Algorithms

algorithms.yaml

Part_1.pdf:
  topics:
    - Algorithms
    - Design and analysis
    - Computational procedures
    - Input/output relationship
    - Sorting problem definition
    - Pseudocode
    - Insertion sort
    - Incremental approach
    - Divide-and-conquer technique
    - Algorithm analysis models
    - Running time
    - Worst-case scenario
    - Average-case analysis
    - Big-oh notation
    - Divide-and-conquer paradigm
    - Subproblems
    - Recursive solutions
    - Merge sort algorithm
    - Merging sorted sequences
    - Loop invariants for algorithm correctness
    - Pseudocode conventions
    - Analysis methodology
    - Efficiency measures
    - Order of growth
    - Linear time algorithms
    - Quadratic time algorithms
    - Algorithmic problem solving strategies
    - Practical application of algorithms
    - Mathematical foundations for algorithm analysis
    - Introduction to data structures
    - Algorithmic techniques for problem solving
    - Hard problems identification
    - NP-completeness
    - Parallel computing
    - Dynamic multithreading
    - Technological impacts on algorithm efficiency
    - Computational models evolution
    - Real-world examples requiring sorting
    - Computational geometry
    - Shortest-path problems
    - Linear programming
    - Polynomial time algorithms
    - Randomization in algorithms
    - Discrete Fourier transforms
    - Number-theoretic algorithms
    - String pattern matching
    - Public-key cryptography
    - Digital signatures
    - Graph algorithms
    - Electronic commerce security
    - Internet routing
    - Database search algorithms
    - Resource allocation problems
    - Linear programming applications
    - Algorithmic implications on modern computing systems
    - Efficient data management
    - Computational problem categorization
    - Algorithmic innovations
    - Computer science education
    - Algorithmic challenges in computational biology
    - Genetic sequencing algorithms
    - Data compression techniques
    - Large integer multiplication
    - Graph representation techniques
    - Sorting algorithms comparison
    - Insertion sort mechanics
    - Divide-and-conquer sorting methods
    - Merge sort detailed analysis
    - Problem-solving through recursion
    - Efficiency of sorting algorithms
    - Comparison of algorithmic efficiencies
    - Importance of algorithm design in software development
    - Influence of algorithms on computer architecture

Part_2.pdf:
  topics:
    - Sorting problem
    - Input sequence of numbers
    - Output permutation
    - Ordered sequence
    - Dictionary operations
    - Satellite data
    - Manipulation of dynamic sets
    - Arrays
    - Linked lists representation
    - Sorting necessity in algorithms
    - Fundamental problem
    - Sorting algorithms variety
    - Algorithmic techniques
    - Insertion sort
    - Merge sort
    - In-place sorting
    - Heapsort
    - Quicksort
    - Comparison sorts
    - Decision-tree model
    - Lower bound for sorting
    - ‚(n lg n) complexity
    - Counting sort
    - Radix sort
    - Bucket sort
    - Linear time sorting under conditions
    - Sorting algorithms performance comparison
    - Worst-case scenario analysis
    - Average-case efficiency
    - Data structure optimizations
    - Engineering considerations
    - Memory hierarchy impact
    - Algorithm vs. program distinction
    - Keys and satellite data
    - Sorting records
    - Sort efficiency on various data structures
    - Heap data structure implementation
    - Priority queue implementation
    - Binary heap properties
    - Max-heaps
    - Min-heaps
    - Heap operations
    - BUILD-MAX-HEAP
    - MAX-HEAPIFY
    - Sorting in place
    - Heap sort algorithm details
    - Recursive algorithms
    - Divide-and-conquer paradigm
    - Algorithmic design techniques
    - Randomization in algorithms
    - Expected running time analysis
    - Partitioning in quicksort
    - Pivot selection
    - Worst-case partitioning
    - Balanced partitioning
    - Performance on distinct elements
    - Analysis of recursive algorithms
    - Random sampling in quicksort
    - Probabilistic analysis
    - Algorithmic problem solving
    - Computational geometry applications
    - NP-complete problems
        - Hamiltonian cycle
        - Boolean satisfiability
        - Subset sum problem
        - Traveling-salesman problem
    - Approximation algorithms
        - Vertex-cover problem
        - 3-CNF satisfiability
        - Set-covering problem
    - Multithreaded algorithms
        - Shared-memory parallel computing
        - Parallelism in algorithms
        - Work-span model
        - Greedy scheduling in parallel algorithms
        - Race conditions
    - Parallel algorithms design
    - Performance analysis
    - Theoretical limits of algorithm design
    - Advanced algorithmic techniques
    - Optimization problems under constraints
    - Cryptographic systems
    - Security applications
    - Pattern matching in text editing
    - Geometry algorithms in computational theory
    - Computational complexity exploration
    - Algorithmic efficiency
    - Problem-solving strategies
    - Mathematical foundations of algorithms
    - Practical applications of theoretical concepts
Part_3.pdf:
  topics:
    - Dynamic sets
    - Finite
    - Manipulation
    - Growth
    - Shrinkage
    - Change
    - Dictionary operations:
        - Insert
        - Delete
        - Test membership
    - Dictionary
    - Min-priority queues
    - Heap data structure
    - Dynamic set implementation
    - Object attributes
    - Pointer manipulation
    - Identifying key
    - Satellite data
    - Totally ordered set:
        - Real numbers
        - Alphabetic ordering
    - Minimum element
    - Operations on dynamic sets:
        - Queries
        - Modifying operations
    - Search
    - Minimum
    - Maximum
    - Successor
    - Predecessor
    - Data structure:
        - Stacks
        - Queues
        - Linked lists
        - Rooted trees
    - Objects
    - Pointers
    - Implementation environments
    - PUSH
    - POP
    - LIFO policy
    - FIFO policy
    - Array implementation
    - Underflow
    - Overflow
    - Linked list representation:
        - Linear order
        - Doubly linked list
        - Singly linked list
        - Sorted list
        - Circular list
    - List searching
    - List insertion
    - List deletion
    - Sentinels
    - Objects and pointers implementation
    - Multiple-array representation
    - Single-array representation
    - Allocating and freeing objects
    - Rooted tree representation
    - Binary trees:
        - Parent
        - Left child
        - Right child pointers
    - Unbounded branching
    - Left-child right-sibling representation
    - Key
    - Satellite data storage
    - Dynamic set operations analysis
    - Random variables
    - Expected running time
    - Searching algorithms
    - Insert and delete operations
    - Average-case time
    - Worst-case scenario
    - Hash tables:
        - Hashing function
        - Collisions
        - Chaining collision resolution
        - Load factor
        - Simple uniform hashing
        - Successful and unsuccessful search average-case time
    - Direct-address tables
    - Bit vectors
    - Mergeable heaps
    - List compacting
    - Search time optimization
    - Direct addressing vs. hashing comparison
    - Efficient memory usage
    - Hash function design:
        - Division method
        - Multiplication method
        - Universal hashing
        - Hash function quality indicators
    - Collision resolution techniques:
        - Chaining
        - Open addressing
        - Perfect hashing
    - Dynamic set management
    - Space efficiency
    - Computational complexity
    - Algorithmic analysis
    - Data structure optimization
    - Memory management
    - Programming environments adaptation
    - Linked data structures
    - Tree data representation
    - Hash table operations
    - Dictionary operation efficiency
    - Average-case performance
    - Worst-case performance avoidance
    - Hash function selection criteria
    - Theoretical vs. practical considerations in data structures
    - Asymptotic time complexity
    - Expected time vs. worst-case time comparison
    - Algorithmic efficiency in dynamic set operations
Part_4.pdf:
  topics:
    - Dynamic programming
    - Optimization problems
    - Choices
    - Subproblems
    - Exponential-time to polynomial-time transformation
    - Greedy algorithms:
        - Local optimal choices
        - Coin-changing
        - Matroid theory
        - Optimal solution
    - Amortized analysis:
        - Sequence of operations
        - Cost analysis
    - Tabular method
    - Overlapping subproblems
    - Recursive solutions
    - Memoization
    - Bottom-up approach
    - Problem-solving steps
    - Characterizing optimal solutions
    - Recursively defining optimal values
    - Computing optimal values
    - Constructing solutions
    - Subproblem graphs
    - Matrix-chain multiplication:
        - Matrix dimensions
        - Parenthesization
        - Scalar multiplications
    - Fibonacci numbers
    - Longest common subsequence
    - Binary search trees:
        - Optimal binary search trees
        - Weighted path lengths
    - Aggregate analysis
    - Knapsack problem:
        - Fractional knapsack
        - 0/1 knapsack
    - Greedy choice property
    - Activity-selection problem:
        - Recursive greedy algorithm
        - Iterative greedy algorithm
    - Huffman codes
    - Greedy algorithms
    - Optimal substructure
    - Elements of dynamic programming:
        - Overlapping subproblems
        - Optimal substructure characterization
    - Subproblem space
    - Polynomial running time
    - Subproblem independence
    - Shortest paths
    - Longest simple paths
    - NP-completeness

Part_5.pdf:
  topics:
    - Fibonacci heaps
    - Mergeable heap operations:
        - MAKE-HEAP
        - INSERT
        - MINIMUM
        - EXTRACT-MIN
        - UNION
        - DECREASE-KEY
        - DELETE
    - Dynamic sets
    - Amortized analysis
        - Potential method
        - Cascading cut
    - Binomial heaps
        - Binomial trees
    - Linked lists
    - Heap-ordered tree
    - Min-heap property
    - Circular doubly linked list
    - Mark and degree attributes
    - Root list
    - Cut and cascading cut operations
    - Child list
    - Consolidating trees
    - Pairwise combine
    - Key decreases and deletions
    - Soft threshold
    - Hard threshold
    - Structured yet flexible data organization
    - Amortized running time optimization
    - Potential function application
    - Tree consolidation
    - Efficient key decrease mechanism
    - Lazy approach to structure maintenance
    - Amortized analysis in action
    - Dynamic set operations efficiency
    - Priority queue operations
    - Graph algorithms optimization
    - Heap operations cost trade-offs
    - Amortized cost versus actual cost comparison

Part_6.pdf:
  topics:
    - Graph algorithms
    - Dynamic exploration
    - Breadth-first search (BFS)
    - Depth-first search (DFS)
    - Shortest paths
    - Minimum spanning trees
    - Directed graphs (digraphs)
    - Undirected graphs
    - Vertices
    - Edges
    - Paths
    - Cycles
    - Acyclic graphs
    - Weighted graphs
    - Unweighted graphs
    - Graph representation:
        - Adjacency lists
        - Adjacency matrices
    - Graph traversal
    - Discovery
    - Finishing
    - Preorder
    - Postorder
    - Topological sort
    - Strongly connected components
    - Directed acyclic graph (DAG)
    - Out-degree
    - In-degree
    - Transpose graph
    - Path exploration
    - White-gray-black vertex coloring
    - Tree edges
    - Back edges
    - Forward edges
    - Cross edges
    - Parenthesis theorem
    - White-path theorem
    - Edge classification
    - Linear-time algorithms
    - DFS-based algorithms
    - BFS-based algorithms
    - SCC algorithms
    - Graph connectivity
    - Reachability
    - Edge relaxation
    - Shortest-path weights
    - Single-source shortest paths
    - All-pairs shortest paths
    - Dijkstra's algorithm
    - Bellman-Ford algorithm
    - Floyd-Warshall algorithm
    - Johnson's algorithm
    - Minimum spanning tree
    - Kruskal's algorithm
    - Prim's algorithm
    - Cut property
    - Cycle property
    - Disjoint-set data structure
    - Maximum flow
    - Ford-Fulkerson method
    - Residual networks
    - Augmenting paths
    - Cut capacity
    - Flow networks
    - Bipartite matching
    - Vertex cover
    - Network flow applications
    - Graph modeling
    - Complexity analysis
    - Greedy algorithms
    - Dynamic programming approaches
    - Amortized analysis
    - Computational geometry
    - Graph-based problems
    - Planar graphs
    - Graph coloring
    - Scheduling problems
    - Transportation networks
    - Social networks analysis
    - Computer networks routing
    - Scientific computing
    - Graph partitioning
    - Network security

Part_7.pdf:
  topics:
    - Selected Topics
    - Computational models
    - Parallel computing
    - Dynamic multithreading
    - Matrix operations
        - LU decomposition
        - LUP decomposition
        - Gaussian elimination
    - Linear programming
        - Simplex algorithm
        - Polynomial time
    - Fast Fourier Transform (FFT)
    - Number-theoretic algorithms
        - Euclid’s algorithm
        - Greatest common divisors
        - Modular linear equations
        - RSA public-key cryptosystem
        - Digital signatures
        - Miller-Rabin randomized primality test
        - Pollard’s “rho” heuristic
    - String pattern matching
        - Rabin-Karp algorithm
        - Finite automata
        - Knuth-Morris-Pratt algorithm
    - Computational geometry
        - Convex hull
            - Graham's scan
            - Jarvis's march
        - Closest pair problem
    - NP-complete problems
        - Hamiltonian cycle
        - Boolean satisfiability
        - Subset sum problem
        - Traveling-salesman problem
    - Approximation algorithms
        - Vertex-cover problem
        - 3-CNF satisfiability
        - Set-covering problem
        - Subset-sum optimization
    - Multithreaded algorithms
        - Shared-memory parallel computers
        - Parallelism quantification
        - Work-span model
        - Greedy scheduling
        - Race conditions
    - Matrix-vector multiplication
    - Strassen's method
    - Merge sort
    - Parallel algorithms design
    - Performance analysis
    - Theoretical limits of algorithm design
    - Advanced algorithmic techniques
    - Optimization problems under constraints
    - Cryptographic systems
    - Security applications
    - Pattern matching in text editing
    - Geometry algorithms
    - Computational complexity
    - Algorithmic efficiency
    - Problem-solving strategies in computational theory
    - Mathematical foundations of algorithms
    - Practical applications of theoretical concepts

mathematical_background.pdf:
  topics:
    - Mathematical tools for algorithms
    - High-school algebra
    - Asymptotic notations
    - Recurrences
    - Evaluating and bounding summations
    - Basic definitions and notations for sets
    - Relations
    - Functions
    - Graphs
    - Trees
    - Counting principles
    - Permutations
    - Combinations
    - Probability
    - Matrices operations
    - Properties
    - Sequences
    - Finite sums
    - Infinite sums
    - Series convergence
    - Linearity property
    - Arithmetic series
    - Sums of squares and cubes
    - Geometric series
    - Harmonic series
    - Integrating and differentiating series
    - Telescoping series
    - Bounding summations
    - Mathematical induction
    - Bounding terms
    - Splitting summations
    - Approximation by integrals
    - Venn diagrams
    - DeMorgan's laws
    - Principle of inclusion and exclusion
    - Countable and uncountable sets
    - Cardinality
    - Power sets
    - Ordered pairs
    - Cartesian products
    - Binary relations
    - Equivalence relations
    - Equivalence classes
    - Partial and total orders
    - Injections
    - Surjections
    - Bijections
    - Graph terminology
    - Directed and undirected graphs
    - Vertices
    - Edges
    - Paths
    - Cycles
    - Subgraphs
    - Isomorphism
    - Connectivity
    - Trees
    - Free trees
    - Unique paths
    - Connected components
    - Acyclic graphs
    - Degrees of vertices
    - Adjacency
    - Forests
    - Dag (directed acyclic graph)
    - Multigraphs
    - Hypergraphs
    - Graph contraction
    - Handshaking lemma
    - Disjoint sets
    - Set operations (intersection, union, difference, complement)