Knowledge Base

This is the space (so-called knowledge base), where I collect all the computer-related documents that I have written over the years. Some of them are out of my college notes. For most algorithm, I try to code the implementation mostly in C or Java and a few recursive algorithm in Scheme, which is interpreted with Dr. Scheme under the grammar rule in Essential Programming Languages 2ed.[3] In addition, this web page is generated using tex4ht under LATEX2ɛ, and SyntaxHighlighter script to do really cool highlighting on my code snippets.
If you see any mistakes, please feel free to drop me a line . Besides, the section with # symbol indicates the page is under development.

Contents

1  Math
1.1 #Set Theory
1.2 #Abstract Algebra
1.2.1 #Function
1.2.2 Monotonicity
1.2.3 Floor And Ceiling
1.2.4 Exponentials
1.2.5 Logarithms
1.2.6 Summation
1.2.7 Factorials
1.2.8 Counting
2  Statistic
2.3 Descriptive Statistic
2.4 Probability Theory
2.4.1 Conditional Probability
2.4.2 Bayes Theorem
2.4.3 #Independence
2.4.4 Probabilistic Inference
2.5 Discrete Random Variable
2.5.1 Expected Value on Discrete Event
2.5.2 Discrete Probability Distribution
2.6 Continuous Random Variable
2.6.1 Expected Value on Continuous Event
2.6.2 Continuous Probability Distribution
3  Algorithm
3.7 Recurrence
3.7.1 Bounding Summations
3.7.2 Substitution Method
3.7.3 Recursive Tree Method
3.7.4 Master Theorem
3.8 Data Structure
3.8.1 Linked List
3.8.2 Stack
3.8.3 Queue
3.8.4 Tree
  3.8.4.1 Binary Search Tree
  3.8.4.2 #Red-Black Tree
  3.8.4.3 #AVL Tree
  3.8.4.4 #B-Tree
3.8.5 Heap
  3.8.5.1 #Binomial Heap
  3.8.5.2 #Fibonacci Heap
  3.8.5.3 #Hash
3.9 Sorting Algorithm
3.9.1 Bubble Sort
3.9.2 Selection Sort
3.9.3 Insertion Sort
3.9.4 #Shell Sort
3.9.5 Merge Sort
3.9.6 Quick Sort
3.9.7 Heap Sort
3.9.8 Counting Sort
3.9.9 Radix Sort
3.9.10 #Bucket Sort
3.10 Searching Algorithm
3.10.1 Binary Search
3.11 Selection Algorithm
3.11.1 Finding Minimum and Maximum
3.11.2 #Randomized Selection
4  NP Complete
4.12 Packing Problem
4.12.1 Independent Set
4.12.2 Set Packing
4.13 Covering Problem
4.13.1 Vertex Cover
4.13.2 Hitting Set
4.13.3 Dominating Set
4.13.4 Set Cover
4.13.5 Clique
4.13.6 Feedback Arc Set
4.13.7 Feedback Vertex Set
4.13.8 K Node Disjoint Path
4.13.9 k-SPANNING TREE
  4.13.9.1 2-Spanning Tree
4.14 Constraint Salification Problem
4.14.1 Circuit Satisfiability
4.14.2 3-SAT
4.14.3 0-1 Linear Programming
4.15 Sequencing Problem
4.15.1 Hamiltonian Path
4.15.2 Hamiltonian Cycle
4.15.3 Directed Hamiltonian Cycle
4.15.4 Travelling Salesman Problem
4.15.5 Longest Path
4.16 Partitioning Problem
4.16.1 3D Matching
4.16.2 Intersection Inference
4.16.3 Graph 3-Colorability
4.17 Numerical Problem
4.17.1 Subset Sum
4.17.2 Number Partitioning
4.17.3 Scheduling
4.17.4 NPC Problem

Click here to go back to my homepage. This document was last modified on November 15, 2008.