⚡ MemoLearning Data Structures and Algorithms II

Advanced trees, heaps, graphs, dynamic programming, and complex algorithms

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Advanced Curriculum Overview

12
Advanced Units
~160
Advanced Skills
8
Algorithm Categories
4
Problem Paradigms
1

Advanced Tree Structures

Master self-balancing trees and specialized tree structures for optimal performance.

  • AVL Trees and rotations
  • Red-Black Trees
  • B-Trees and B+ Trees
  • Splay Trees
  • Tree balancing algorithms
  • Height-balanced operations
  • Tree rotation techniques
  • Performance analysis of balanced trees
2

Heap Data Structures

Deep dive into heap variations and their applications in priority-based algorithms.

  • Binary Heaps (Min/Max)
  • Fibonacci Heaps
  • Binomial Heaps
  • Priority Queue implementations
  • Heap Sort algorithm
  • Heapify operations
  • Mergeable heap operations
  • Applications in graph algorithms
3

Hash Tables & Advanced Hashing

Explore sophisticated hashing techniques and collision resolution strategies.

  • Advanced hash functions
  • Universal hashing
  • Perfect hashing
  • Cuckoo hashing
  • Robin Hood hashing
  • Consistent hashing
  • Bloom filters
  • Hash table optimization techniques
4

Graph Algorithms

Master complex graph algorithms for pathfinding, connectivity, and optimization.

  • Advanced graph traversal
  • Dijkstra's shortest path
  • Bellman-Ford algorithm
  • Floyd-Warshall algorithm
  • Minimum Spanning Trees (Kruskal, Prim)
  • Topological sorting
  • Strongly connected components
  • Network flow algorithms
5

Advanced Sorting Algorithms

Learn sophisticated sorting techniques and their specialized applications.

  • Merge Sort variations
  • Quick Sort optimizations
  • Heap Sort implementation
  • Radix Sort and Counting Sort
  • Bucket Sort
  • External sorting algorithms
  • Parallel sorting algorithms
  • Sorting algorithm selection criteria
6

Dynamic Programming

Master the art of solving complex problems through optimal substructure decomposition.

  • DP principles and characteristics
  • Memoization vs Tabulation
  • Classic DP problems (Knapsack, LCS, LIS)
  • Matrix chain multiplication
  • Edit distance algorithms
  • DP on trees and graphs
  • Space optimization techniques
  • Advanced DP patterns
7

String Algorithms

Explore efficient algorithms for string processing and pattern matching.

  • String matching algorithms
  • KMP (Knuth-Morris-Pratt)
  • Rabin-Karp algorithm
  • Boyer-Moore algorithm
  • Suffix arrays and trees
  • String hashing techniques
  • Longest common substring
  • String compression algorithms
8

Greedy Algorithms

Learn when and how to apply greedy strategies for optimal solutions.

  • Greedy algorithm principles
  • Activity selection problem
  • Fractional knapsack
  • Huffman coding
  • Job scheduling algorithms
  • Greedy graph algorithms
  • Proving greedy correctness
  • When greedy fails
9

Divide and Conquer

Master the divide and conquer paradigm for solving complex algorithmic problems.

  • Divide and conquer principles
  • Merge sort analysis
  • Quick sort variations
  • Binary search extensions
  • Closest pair of points
  • Matrix multiplication (Strassen)
  • Fast Fourier Transform basics
  • Recurrence relation solving
10

Advanced Data Structures

Explore specialized data structures for specific problem domains.

  • Disjoint Set (Union-Find)
  • Segment Trees
  • Binary Indexed Trees (Fenwick)
  • Trie data structure
  • Suffix trees and arrays
  • Skip lists
  • Persistent data structures
  • Lock-free data structures
11

Network Flow Algorithms

Study algorithms for maximum flow and minimum cut problems in networks.

  • Flow network concepts
  • Ford-Fulkerson method
  • Edmonds-Karp algorithm
  • Dinic's algorithm
  • Push-relabel algorithms
  • Minimum cut problems
  • Bipartite matching
  • Applications in real networks
12

Computational Complexity

Understand algorithm complexity classes and computational limits.

  • P vs NP problem
  • NP-completeness
  • NP-hard problems
  • Reduction techniques
  • Approximation algorithms
  • Randomized algorithms
  • Amortized analysis
  • Lower bound techniques

Unit 1: Advanced Tree Structures

Master self-balancing trees and specialized tree structures for optimal performance.

AVL Trees and Rotations

Learn height-balanced binary search trees with automatic rebalancing through single and double rotations.

Red-Black Trees

Master color-based balancing properties and understand insertion/deletion rebalancing procedures.

B-Trees and B+ Trees

Understand multi-way search trees optimized for disk storage and database indexing systems.

Splay Trees

Learn self-adjusting binary search trees that move frequently accessed elements to the root.

Tree Balancing Algorithms

Compare different balancing strategies and understand when to use each tree type.

Height-Balanced Operations

Implement insertion, deletion, and search operations while maintaining tree balance invariants.

Tree Rotation Techniques

Master left and right rotations, and understand how they preserve BST properties while rebalancing.

Performance Analysis

Analyze time complexity guarantees and understand why balanced trees ensure O(log n) operations.

Unit 2: Heap Data Structures

Deep dive into heap variations and their applications in priority-based algorithms.

Binary Heaps (Min/Max)

Master complete binary tree implementation with heap property maintenance and array representation.

Fibonacci Heaps

Learn advanced heap structure with better amortized performance for decrease-key operations.

Binomial Heaps

Understand mergeable heaps with binomial tree structure for efficient union operations.

Priority Queue Implementations

Compare different heap implementations for priority queues and their performance trade-offs.

Heap Sort Algorithm

Implement in-place sorting using binary heaps with O(n log n) time complexity.

Heapify Operations

Master bottom-up and top-down heapify procedures for building and maintaining heaps.

Mergeable Heap Operations

Learn how to efficiently merge two heaps while maintaining heap properties.

Applications in Graph Algorithms

Understand how heaps optimize Dijkstra's algorithm and Prim's minimum spanning tree algorithm.

Unit 3: Hash Tables & Advanced Hashing

Explore sophisticated hashing techniques and collision resolution strategies.

Advanced Hash Functions

Design and analyze cryptographic and non-cryptographic hash functions for different applications.

Universal Hashing

Learn probabilistic hashing techniques that guarantee good performance regardless of input.

Perfect Hashing

Understand collision-free hashing for static sets with guaranteed O(1) lookup time.

Cuckoo Hashing

Master worst-case O(1) lookup time with two hash functions and displacement resolution.

Robin Hood Hashing

Learn open addressing with variance reduction for more predictable performance.

Consistent Hashing

Understand distributed hashing for load balancing in distributed systems.

Bloom Filters

Learn space-efficient probabilistic data structures for membership testing.

Hash Table Optimization

Explore cache-friendly implementations and memory layout optimizations.

Unit 4: Graph Algorithms

Master complex graph algorithms for pathfinding, connectivity, and optimization.

Advanced Graph Traversal

Extend DFS and BFS for cycle detection, connectivity analysis, and topological applications.

Dijkstra's Shortest Path

Implement single-source shortest path for non-negative weights using priority queues.

Bellman-Ford Algorithm

Handle negative weight edges and detect negative cycles in directed graphs.

Floyd-Warshall Algorithm

Compute all-pairs shortest paths using dynamic programming approach.

Minimum Spanning Trees

Master Kruskal's and Prim's algorithms for finding minimum cost spanning trees.

Topological Sorting

Order vertices in directed acyclic graphs for dependency resolution and scheduling.

Strongly Connected Components

Find maximal strongly connected subgraphs using Tarjan's and Kosaraju's algorithms.

Network Flow Algorithms

Solve maximum flow problems with Ford-Fulkerson and more advanced flow algorithms.

Unit 5: Advanced Sorting Algorithms

Learn sophisticated sorting techniques and their specialized applications.

Merge Sort Variations

Explore bottom-up merge sort, natural merge sort, and space-optimized implementations.

Quick Sort Optimizations

Learn pivot selection strategies, 3-way partitioning, and hybrid approaches.

Heap Sort Implementation