graph TD
    ROOT[Algorithm Library<br/>300+ Implementations]
    
    ROOT --> GT[Graph Theory<br/>90 algorithms]
    ROOT --> DS[Data Structures<br/>62 implementations]
    ROOT --> DP[Dynamic Programming<br/>22 optimizations]
    ROOT --> MATH[Mathematics<br/>60 algorithms]
    ROOT --> STR[Strings<br/>24 algorithms]
    ROOT --> NT[Number Theory<br/>74 algorithms]
    ROOT --> QC[Quantum Computing<br/>8 Rust implementations]
    ROOT --> OTHER[Geometry + Game Theory<br/>+ Miscellaneous]
    
    GT --> GT1[Traversal & Search]
    GT --> GT2[Shortest Path]
    GT --> GT3[Network Flow]
    GT --> GT4[Matching]
    GT --> GT5[MST]
    GT --> GT6[Connectivity]
    GT --> GT7[Tree Algorithms]
    
    GT1 --> GT1A[BFS<br/>DFS<br/>Topological Sort]
    GT2 --> GT2A[Dijkstra<br/>Bellman-Ford<br/>Floyd-Warshall<br/>Johnson<br/>SPFA<br/>A*]
    GT3 --> GT3A[Max Flow: Dinic, Ford-Fulkerson<br/>Min Cost Max Flow<br/>Push-Relabel<br/>L-R Flow]
    GT4 --> GT4A[Bipartite: Hungarian, Hopcroft-Karp, Kuhn<br/>General: Blossom]
    GT5 --> GT5A[Kruskal<br/>Prim<br/>Boruvka<br/>Directed MST]
    GT6 --> GT6A[SCC: Tarjan, Kosaraju<br/>Bridges & Articulation<br/>2-SAT, 3-SAT<br/>Block-Cut Tree]
    GT7 --> GT7A[LCA variants<br/>HLD<br/>Centroid Decomp<br/>Link-Cut Tree]
    
    DS --> DS1[Range Query]
    DS --> DS2[Tree Structures]
    DS --> DS3[Union-Find]
    DS --> DS4[String DS]
    DS --> DS5[Specialized]
    
    DS1 --> DS1A[Segment Tree variants<br/>Fenwick Tree<br/>Sparse Table<br/>SQRT Decomposition]
    DS2 --> DS2A[Treap variants<br/>BST<br/>Cartesian Tree]
    DS3 --> DS3A[DSU<br/>Persistent DSU<br/>Rollback DSU]
    DS4 --> DS4A[Trie<br/>Suffix Array<br/>Suffix Automaton<br/>Palindromic Tree]
    DS5 --> DS5A[Mo's Algorithm<br/>KD Tree<br/>Link-Cut Tree<br/>Top Tree]
    
    DP --> DP1[Optimization Techniques]
    DP1 --> DP1A[Convex Hull Trick<br/>Divide & Conquer<br/>Knuth<br/>Li Chao Tree<br/>SOS DP]
    
    MATH --> MATH1[Transforms]
    MATH --> MATH2[Linear Algebra]
    MATH --> MATH3[Polynomials]
    
    MATH1 --> MATH1A[FFT<br/>NTT variants<br/>FWHT]
    MATH2 --> MATH2A[Gaussian Elimination<br/>Matrix Exponentiation<br/>Determinant<br/>Simplex]
    MATH3 --> MATH3A[Lagrange<br/>Berlekamp-Massey<br/>Polynomial Operations]
    
    STR --> STR1[Pattern Matching]
    STR --> STR2[Structures]
    
    STR1 --> STR1A[KMP<br/>Z-Algorithm<br/>Aho-Corasick<br/>String Hashing]
    STR2 --> STR2A[Suffix Array<br/>Suffix Automaton<br/>Palindromic Tree<br/>Manacher]
    
    NT --> NT1[Primes]
    NT --> NT2[Modular Arithmetic]
    NT --> NT3[Combinatorics]
    
    NT1 --> NT1A[Sieve variants<br/>Miller-Rabin<br/>Pollard Rho]
    NT2 --> NT2A[Extended Euclid<br/>CRT<br/>Discrete Log/Root<br/>Modular Inverse]
    NT3 --> NT3A[nCr variants<br/>Stirling Numbers<br/>Bell Numbers<br/>Lucas]

graph TB
    %% Foundational Layer
    ARR[Arrays & Basic Operations] --> SORT[Sorting Algorithms]
    ARR --> SEARCH[Binary Search]
    
    %% Graph Foundations
    GRAPH[Graph Representation] --> BFS
    GRAPH --> DFS
    
    %% BFS Applications
    BFS[BFS] --> SSSP_U[Shortest Path<br/>Unweighted]
    BFS --> BIPARTITE[Bipartite Check]
    BFS --> LEVEL[Level Ancestor]
    
    %% DFS Applications
    DFS[DFS] --> TOPO[Topological Sort]
    DFS --> SCC[Strongly Connected<br/>Components]
    DFS --> BRIDGES[Bridges &<br/>Articulation Points]
    DFS --> TREE[Tree Algorithms]
    
    %% Shortest Path Chain
    SSSP_U --> DIJKSTRA[Dijkstra's<br/>Algorithm]
    DIJKSTRA --> ASTAR[A* Search]
    DIJKSTRA --> JOHNSON[Johnson's<br/>Algorithm]
    BFS --> BELLMAN[Bellman-Ford]
    BELLMAN --> SPFA[SPFA]
    BELLMAN --> JOHNSON
    DIJKSTRA --> FW[Floyd-Warshall]
    
    %% Network Flow Chain
    DFS --> MAXFLOW_BASIC[Basic Max Flow]
    MAXFLOW_BASIC --> DINIC[Dinic's Algorithm]
    MAXFLOW_BASIC --> EDMONDS[Edmonds-Karp]
    DINIC --> MCMF[Min Cost<br/>Max Flow]
    MAXFLOW_BASIC --> PUSHRELABEL[Push-Relabel]
    
    %% Matching Chain  
    DFS --> KUHN[Kuhn's Matching]
    KUHN --> HOPCROFT[Hopcroft-Karp]
    MAXFLOW_BASIC --> HUNGARIAN[Hungarian<br/>Algorithm]
    MAXFLOW_BASIC --> BLOSSOM[Blossom Algorithm]
    
    %% MST Chain
    DSU[Union-Find] --> KRUSKAL[Kruskal's MST]
    DIJKSTRA --> PRIM[Prim's MST]
    DSU --> BORUVKA[Boruvka's MST]
    
    %% Tree Algorithms Chain
    TREE --> LCA[Lowest Common<br/>Ancestor]
    TREE --> HLD[Heavy-Light<br/>Decomposition]
    TREE --> CENTROID[Centroid<br/>Decomposition]
    TREE --> LINKCUT[Link-Cut Tree]
    
    %% Data Structure Dependencies
    ARR --> PREFIXSUM[Prefix Sum]
    PREFIXSUM --> BIT[Fenwick Tree]
    BIT --> BIT2D[2D Fenwick]
    ARR --> SEGTREE[Segment Tree]
    SEGTREE --> SEGLAZY[Lazy Propagation]
    SEGLAZY --> SEG2D[2D Segment Tree]
    SEGTREE --> PERSISTENT[Persistent<br/>Segment Tree]
    
    %% String Algorithm Chain
    ARR --> HASH[String Hashing]
    DFS --> KMP[KMP Algorithm]
    KMP --> ZARRAY[Z-Algorithm]
    TRIE[Trie] --> AHOC[Aho-Corasick]
    ARR --> SUFFIX[Suffix Array]
    SUFFIX --> LCP[LCP Array]
    SUFFIX --> SUFFTREE[Suffix Tree]
    
    %% Number Theory Chain
    SEARCH --> GCD[Euclidean GCD]
    GCD --> EXTGCD[Extended Euclid]
    EXTGCD --> MODINV[Modular Inverse]
    EXTGCD --> DIOPHANTINE[Diophantine<br/>Equations]
    EXTGCD --> CRT[Chinese Remainder<br/>Theorem]
    
    %% Primality Chain
    SEARCH --> SIEVE[Sieve of<br/>Eratosthenes]
    SIEVE --> SEGMENTED[Segmented Sieve]
    SIEVE --> LINEAR[Linear Sieve]
    MODINV --> MILLERRABIN[Miller-Rabin]
    MILLERRABIN --> POLLARD[Pollard Rho]
    
    %% DP Optimization Chain
    DP_BASIC[Basic DP] --> CHT[Convex Hull<br/>Trick]
    DP_BASIC --> DNC_OPT[Divide &<br/>Conquer Opt]
    DP_BASIC --> KNUTH_OPT[Knuth<br/>Optimization]
    CHT --> LICHAO[Li Chao Tree]
    
    %% Math Chain
    ARR --> FFT[Fast Fourier<br/>Transform]
    FFT --> NTT[Number Theoretic<br/>Transform]
    FFT --> FWHT[Fast Walsh-Hadamard<br/>Transform]
    ARR --> MATRIX[Matrix Operations]
    MATRIX --> GAUSSIAN[Gaussian<br/>Elimination]
    MATRIX --> MATEXP[Matrix<br/>Exponentiation]
    MATRIX --> DET[Determinant]
    
    style BFS fill:#4CAF50
    style DFS fill:#4CAF50
    style DIJKSTRA fill:#2196F3
    style DINIC fill:#FF9800
    style SEGTREE fill:#9C27B0
    style FFT fill:#F44336
    style MILLERRABIN fill:#00BCD4

graph TD
    START{What type of<br/>problem?}
    
    START -->|Graph| GRAPH_Q{Weighted<br/>edges?}
    START -->|Array/Range| ARRAY_Q{Updates?}
    START -->|String| STRING_Q{Pattern<br/>matching?}
    START -->|Number| NUMBER_Q{Prime-related?}
    
    %% Graph Branch
    GRAPH_Q -->|Yes| WEIGHTED{Negative<br/>weights?}
    GRAPH_Q -->|No| UNWEIGHTED{What to<br/>find?}
    
    WEIGHTED -->|Yes| BELLMAN[Bellman-Ford<br/>or SPFA]
    WEIGHTED -->|No| POSITIVE{All-pairs or<br/>single-source?}
    POSITIVE -->|Single| DIJKSTRA_F[Dijkstra's<br/>Algorithm]
    POSITIVE -->|All-pairs| DENSE{Dense<br/>graph?}
    DENSE -->|Yes| FW_F[Floyd-Warshall]
    DENSE -->|No| JOHNSON_F[Johnson's<br/>Algorithm]
    
    UNWEIGHTED -->|Shortest Path| BFS_F[BFS]
    UNWEIGHTED -->|Connected Components| DFS_UNION{Need to<br/>maintain?}
    DFS_UNION -->|Yes| DSU_F[Union-Find]
    DFS_UNION -->|No| DFS_F[DFS]
    UNWEIGHTED -->|Cycle Detection| DIRECTED{Directed?}
    DIRECTED -->|Yes| TOPO_F[Topological Sort<br/>+ DFS]
    DIRECTED -->|No| DFS_COLOR[DFS with<br/>coloring]
    
    %% Array/Range Branch
    ARRAY_Q -->|Yes| UPDATE_TYPE{Update<br/>type?}
    ARRAY_Q -->|No| STATIC_QUERY{Query<br/>type?}
    
    UPDATE_TYPE -->|Point| POINT_Q{Query type?}
    UPDATE_TYPE -->|Range| SEGLAZY_F[Segment Tree<br/>with Lazy Prop]
    POINT_Q -->|Range Sum| BIT_F[Fenwick Tree]
    POINT_Q -->|Range Min/Max| SEGTREE_F[Segment Tree]
    
    STATIC_QUERY -->|RMQ/GCD| SPARSE_F[Sparse Table<br/>O1 query]
    STATIC_QUERY -->|Range Sum| PREFIX_F[Prefix Sum]
    
    %% String Branch
    STRING_Q -->|Yes| MULTI_PATTERN{Multiple<br/>patterns?}
    STRING_Q -->|No| STRING_OP{Operation?}
    
    MULTI_PATTERN -->|Yes| AHOC_F[Aho-Corasick]
    MULTI_PATTERN -->|No| SINGLE_MATCH{Pattern<br/>has wildcards?}
    SINGLE_MATCH -->|No| SIMPLE_MATCH{Which to<br/>use?}
    SIMPLE_MATCH --> KMP_F[KMP simpler<br/>failure function]
    SIMPLE_MATCH --> Z_F[Z-Algorithm<br/>simpler code]
    
    STRING_OP -->|Palindromes| MANACHER_F[Manacher's<br/>Algorithm]
    STRING_OP -->|All substrings| SUFFIX_F[Suffix Array<br/>or Tree]
    STRING_OP -->|Autocomplete| TRIE_F[Trie]
    
    %% Number Theory Branch  
    NUMBER_Q -->|Yes| PRIME_OP{Operation?}
    NUMBER_Q -->|No| MOD_Q{Modular<br/>arithmetic?}
    
    PRIME_OP -->|Test primality| SIZE{Number<br/>size?}
    SIZE -->|Small 10^6| SIEVE_F[Sieve]
    SIZE -->|Large 10^18| MILLER_F[Miller-Rabin]
    PRIME_OP -->|Factorize| POLLARD_F[Pollard Rho]
    PRIME_OP -->|Generate primes| RANGE{Range<br/>size?}
    RANGE -->|Small| SIEVE_F
    RANGE -->|Large| SEGMENTED_F[Segmented<br/>Sieve]
    
    MOD_Q -->|Yes| MOD_OP{Operation?}
    MOD_OP -->|Inverse| EXTGCD_F[Extended<br/>Euclid]
    MOD_OP -->|System of congruences| CRT_F[Chinese<br/>Remainder Theorem]
    MOD_OP -->|x^k = a mod p| DISCRETE_F[Discrete<br/>Root/Log]
    
    style DIJKSTRA_F fill:#4CAF50
    style BFS_F fill:#4CAF50
    style SEGTREE_F fill:#2196F3
    style KMP_F fill:#FF9800
    style MILLER_F fill:#9C27B0

graph LR
    subgraph "Graph Theory"
        GT_BFS[BFS/DFS]
        GT_FLOW[Network Flow]
        GT_MST[MST Algorithms]
        GT_MATCHING[Matching]
    end
    
    subgraph "Data Structures"
        DS_SEGTREE[Segment Tree]
        DS_DSU[Union-Find]
        DS_TRIE[Trie]
        DS_BIT[Fenwick Tree]
    end
    
    subgraph "Dynamic Programming"
        DP_CHT[Convex Hull Trick]
        DP_SOS[SOS DP]
        DP_DIGIT[Digit DP]
    end
    
    subgraph "Math"
        MATH_FFT[FFT/NTT]
        MATH_MATRIX[Matrix Ops]
        MATH_SIMPLEX[Simplex]
    end
    
    subgraph "Strings"
        STR_KMP[KMP]
        STR_SUFFIX[Suffix DS]
        STR_HASH[Hashing]
    end
    
    subgraph "Number Theory"
        NT_CRT[CRT]
        NT_PRIME[Primality]
        NT_GCD[GCD/Euclid]
    end
    
    %% Interconnections
    GT_MST -.->|uses| DS_DSU
    GT_BFS -.->|implements| DS_TRIE
    GT_FLOW -.->|optimized by| MATH_SIMPLEX
    
    DS_SEGTREE -.->|enables| DP_CHT
    DS_BIT -.->|range queries in| DP_SOS
    
    MATH_FFT -.->|polynomial in| DP_DIGIT
    MATH_MATRIX -.->|path counting in| GT_BFS
    
    STR_SUFFIX -.->|uses| DS_SEGTREE
    STR_KMP -.->|similar to| GT_BFS
    STR_HASH -.->|uses| NT_PRIME
    
    NT_CRT -.->|modular in| MATH_FFT
    NT_GCD -.->|used in| GT_FLOW
    
    GT_MATCHING -.->|reduces to| GT_FLOW
    DP_CHT -.->|uses| MATH_MATRIX

graph TD
    subgraph "Time Complexity Ladder"
        A1["BFS: O(V+E)<br/>Unweighted only"]
        A2["Dijkstra: O(E log V)<br/>Non-negative weights"]
        A3["Bellman-Ford: O(VE)<br/>Negative weights OK"]
        A4["SPFA: O(VE) worst, O(E) avg<br/>Negative weights OK"]
        A5["Floyd-Warshall: O(V³)<br/>All-pairs, dense graphs"]
        A6["Johnson: O(V² log V + VE)<br/>All-pairs, sparse graphs"]
    end
    
    A1 -.->|faster| A2
    A2 -.->|faster| A4
    A4 -.->|same worst| A3
    A2 -.->|for all-pairs| A6
    A6 -.->|beats for sparse| A5

graph LR
    subgraph "Range Query Structures"
        direction TB
        B1["Prefix Sum<br/>Build: O(N)<br/>Query: O(1)<br/>Update: ❌"]
        B2["Sparse Table<br/>Build: O(N log N)<br/>Query: O(1)<br/>Update: ❌"]
        B3["Fenwick Tree<br/>Build: O(N)<br/>Query: O(log N)<br/>Update: O(log N)"]
        B4["Segment Tree<br/>Build: O(N)<br/>Query: O(log N)<br/>Update: O(log N)<br/>More versatile"]
    end
    
    B1 -.->|if updates needed| B3
    B2 -.->|if updates needed| B4
    B3 -.->|if complex queries| B4

timeline
    title Evolution of Key Algorithms
    
    section 1950s-1960s
        1956 : Dijkstra's Algorithm
        1957 : Bellman-Ford
        1959 : Dijkstra publishes shortest path
        1962 : Floyd-Warshall
    
    section 1970s
        1970 : Dinic's Max Flow
        1972 : Hopcroft-Karp Matching
        1973 : Aho-Corasick
        1975 : Tarjan's SCC
        1977 : KMP String Matching
    
    section 1980s
        1982 : Union-Find optimizations
        1984 : Simplex Algorithm refinements
        1985 : Heavy-Light Decomposition
        1987 : Suffix Trees
    
    section 1990s
        1994 : Link-Cut Trees
        1995 : Manacher's Algorithm
        1997 : Segment Tree Beats
        1999 : Persistent Data Structures
    
    section 2000s
        2000 : Mo's Algorithm
        2004 : Convex Hull Trick optimization
        2007 : Miller-Rabin deterministic
        2009 : Centroid Decomposition applications
    
    section 2010s-2020s
        2010 : Modern Competitive Programming
        2015 : Li Chao Tree
        2020 : Advanced persistent structures
        2024 : This Library! 750+ implementations

graph TB
    subgraph "Preprocessing Layer"
        MAP_DATA[Map Data<br/>OSM, proprietary] --> GRAPH_BUILD[Graph Construction<br/>Nodes = Intersections<br/>Edges = Roads]
        GRAPH_BUILD --> CH_PREP[Contraction Hierarchies<br/>Preprocessing]
        GRAPH_BUILD --> ARCFLAGS[Arc Flags<br/>Computation]
    end
    
    subgraph "Query Processing Layer"
        USER_QUERY[User Query<br/>A → B] --> REGION_CHECK{Same<br/>region?}
        REGION_CHECK -->|Yes| LOCAL_ALG[Local Dijkstra<br/>Small area]
        REGION_CHECK -->|No| CH_QUERY[CH Query<br/>Bidirectional]
        
        CH_QUERY --> CH_PATH[Path in<br/>CH Graph]
        CH_PATH --> UNPACK[Unpack<br/>Shortcuts]
    end
    
    subgraph "Real-time Layer"
        TRAFFIC_DATA[Live Traffic<br/>Sensors, crowd-sourced] --> ML_MODEL[ML Traffic<br/>Prediction]
        ML_MODEL --> WEIGHT_UPDATE[Edge Weight<br/>Updates]
        WEIGHT_UPDATE --> RECOMPUTE{Significant<br/>change?}
        RECOMPUTE -->|Yes| REROUTE[SPFA<br/>Incremental Update]
        RECOMPUTE -->|No| KEEP[Keep Current<br/>Route]
    end
    
    subgraph "Post-processing Layer"
        UNPACK --> TURN_COST[Turn Restrictions<br/>Cost Adjustment]
        TURN_COST --> LANE_GUIDE[Lane Guidance<br/>Generation]
        LANE_GUIDE --> ETA[ETA Calculation<br/>Historical Data]
        ETA --> FINAL[Final Route]
    end
    
    subgraph "Fallback Layer"
        LOCAL_ALG --> TIMEOUT{Timeout?}
        TIMEOUT -->|Yes| GREEDY[Greedy<br/>Closest Next]
        TIMEOUT -->|No| SUCCESS[Route Found]
        
        CH_QUERY --> FAIL{Failed?}
        FAIL -->|Yes| STANDARD_DIJ[Standard<br/>Dijkstra]
    end
    
    REROUTE --> FINAL
    KEEP --> FINAL
    SUCCESS --> TURN_COST
    GREEDY --> TURN_COST
    
    style CH_PREP fill:#4CAF50
    style CH_QUERY fill:#2196F3
    style ML_MODEL fill:#FF9800
    style REROUTE fill:#9C27B0

graph TB
    %% Foundation Layer
    ARRAY[Array Basics] --> PREFIX[Prefix Sum]
    ARRAY --> TWOPTR[Two Pointers]
    ARRAY --> SLIDING[Sliding Window]
    ARRAY --> BINSEARCH[Binary Search]
    
    %% String builds on Array
    STRING[String Basics] --> ARRAY
    STRING --> HASH[Hashing]
    STRING --> TRIE[Trie]
    
    %% Two Pointers variations
    TWOPTR --> FASTSL[Fast & Slow Pointers]
    TWOPTR --> DUTCH[Dutch National Flag]
    FASTSL --> CYCLE[Cycle Detection]
    
    %% Sliding Window to Two Pointers
    SLIDING --> TWOPTR
    SLIDING --> HASH
    
    %% Binary Search variations
    BINSEARCH --> BSANSWER[Binary Search on Answer]
    BINSEARCH --> ROTATED[Rotated Array Search]
    
    %% Dynamic Programming Foundation
    RECURSION[Recursion] --> MEMO[Memoization]
    MEMO --> DP[Dynamic Programming]
    DP --> LINEAR_DP[Linear DP]
    DP --> KNAPSACK[Knapsack DP]
    DP --> SUBSTRING_DP[Substring DP]
    DP --> TREE_DP[Tree DP]
    DP --> BITMASK_DP[Bitmask DP]
    
    %% Tree Patterns
    TREE[Tree Basics] --> TREE_BFS[Tree BFS]
    TREE --> TREE_DFS[Tree DFS]
    TREE_DFS --> TREE_DP
    TREE_BFS --> LEVEL_ORDER[Level Order]
    
    %% Graph builds on Tree
    GRAPH[Graph Basics] --> TREE
    GRAPH --> GRAPH_BFS[Graph BFS]
    GRAPH --> GRAPH_DFS[Graph DFS]
    GRAPH_DFS --> SCC[SCC - Tarjan/Kosaraju]
    GRAPH_DFS --> TOPO[Topological Sort]
    GRAPH_BFS --> SHORTEST[Shortest Path - BFS]
    
    %% Union-Find
    UF[Union-Find] --> MST_KRUSKAL[Kruskal's MST]
    UF --> CONN_COMP[Connected Components]
    
    %% Backtracking
    RECURSION --> BACKTRACK[Backtracking]
    BACKTRACK --> PERMUTE[Permutations]
    BACKTRACK --> COMBO[Combinations]
    BACKTRACK --> SUBSET[Subsets]
    
    %% Advanced Structures
    STACK[Stack] --> MONO_STACK[Monotonic Stack]
    QUEUE[Queue] --> MONO_QUEUE[Monotonic Queue]
    MONO_QUEUE --> SLIDING
    
    %% Interval Patterns
    SORT[Sorting] --> INTERVAL[Interval Patterns]
    INTERVAL --> MERGE_INT[Merge Intervals]
    INTERVAL --> SWEEP[Sweep Line]
    
    %% Heap Patterns
    HEAP[Heap/Priority Queue] --> TOPK[Top K Elements]
    HEAP --> KWAY[K-way Merge]
    
    style DP fill:#9C27B0
    style GRAPH fill:#4CAF50
    style SLIDING fill:#2196F3
    style BACKTRACK fill:#FF9800