    Introduction
    
    我写了套框架-把滑动窗口算法变成了默写题
    我写了套框架-把滑动窗口算法变成了默写题
    
    Introduction
    
    LeetCode-3-无重复字符的最长子串
    LeetCode-3-无重复字符的最长子串
    
    Introduction
    
    LeetCode-剑指-Offer-48-最长不含重复字符的子字符串
    LeetCode-剑指-Offer-48-最长不含重复字符的子字符串
    
    Introduction
    
    LeetCode-76-最小覆盖子串
    LeetCode-76-最小覆盖子串
    
    Introduction
    
    LeetCode-438-找到字符串中所有字母异位词
    LeetCode-438-找到字符串中所有字母异位词
    
    Introduction
    
    LeetCode-567-字符串的排列
    LeetCode-567-字符串的排列
    
    Introduction
    
    双指针-滑动窗口-VS-暴力
    双指针-滑动窗口-VS-暴力
    
    Introduction
  - n-sum问题
    n-sum问题
    
    Introduction
    
    Two-Sum-问题的核心思想
    Two-Sum-问题的核心思想
    
    Introduction
    
    一个函数秒杀-2Sum-3Sum-4Sum-问题
    一个函数秒杀-2Sum-3Sum-4Sum-问题
    
    Introduction
    
    LeetCode-15-三数之和
    LeetCode-15-三数之和
    
    Introduction
    
    LeetCode-18-四数之和
    LeetCode-18-四数之和
    
    Introduction
    
    LeetCode-1711-大餐计数
    LeetCode-1711-大餐计数
    
    Introduction
  - 双指针技巧秒杀四道数组链表题目
    双指针技巧秒杀四道数组链表题目
    
    Introduction
    
    LeetCode-27-移除元素
    LeetCode-27-移除元素
    
    Introduction
    
    LeetCode-283-移动零
    LeetCode-283-移动零
    
    Introduction
- 3.1-回溯算法(DFS算法)系列
  3.1-回溯算法(DFS算法)系列
  - 回溯算法详解
    回溯算法详解
    
    Introduction
  - 回溯算法团灭排列-组合-子集问题
    回溯算法团灭排列-组合-子集问题
    
    Introduction
  - 回溯算法最佳实践-解数独
    回溯算法最佳实践-解数独
    
    Introduction
    
    TODO-LeetCode-37-解数独-困难
    TODO-LeetCode-37-解数独-困难
    
    Introduction
  - 回溯算法最佳实践-括号生成
    回溯算法最佳实践-括号生成
    
    Introduction
    
    LeetCode-22-括号生成
    LeetCode-22-括号生成
    
    Introduction
  - 回溯算法牛逼
    回溯算法牛逼
    
    Introduction
- 3.2-BFS算法系列
  3.2-BFS算法系列
  - BFS算法框架套路详解
    BFS算法框架套路详解
    
    Introduction
    
    LeetCode-111-二叉树的最小深度
    LeetCode-111-二叉树的最小深度
    
    Introduction
    
    LeetCode-752-打开转盘锁-中等
    LeetCode-752-打开转盘锁-中等
    
    Introduction
  - 如何用BFS算法秒杀各种智力题
    如何用BFS算法秒杀各种智力题
    
    Introduction
    
    LeetCode-773-滑动谜题-困难
    LeetCode-773-滑动谜题-困难
    
    Introduction
- 3.3-其他算法篇
  3.3-其他算法篇
  - 快速排序亲兄弟-快速选择算法
    快速排序亲兄弟-快速选择算法
    
    Introduction
    
    LeetCode-215-数组中的第K个最大元素
    LeetCode-215-数组中的第K个最大元素
    
    Introduction
  - 分治算法详解-运算优先级
    分治算法详解-运算优先级
    
    Introduction
- 3.4-数学运算技巧
  3.4-数学运算技巧
  - 如何同时寻找缺失和重复的元素
    如何同时寻找缺失和重复的元素
    
    Introduction
    
    LeetCode-645-错误的集合
    LeetCode-645-错误的集合
    
    Introduction
  - Randomized-algorithm
    Randomized-algorithm
    
    洗牌算法详解
    洗牌算法详解
    
    Introduction
    
    随机算法之水塘抽样算法
    随机算法之水塘抽样算法
    
    Introduction
    
    LeetCode-382-链表随机节点-中等
    LeetCode-382-链表随机节点-中等
    
    Introduction
    
    LeetCode-398-随机数索引
    LeetCode-398-随机数索引
    
    Introduction
- 4-高频面试系列
  4-高频面试系列
  - 手把手搞懂接雨水问题的多种解法
    手把手搞懂接雨水问题的多种解法
    
    Introduction
  - 如何判定括号合法性
    如何判定括号合法性
    
    Introduction
  - 如何拆解复杂问题-实现一个计算器
    如何拆解复杂问题-实现一个计算器
    
    Introduction
    
    LeetCode-224-基本计算器
    LeetCode-224-基本计算器
    
    Introduction
- 手撕力扣高频面试题-56个
  手撕力扣高频面试题-56个
  - Introduction
- 去重
  去重
  - 如何高效对有序数组链表去重
    如何高效对有序数组链表去重
    
    Introduction
  - 一道数组去重的算法题把东哥整不会了
    一道数组去重的算法题把东哥整不会了
    
    Introduction
  - LeetCode-26-删除有序数组中的重复项
    LeetCode-26-删除有序数组中的重复项
    
    Introduction
  - LeetCode-80-删除排序数组中的重复项-II
    LeetCode-80-删除排序数组中的重复项-II
    
    Introduction
- 中位数-中点
  中位数-中点
  - 一道找中位数的算法题
    一道找中位数的算法题
    
    Introduction
    
    LeetCode-剑指-Offer-41-数据流中的中位数
    LeetCode-剑指-Offer-41-数据流中的中位数
    
    Introduction
- Palindrome-回文
  Palindrome-回文
  - Introduction
  - 最长回文子串
    最长回文子串
    
    Introduction
    
    LeetCode-5-最长回文子串
    LeetCode-5-最长回文子串
    
    Introduction
    
    LeetCode-409-最长回文串
    LeetCode-409-最长回文串
    
    Introduction
    
    LeetCode-647-回文子串
    LeetCode-647-回文子串
    
    Introduction
  - 如何高效判断回文单链表
    如何高效判断回文单链表
    
    Introduction
    
    LeetCode-234-回文链表-简单
    LeetCode-234-回文链表-简单
    
    Introduction
  - 构造回文的最小插入次数
    构造回文的最小插入次数
    
    Introduction
Expert-画解算法
Expert-画解算法
- Introduction
Expert-martinbroadhurst
Expert-martinbroadhurst
- Introduction
Expert-Emre-Bolat
Expert-Emre-Bolat
- Introduction
- Coding-Patterns-Staircase楼梯(DP)
  Coding-Patterns-Staircase楼梯(DP)
  - Introduction
- Coding-Patterns-K-way-Merge
  Coding-Patterns-K-way-Merge
  - Introduction
- Coding-Patterns-Merge-Intervals
  Coding-Patterns-Merge-Intervals
  - Introduction
Course-YSC2229-Introductory-Data-Structures-and-Algorithms
Course-YSC2229-Introductory-Data-Structures-and-Algorithms
- Introduction
- 4.4-Complexity-of-Divide-and-Conquer-Algorithms
  4.4-Complexity-of-Divide-and-Conquer-Algorithms
  - Introduction
Course-cornell-cs3110
Course-cornell-cs3110
- Introduction
Book-Foundations-of-Computer-Science
Book-Foundations-of-Computer-Science
- Introduction
TODO
TODO
- stack-order
- 20201028-thoughts

Optimal substructure

以"结构化思维"来看到substructure

"substructure"的"sub"提升了我们它对应的是"nest、contain关系"。

最优子结构其实就具备递归性质：全问题的最优解蕴含着子问题的最优解。

所以我们即可以自顶向下来运用递归关系也可以自底向上来运用递归关系。动态规划就是自底向上的。

labuladong 动态规划详解 # 二、凑零钱问题

其中给出了非常好的解释:

一、使用了高考刺成绩的例子

二、强调了 "子问题相互独立"

wikipedia Optimal substructure

In computer science, a problem is said to have optimal substructure if an optimal solution can be constructed from optimal solutions of its subproblems. This property is used to determine the usefulness of dynamic programming and greedy algorithms for a problem.[1]

NOTE:

1、optimal substructure其实也体现了递归关系；

2、原问题和子问题

Typically, a greedy algorithm is used to solve a problem with optimal substructure if it can be proven by induction that this is optimal at each step.[1] Otherwise, provided the problem exhibits overlapping subproblems as well, dynamic programming is used. If there are no appropriate greedy algorithms and the problem fails to exhibit overlapping subproblems, often a lengthy but straightforward search of the solution space is the best alternative（使用搜索算法）.

In the application of dynamic programming to mathematical optimization, Richard Bellman's Principle of Optimality is based on the idea that in order to solve a dynamic optimization problem from some starting period t to some ending period T, one implicitly has to solve subproblems starting from later dates s, where t<s<T. This is an example of optimal substructure. The Principle of Optimality is used to derive the Bellman equation, which shows how the value of the problem starting from t is related to the value of the problem starting from s.

Problems with optimal substructure

1、Longest common subsequence problem

2、Longest increasing subsequence

3、Longest palindromic substring

4、All-Pairs Shortest Path

5、Any problem that can be solved by dynamic programming.

Problems without optimal substructure

1、Longest path problem

2、Least-cost airline fare. (Using online flight search, we will frequently find that the cheapest flight from airport A to airport B involves a single connection through airport C, but the cheapest flight from airport A to airport C involves a connection through some other airport D.)