Detailed explanation of algorithms: Stanford University’s classic video course

The first volume of the four-part Detailed Explanation of Algorithms explains the basics of algorithms in detail and shows the essence of algorithms. It integrates many years of teaching experience of Stanford University professors and explains the profound things in a simple and easy-to-understand way.

Algorithms are the core and soul of computer science. Algorithms have a wide range of applications and are required for the implementation of network routing, computational genomics, public key cryptography and database systems. Studying algorithms can help us become better programmers, enable us to think more carefully, and successfully cope with technical interviews on various occasions.

This is a very easy-to-use introductory book on algorithms. It can be used as a learning book for programmers, and is also suitable for readers who want to learn algorithms and improve their algorithmic thinking skills.

This book mainly includes the following contents:
asymptotic analysis;
Big O notation;
master method;
fast divide and conquer algorithm;
randomization algorithm;
sorting algorithm;

Choose an algorithm.

Algorithms are the core and soul of computer science. Algorithms have a wide range of applications and are required for the implementation of network routing, computational genomics, public key cryptography and database systems. Studying algorithms can help us become better programmers, enable us to think more carefully, and successfully cope with technical interviews on various occasions.
This is a very easy-to-use introductory book on algorithms. It can be used as a learning book for programmers, and is also suitable for readers who want to learn algorithms and improve their algorithmic thinking skills.
This book mainly includes the following contents:
graph search and application;
hash table;
shortest path algorithm;
Bloom filter;
randomization algorithm;
heap;
search tree.

• Chapter 1：Why Study Algorithms (4 minutes and 15 seconds)

• Chapter 2：Integer Multiplication (8 minutes and 38 seconds)

• Chapter 3：Karatsuba Multiplication (12 minutes and 39 seconds)

• Chapter 4：Merge Sort Motivation and Example (8 minutes and 44 seconds)

• Chapter 5：Merge Sort Pseudocode (12 minutes and 51 seconds)

• Chapter 6：Merge Sort Analysis (9 minutes and 2 seconds)

• Chapter 7：Guiding Principles for Analysis of Algorithms (15 minutes and 16 seconds)

• Chapter 8：The Gist (14 minutes and 12 seconds)

• Chapter 9：Big Oh Notation (4 minutes and 9 seconds)

• Chapter 10：Basic Examples (7 minutes and 27 seconds)

• Chapter 11：Big Omega and Theta (7 minutes and 31 seconds)

• Chapter 12：Additional Examples Review Optional (7 minutes and 51 seconds)

• Chapter 13：On log n Algorithm for Counting Inversions I (12 minutes and 35 seconds)

• Chapter 14：On log n Algorithm for Counting Inversions II (16 minutes and 33 seconds)

• Chapter 15：Strassen's Subcubic Matrix Multiplication Algorithm (22 minutes and 31 seconds)

• Chapter 16：On log n Algorithm for Closest Pair I Advanced Optional (31 minutes and 46 seconds)

• Chapter 17：On log n Algorithm for Closest Pair II Advanced Optional (18 minutes and 58 seconds)

• Chapter 18：Motivation (7 minutes and 47 seconds)

• Chapter 19：Formal Statement (9 minutes and 57 seconds)

• Chapter 20：Examples (13 minutes and 5 seconds)

• Chapter 21：Proof I (9 minutes and 57 seconds)

• Chapter 22：Interpretation of the 3 Cases (10 minutes and 46 seconds)

• Chapter 23：Proof II (16 minutes and 16 seconds)

• Chapter 24：Quicksort Overview (12 minutes and 8 seconds)

• Chapter 25：Partitioning Around a Pivot (24 minutes and 55 seconds)

• Chapter 26：Choosing a Good Pivot (22 minutes and 25 seconds)

• Chapter 27：Analysis IA Decomposition Principle Advanced Optional (21 minutes and 48 seconds)

• Chapter 28：Analysis II The Key Insight Advanced Optional (11 minutes and 47 seconds)

• Chapter 29：Analysis III Final Calculations Advanced Optional (8 minutes and 57 seconds)

• Chapter 30：Omegan log n Lower Bound for Comparison Based Sorting Advanced Optional (13 minutes and 29 seconds)

• Chapter 31：Randomized Selection Algorithm (21 minutes and 39 seconds)

• Chapter 32：Randomized Selection Analysis (20 minutes and 34 seconds)

• Chapter 33：Deterministic Selection Algorithm Advanced Optional (16 minutes and 56 seconds)

• Chapter 34：Deterministic Selection Analysis I Advanced Optional (22 minutes and 1 seconds)

• Chapter 35：Deterministic Selection Analysis II Advanced Optional (12 minutes and 41 seconds)

• Chapter 36：Correctness of Quicksort Review Optional (10 minutes and 38 seconds)

• Chapter 37：Part I Review Optional (25 minutes and 57 seconds)

• Chapter 38：Graphs and Minimum Cuts (15 minutes and 50 seconds)

• Chapter 39：Graph Representations (14 minutes and 22 seconds)

• Chapter 40：Graph Search Overview (23 minutes and 19 seconds)

• Chapter 41：Breadth First Search BFS The Basics (14 minutes and 12 seconds)

• Chapter 42：BFS and Shortest Paths (7 minutes and 43 seconds)

• Chapter 43：BFS and Undirected Connectivity (13 minutes and 18 seconds)

• Chapter 44：Depth First Search DFS The Basics (7 minutes and 24 seconds)

• Chapter 45：Topological Sort (21 minutes and 53 seconds)

• Chapter 46：Computing Strong Components The Algorithm (29 minutes and 21 seconds)

• Chapter 47：Computing Strong Components The Analysis (26 minutes and 2 seconds)

• Chapter 48：Structure of the Web Optional (18 minutes and 50 seconds)

• Chapter 49：Dijkstra's Shortest Path Algorithm (20 minutes and 45 seconds)

• Chapter 50：Dijkstra's Algorithm Examples (12 minutes and 45 seconds)

• Chapter 51：Correctness of Dijkstra's Algorithm Advanced Optional (19 minutes and 17 seconds)

• Chapter 52：Dijkstra's Algorithm Implementation and Running Time (26 minutes and 27 seconds)

• Chapter 53：Data Structures Overview (4 minutes and 36 seconds)

• Chapter 54：Heaps Operations and Applications (18 minutes and 11 seconds)

• Chapter 55：Heaps Implementation Details Advanced Optional (20 minutes and 57 seconds)

• Chapter 56：Balanced Search Trees Operations and Applications (10 minutes and 55 seconds)

• Chapter 57：Binary Search Tree Basics, Part I (13 minutes and 7 seconds)

• Chapter 58：Binary Search Tree Basics, Part II (30 minutes and 9 seconds)

• Chapter 59：Rotations Advanced Optional (7 minutes and 36 seconds)

• Chapter 60：Hash Tables Operations and Applications (19 minutes and 20 seconds)

• Chapter 61：Hash Tables Implementation Details, Part I (18 minutes and 58 seconds)

• Chapter 62：Hash Tables Implementation Details, Part II (22 minutes and 13 seconds)

• Chapter 63：Pathological Data Sets and Universal Hashing Motivation (21 minutes and 54 seconds)

• Chapter 64：Bloom Filters The Basics (15 minutes and 22 seconds)

• Chapter 65：Bloom Filters Heuristic Analysis (13 minutes and 26 seconds)

• Chapter 66：INTRODUCTION TO GREEDY ALGORITHMS- Greedy Algorithms (12 minutes and 35 seconds)

• Chapter 67：A SCHEDULING APPLICATION-Problem Definition (5 minutes and 48 seconds)

• Chapter 68：A SCHEDULING APPLICATION- Greedy Algorithm (12 minutes and 57 seconds)

• Chapter 69：A SCHEDULING APPLICATION-Correctness Proof-Part I (6 minutes and 57 seconds)

• Chapter 70：A SCHEDULING APPLICATION-Correctness Proof-Part II (4 minutes and 41 seconds)

• Chapter 71：A SCHEDULING APPLICATION- Handling Ties (7 minutes and 14 seconds)

• Chapter 72：HUFFMAN CODES- Introduction and Motivation (9 minutes and 19 seconds)

• Chapter 73：HUFFMAN CODES- Problem Definition (10 minutes and 17 seconds)

• Chapter 74：HUFFMAN CODES- A Greedy Algorithm (16 minutes and 43 seconds)

• Chapter 75：HUFFMAN CODES- A More Complex Example (4 minutes and 2 seconds)

• Chapter 76：HUFFMAN CODES- Correctness Proof 1 (10 minutes and 6 seconds)

• Chapter 77：HUFFMAN CODES- Correctness Proof 2 (12 minutes and 46 seconds)

• Chapter 78：PRIM'S MINIMUM SPANNING TREE ALGORITHM- MST Problem Definition (11 minutes and 16 seconds)

• Chapter 79：PRIM'S MINIMUM SPANNING TREE ALGORITHM- Prims MST Algorithm (7 minutes and 32 seconds)

• Chapter 80：PRIM'S MINIMUM SPANNING TREE ALGORITHM- Fast Implementation 1 (14 minutes and 49 seconds)

• Chapter 81：PRIM'S MINIMUM SPANNING TREE ALGORITHM- Fast Implementation 2 (9 minutes and 50 seconds)

• Chapter 82：PRIM'S MINIMUM SPANNING TREE ALGORITHM- Correctness Proof 1 (15 minutes and 30 seconds)

• Chapter 83：PRIM'S MINIMUM SPANNING TREE ALGORITHM- Correctness Proof 2 (8 minutes and 9 seconds)

• Chapter 84：KRUSKAL'S MINIMUM SPANNING TREE ALGORITHM- Kruskals MST Algorithm (7 minutes and 27 seconds)

• Chapter 85：KRUSKAL'S MINIMUM SPANNING TREE ALGORITHM- Implementing Kruskals Algorithm via Union Find (9 minutes and 21 seconds)

• Chapter 86：KRUSKAL'S MINIMUM SPANNING TREE ALGORITHM- Implementing Kruskals Algorithm via Union Find 2 (13 minutes and 35 seconds)

• Chapter 87：ADVANCED UNION-FIND- Lazy Unions (10 minutes and 3 seconds)

• Chapter 88：KRUSKAL'S MINIMUM SPANNING TREE ALGORITHM- Correctness of Kruskals Algorithm (9 minutes and 22 seconds)

• Chapter 89：CLUSTERING - Application to Clustering (11 minutes and 32 seconds)

• Chapter 90：INTRODUCTION TO DYNAMIC PROGRAMMING- Introduction - Weighted Independent Sets in Path Graphs (7 minutes and 55 seconds)

• Chapter 91：INTRODUCTION TO DYNAMIC PROGRAMMING- WIS in Path Graphs - Optimal Substructure (9 minutes and 27 seconds)

• Chapter 92：INTRODUCTION TO DYNAMIC PROGRAMMING- WIS in Path Graphs - A Linear Time Algorithm (9 minutes and 56 seconds)

• Chapter 93：INTRODUCTION TO DYNAMIC PROGRAMMING- WIS in Path Graphs - A Reconstruction Algorithm (6 minutes and 53 seconds)

• Chapter 94：INTRODUCTION TO DYNAMIC PROGRAMMING- Principles of Dynamic Programming (7 minutes and 57 seconds)

• Chapter 95：THE KNAPSACK PROBLEM- The Knapsack Problem (9 minutes and 47 seconds)

• Chapter 96：THE KNAPSACK PROBLEM- A Dynamic Programming Algorithm (9 minutes and 59 seconds)

• Chapter 97：THE KNAPSACK PROBLEM- Example (12 minutes and 53 seconds)

• Chapter 98：SEQUENCE ALIGNMENT- Optimal Substructure (13 minutes and 44 seconds)

• Chapter 99：SEQUENCE ALIGNMENT- A Dynamic Programming Algorithm (12 minutes and 28 seconds)

• Chapter 100：OPTIMAL BINARY SEARCH TREES- Problem Definition (12 minutes and 24 seconds)

• Chapter 101：OPTIMAL BINARY SEARCH TREES- Optimal Substructure (9 minutes and 34 seconds)

• Chapter 102：OPTIMAL BINARY SEARCH TREES- Proof of Optimal Substructure (6 minutes and 40 seconds)

• Chapter 103：OPTIMAL BINARY SEARCH TREES- A Dynamic Programming Algorithm 1 (9 minutes and 45 seconds)

• Chapter 104：OPTIMAL BINARY SEARCH TREES- A Dynamic Programming Algorithm 2 (9 minutes and 27 seconds)

• Chapter 105：THE BELLMAN-FORD ALGORITHM- Single-Source Shortest Paths, Revisited (10 minutes and 51 seconds)

• Chapter 106：THE BELLMAN-FORD ALGORITHM- Optimal Substructure (10 minutes and 46 seconds)

• Chapter 107：THE BELLMAN-FORD ALGORITHM- The Basic Algorithm 1 (8 minutes and 35 seconds)

• Chapter 108：THE BELLMAN-FORD ALGORITHM- The Basic Algorithm 2 (10 minutes and 55 seconds)

• Chapter 109：THE BELLMAN-FORD ALGORITHM- Detecting Negative Cycles (9 minutes and 18 seconds)

• Chapter 110：ALL-PAIRS SHORTEST PATHS- Problem Definition (7 minutes and 1 seconds)

• Chapter 111：ALL-PAIRS SHORTEST PATHS- Optimal Substructure (12 minutes and 2 seconds)

• Chapter 112：ALL-PAIRS SHORTEST PATHS- The Floyd Warshall Algorithm (13 minutes and 30 seconds)

• Chapter 113：A Field Guide to Algorithm Design (Epilogue to the Algorithms Illuminated book series) (18 minutes and 46 seconds)

• Chapter 114：Overview and Prerequisites (10 minutes and 4 seconds)

• Chapter 115：The Algorithmic Mystery of MST vs. TSP (16 minutes and 18 seconds)

• Chapter 116：Possible Levels of Expertise (4 minutes and 25 seconds)

• Chapter 117：Easy and Hard Problems (22 minutes and 55 seconds)

• Chapter 118：Algorithmic Strategies for NP-Hard Problems (24 minutes and 39 seconds)

• Chapter 119：A Simple Recipe for Proving NP-Hardness (26 minutes and 6 seconds)

• Chapter 120：Rookie Mistakes (9 minutes and 52 seconds)

• Chapter 121：Makespan Minimization Part 1 (19 minutes and 17 seconds)

• Chapter 122：Makespan Minimization Part 2 (21 minutes and 37 seconds)

• Chapter 123：A Greedy Heuristic for Maximum Coverage Part 1 (20 minutes and 9 seconds)

• Chapter 124：A Greedy Heuristic for Maximum Coverage Part 2 (21 minutes and 43 seconds)

• Chapter 125：A Greedy Heuristic for Influence Maximization 1 (19 minutes and 8 seconds)

• Chapter 126：A Greedy Heuristic for Influence Maximization 2 (18 minutes and 41 seconds)

• Chapter 127：The 2-OPT Heuristic for the TSP Part 1 (12 minutes and 44 seconds)

• Chapter 128：The 2-OPT Heuristic for the TSP Part 2 (11 minutes and 57 seconds)

• Chapter 129：Principles of Local Search Part 1 (23 minutes and 11 seconds)

• Chapter 130：Principles of Local Search Part 2 (24 minutes and 48 seconds)

• Chapter 131：The Bellman-Held-Karp Algorithm for TSP Part 1 (19 minutes and 34 seconds)

• Chapter 132：The Bellman-Held-Karp Algorithm for TSP Part 2 (15 minutes and 47 seconds)

• Chapter 133：Color Coding Part 1 (28 minutes and 29 seconds)

• Chapter 134：Color Coding Part 2 (15 minutes and 47 seconds)

• Chapter 135：Problem-Specific Algorithms vs. Magic Boxes (8 minutes and 23 seconds)

• Chapter 136：Mixed Integer Programming Solvers (16 minutes and 59 seconds)

• Chapter 137：Satisfiability Solvers (24 minutes and 26 seconds)

• Chapter 138：Reductions Revisited (9 minutes and 22 seconds)

• Chapter 139：SAT and the Cook-Levin Theorem (7 minutes and 29 seconds)

• Chapter 140：The Big Picture (25 minutes and 6 seconds)

• Chapter 141：Independent Set Is NP-Hard (27 minutes and 16 seconds)

• Chapter 142：Directed Hamiltonian Path Is NP-Hard (26 minutes and 24 seconds)

• Chapter 143：The TSP Is NP-Hard (12 minutes and 31 seconds)

• Chapter 144：Subset Sum Is NP-Hard (26 minutes and 24 seconds)

• Chapter 145：Amassing Evidence of Intractability (11 minutes and 11 seconds)

• Chapter 146：Decision, Search, and Optimization (7 minutes and 36 seconds)

• Chapter 147：NP- Problems with Easily Recognized Solutions (24 minutes and 57 seconds)

• Chapter 148：The P!=NP Conjecture (12 minutes and 4 seconds)

• Chapter 149：The Exponential Time Hypothesis (18 minutes and 45 seconds)

• Chapter 150：NP-Completeness (19 minutes and 17 seconds)

• Chapter 151：Repurposing Wireless Spectrum (11 minutes and 15 seconds)

• Chapter 152：Greedy Heuristics for Buying Back Licenses Pt 1 (22 minutes and 2 seconds)

• Chapter 153：Greedy Heuristics for Buying Back Licenses Pt 2 (14 minutes and 7 seconds)

• Chapter 154：Feasibility Checking Pt 1 (17 minutes and 18 seconds)

• Chapter 155：Feasibility Checking Pt 2 (26 minutes and 24 seconds)

• Chapter 156：Implementation as a Descending Clock Auction (28 minutes and 46 seconds)

• Chapter 157：The Final Outcome (6 minutes and 11 seconds)

• Chapter 158：A Field Guide to Algorithm Design (Epilogue to the Algorithms Illuminated book series) (18 minutes and 46 seconds)