Breadth-First Search, Depth-First Search, Shortest Path, Arbitrage, Strongly Connected Components and Maximum Flow
What you'll learn
Learn about the applications of data structures
Learn about the fundamental basics of graphs and graph theory
Implement advanced algorithms (graph algorithms) efficiently
Learn graph traversing such as breadth-first search and depth-first search
Learn about topological ordering and cycle detection
Learn about shortest path algorithms (Dijkstra's and Bellman-Ford algorithms)
Learn about spanning trees
Learn about strongly connected components
Learn about Hamiltonian cycles and Eulerian cycles
Learn about maximum flow (max flow min cut theorem)
Requirements
Internet connection
Basic knowledge of data structures
Description
This course is about advanced algorithms (graph algorithms) focusing on graph traversal, shortest path problems, spanning trees and maximum flow problems and a lots of its applications from Google Web Crawler to taking advantage of stock market arbitrage situations. Section 1 - Graphs Theory Basics:what is a G(V,E) graphadjacency matrix representationadjacency list representationSection 2 - Graph Traversal (Breadth-First Search)what is breadth-first search?how to use BFS for WebCrawling in search engines?Section 3 - Graph Traversal (Depth-First Search)what is depth-first search?how to use recursion to implement DFSapplications of DFS such as topological ordering and cycle detectionfind way out of a maze with DFSSection 4 - Topological Orderingwhat is topological ordering (topological sort)directed acyclic graphs (DAGs)DAG shortest path and longest pathcritical path methods and project managementSection 5 - Cycle Detectionwhat are cycles in a graph?forward edges and backward edgescycle detection algorithms (Tarjan's algorithm with DFS)Section 6 - Dijkstra's Shortest Path Algorithmwhat is a shortest path in a G(V,E) graphDijkstra's shortest path algorithmSection 7 - Bellman-Ford Shortest Path AlgorithmBellman-Ford algorithmhow to handle negative cyclesfinding arbitrage opportunities on the FOREXSection 8: - Spanning Trees (Kruskal and Prim's Algorithms)what are spanning trees?union find data structuresKruskal's algorithmPrim's algorithmSection 9 - Strongly Connected Components (SCCs)what are strongly connected componentsKosaraju's algorithmTarjan's algorithmSection 10 - Maximum Flow Problemthe famous maximum flow problemhow to reduce most of the hard problems to maximum flow problemFord-Fulkerson algorithmbipartite matching problemSection 9 - Travelling Salesman Problem and Hamiltonian Cycles:travelling salesman problem (TSP)how to deal with NP-hard problemswhat are meta-heuristicsSection 10 - Eulerian Pathseulerian paths and eulerian cyclesHierholzer algorithm and the Chinese Postman ProblemSection 11 - Algorithms Analysishow to measure the running time of algorithmsrunning time analysis with big O (ordo), big Ω (omega) and big θ (theta) notationscomplexity classespolynomial (P) and non-deterministic polynomial (NP) algorithmsO(1), O(logN), O(N) and several other running time complexitiesThe course is going to take approximately 11 hours to completely but I highly suggest you typing these algorithms out several times in order to get a good grasp of it. You can download the source code of the whole course at the last lecture. You should definitely take this course if you are interested in advanced topics concerning algorithms. There are a bunch of fields where these methods can be used: from software engineering to scientific research.Thanks for joining the course, let's get started!
Overview
Section 1: Introduction
Lecture 1 Introduction
Lecture 2 Complexity theory basics
Section 2: Graph Theory Overview
Lecture 3 Graph theory overview
Lecture 4 Adjacency matrix and adjacency list
Lecture 5 Adjacency matrix and adjacency list implementation
Lecture 6 Applications of graphs
Section 3: Breadth-First Search (BFS)
Lecture 7 Breadth-first search introduction
Lecture 8 Breadth-first search implementation
Section 4: Course Challenge

1 - WebCrawler
Lecture 9 Breadth-first search - WebCrawler (core of search engines)
Lecture 10 Breadth-first search - WebCrawler implementation
Section 5: Depth-First Search (DFS)
Lecture 11 Depth-first search introduction
Lecture 12 DFS implementation I - with stack
Lecture 13 DFS implementation II - with recursion
Lecture 14 Depth-first search and stack memory visualisation
Lecture 15 Memory management: BFS vs DFS
Section 6: Course Challenge 2- Maze Escape
Lecture 16 Maze problem introduction
Lecture 17 Course challenge 1 - maze escape
Lecture 18 Maze solving algorithm implementation
Section 7: Topological Ordering
Lecture 19 What is topological ordering?
Lecture 20 Topological ordering implementation I
Lecture 21 Topological ordering implementation II
Lecture 22 Finding the shortest path with topological ordering
Lecture 23 Topological ordering shortest path implementation I
Lecture 24 Topological ordering shortest path implementation II
Lecture 25 Dynamic programming with topological sort
Section 8: Cycle Detection
Lecture 26 Cycle detection introduction
Lecture 27 Cycle detection implementation I
Lecture 28 Cycle detection implementation II
Section 9: Shortest Path Methods - Dijkstra's Algorithm
Lecture 29 What is the shortest path problem?
Lecture 30 Dijkstra algorithm visualization
Lecture 31 Dijkstra algorithm implementation I
Lecture 32 Dijkstra algorithm implementation II
Lecture 33 Dijkstra algorithm implementation III
Lecture 34 Dijktsra's algorithm with adjacency matrix representation
Lecture 35 Shortest path algorithms applications
Section 10: Course Challenge 3 - Longest Path
Lecture 36 The critical path method (CPM) and longest paths
Lecture 37 Course challenge 3 - DAG shortest path
Lecture 38 Longest path implementation
Section 11: Shortest Path Methods - Bellman-Ford Algorithm
Lecture 39 What is the Bellman-Ford algorithm?
Lecture 40 Bellman-Ford algorithm visualisation
Lecture 41 Bellman-Ford algorithm implementation I
Lecture 42 Bellman-Ford algorithm implementation II
Lecture 43 Greedy algorithm or dynamic programming approach?
Section 12: Course Challenge 4 - Arbitrage on FOREX
Lecture 44 Arbitrage situations on FOREX introduction
Lecture 45 Arbitrage situations on FOREX implementation
Section 13: Spanning Trees - Kruskal's Algorithm
Lecture 46 What is the disjoint set data structure?
Lecture 47 Disjoint sets visualization
Lecture 48 Kruskal's algorithm introduction
Lecture 49 Kruskal algorithm implementation I
Lecture 50 Kruskal algorithm implementation II
Lecture 51 Kruskal algorithm implementation III
Section 14: Spanning Trees - Prim's Algorithm
Lecture 52 What is the lazy Prim's algorithm?
Lecture 53 Lazy Prim's algorithm implementation I
Lecture 54 Lazy Prim's algorithm implementation II
Lecture 55 What is the eager Prim's algorithm?
Lecture 56 Eager Prim's algorithm implementation
Lecture 57 Comparison of minimum spanning tree algorithms
Lecture 58 Applications of spanning trees
Section 15: Strongly Connected Components - Kosaraju's Algorithm
Lecture 59 Strongly connected components introduction
Lecture 60 Kosaraju algorithm introduction
Lecture 61 Kosaraju algorithm implementation I
Lecture 62 Kosaraju algorithm implementation II
Lecture 63 Kosaraju algorithm implementation III
Section 16: Strongly Connected Components - Tarjan's Algorithm
Lecture 64 Tarjan algorithm introduction
Lecture 65 Tarjan algorithm visualization
Lecture 66 Tarjan algorithm implementation
Lecture 67 Applications of strongly connected components
Section 17: Maximum Flow Problem
Lecture 68 Maximum flow introduction - basics
Lecture 69 Maximum flow introduction - properties
Lecture 70 Maximum flow introduction - cuts
Lecture 71 Maximum flow introduction - residual networks
Lecture 72 Maximum flow introduction - Ford-Fulkerson algorithm
Lecture 73 Maximum flow introduction - example
Lecture 74 Maximum flow implementation I - Edge, Vertex
Lecture 75 Maximum flow implementation II - FlowNetwork class
Lecture 76 Maximum flow implementation III - Ford-Fulkerson algorithm
Lecture 77 Maximum flow implementation IV - augmentation
Lecture 78 Maximum flow implementation V - testing
Lecture 79 Applications of maximum flow problem
Lecture 80 Article on maximum flow problem
Section 18: Hamiltonian Cycles - Travelling Salesman Problem (TSP)
Lecture 81 What are Hamiltonian cycles?
Lecture 82 The travelling salesman problem
Lecture 83 Travelling salesman problem implementation I
Lecture 84 Travelling salesman problem implementation II
Lecture 85 TSP and stack memory visualization
Lecture 86 Why to use meta-heuristics?
Section 19: Eulerian Cycles - Chinese Postman Problem
Lecture 87 Eulerian cycles introduction
Lecture 88 Eulerian cycles application
Section 20: APPENDIX - COMPLEXITY THEORY CRASH COURSE
Lecture 89 How to measure the running times of algorithms?
Lecture 90 Complexity theory illustration
Lecture 91 Complexity notations - big (O) ordo
Lecture 92 Complexity notations - big Ω (omega)
Lecture 93 Complexity notations - big (θ) theta
Lecture 94 Algorithm running times
Lecture 95 Complexity classes
Lecture 96 Analysis of algorithms - loops
Lecture 97 Case study - O(1)
Lecture 98 Case study - O(logN)
Lecture 99 Case study - O(N)
Lecture 100 Case study - O(N*N)
Section 21: Algorhyme FREE Algorithms Visualizer App
Lecture 101 Algorithms Visualization App
Lecture 102 Algorhyme - Algorithms and Data Structures
Section 22: Course Materials (DOWNLOADS)
Lecture 103 Course materials
This course is meant for everyone from scientists to software developers who want to get closer to algorithmic thinking in the main
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