Combinatorics and Algorithms Design

Combinatorics and Algorithms Design课程：前往报名学习

Combinatorics and Algorithms Design视频慕课课程简介：

This course covers topics in Combinatorics and Algorithms Design. We comprehensively discuss basic concepts, theories, methods, and instances in Combinatorics while focusing on concepts and ideas. We also discuss basic mathematics concepts in algorithms design including growth of function, Big-O notations and recurrence relations etc., and basic strategies of algorithms design including randomized algorithms, divide and conquer, and dynamic programming etc.

前往报名学习

Combinatorics and Algorithms Design课程列表：

Introduction to Combinatorial Mathematics

-What's Combinatorial Mathematics

--What's Combinatorial Mathematics

--What's Combinatorial Mathematics--Homework

-The Most Ingenious Arrangement - Magic Square

--The Most Ingenious Arrangement - Magic Square

--The Most Ingenious Arrangement - Magic Square--Homework

-Suffering Parchment Roll

--Suffering parchment roll

--Suffering Parchment Roll--Homework

-Is Your Phone Password Safe

--Is Your Phone Password Safe

--Talking About Combinatorial Mathematics--Is Your P

-Brute-force Enumaration OR Abstract Conversion

--A problem caused by the world cup

--Correspondence

--seven bridge problem

--Summary

--Brute-force Enumaration OR Abstract Conversion--Homework

-Homework 1

--Discussion rules

--Homework 1

Combinatorial trip of a Pingpong ball

-Counting with "+" "-" "*" "/"

--Fundamental Counting Principles

-Permutation or Combination?

--Definition of Permutation and Combination

--Models of Combination and Combinatorial Identities

--Combinatorial trip of a Pingpong ball--Permutation

-Various Permutations

--Circular Permutation and Necklace Permutation

--Permutations of Multisets

--Combinatorial trip of a Pingpong ball--Various Per

-Different Kinds of Combinations

--Combinations of Multisets

--Non-adjacent Combination

--Combinatorial trip of a Pingpong ball--Different K

-Permutation In The Bell Ring

--Permutation In The Bell Ring

--Lexicographic Order

--Steinhaus–Johnson–Trotter Algorithm

--Industrial Support and Stirling approximation

--Combinatorial trip of a Pingpong ball--Permutation

-Homework 2

--GT

--Homework 2

Generating Function

-Generating Function & Counting Rules

--Definition Of Generating Function

--Generating Function & Counting Rules--Homework

-Simple Application Of Generating Function

--Simple Application Of Generating Function（1）

--Simple Application Of Generating Function (2)

--Generating Function--Simple Application Of Generat

-Integer Partition

--Integer Partition (1)

--Integer Partition (2)

-Ferrers Diagram

--Ferrers Diagram

--Ferrers Diagram--Homework

-Generating Function And Recurrence Relation

--What Can We Do With Generating Function

--hanoi problem (1)

--hanoi problem (2)

--summay

-Homework 3

--Homework 3

Linear Homogeneous Recurrence Relation

-Fibonacci Sequence

--Fibonacci Rabbits

--Fibonacci Sequence

--Fibonacci Sequence--Homework

-Application Of The Fibonacci Sequence

--Magic Show

--Expression of Fibonacci Numbers

--Applications in Optimization Methods

--Elliott Wave

--Linear Homogeneous Recurrence Relation--Applicatio

-Linear Homogeneous Recurrence Relation

--Definition

--Characteristic Polynomial

--Generating Function And Characteristic Polynomial

--Getting Solution By Characteristic Polynomial (1)

--Getting Solution By Characteristic Polynomial (2)

--Linear Homogeneous Recurrence Relation--Homework

-Examples

--Example(1)

--Example(2)

-Homework Of Week 4

--GT

--Homework Of Week 4

-Behind the scenes extra

-- Behind the scenes extra

Magical Sequences

-Catalan Numbers

--Amazing World of Computers

--Catalan Numbers

--Examples of Catalan Numbers

--Magical Sequences--Catalan Numbers

-Exponential Generating Functions

--Exponential Generating Functions

--Applications of Exponential Generating Functions

--Exponential Generating Functions--Homework

-Derangements

--Derangements (1)

--Derangements (2)

--Magical Sequences--Derangements

-Stirling Numbers

--Stirling Numbers of The First Kind

--Stirling Numbers of The Second Kind

--Magical Sequences--Stirling Numbers

-Summary of Generating Function

--Summary of Generating Function

-Homework of Week 5

--Magical Sequences--Homework of Week 5

Inclusion-Exclusion Principle And Pigeonhole Principle

-Inclusion And Exclusion Principle

--inclusion and exclusion principle

--The Proof Of Inclusion And Exclusion Theorem

--Inclusion-Exclusion Principle And Pigeonhole Princ

-The Elegancy Of Inclusion-Exclusion Principle

--The Application of Inclusion-Exclusion Principle (1)

--The Application of Inclusion-Exclusion Principle (2)

--The Application of Inclusion-Exclusion Principle (3)

-New solutions to old problems

--The Application Of Inclusion-Exclusion Principle (4)

--The Application Of Inclusion-Exclusion Principle (5)

-Pigeonhole Principle

--pigeonhole principle

--The Application of Pigeonhole Principle (1)

--Inclusion-Exclusion Principle And Pigeonhole Princ

-Visible Pigeonholes

--The Application of Pigeonhole Principle (2)

--Hanxin counts soldiers

--Chinese Remainder Theorem

--Inclusion-Exclusion Principle And Pigeonhole Princ

-6 People And Ramsey

--6 People

--Ramsey Number

--Summary

-Homework Of Week 6

--GT

--Inclusion-Exclusion Principle And Pigeonhole Princ

Introduction to Algorithms Design

-What is Algorithm?

--What is Algorithm?

-Example: Majority Element

--Majority Element

--Q: Majority Element

-Algorihtm Complexity

--Algorihtm Complexity

--Q:Algorithm Complexity

-Asymptotic Analysis

--Asymptotic Analysis

--Q:Asymptotic Analysis

-Homework of Week 7

--Homework of Week 7

Incremental Algorithms

-Elements of Incremental Algorithms

--Elements of Incremental Algorithms

-Loop Invariant

--Loop Invariant

--Q:Loop Invariant

-Example: Insertion Sort

--Insertion Sort

--Q:Insertion Sort

-Example: 2-Color Dutch National Flag Problem

--2-Color Dutch National Flag Problem

--Q:2-Color Dutch National Flag Problem

-Homework of Week 8

--Homework of Week 8

Divide and Conquer

-Design Paradigm

--Design Paradigm

-Example: Merge Sort

--Merge Sort

--Q: Merge Sort

-Example: Order Statistics: Select: Partition

--Order Statistics: Select: Partition

--Q: Select: Partition

-Example: Order Statistics: Select: Linear Time

--Order Statistics: Select: Linear Time

--Q:Select: Linear Time

-Substitution Method

--Substitution Method

--Q:Substitution Method

-Recursion Tree Method

--Recursion Tree Method

--Q:Recursion Tree Method

-The Master Method

--The Master Method

--Q: The Master Method

-Homework of Week 9

--Homework of Week 9

Randomized Algorithms

-Indicator Random Variable

--Indicator Random Variable

--Q: Indicator Random Variable

-Hiring Problem

--Hiring Problem

--Q:Hiring Problem

-On-line Hiring Problem

--On-line Hiring Problem

-Randomized Algorihtm

--Randomized Algorihtm

--Q:Randomized Algorihtm

-Example: Randomized Select

--Randomized Select

-Example: Randomized Select Analysis

--Randomized Select Analysis

--Q:Randomized Select

-Homework of Week 10

--Homework of Week 10

Dynamic Programming

-Maximum Subarray: D&C solution

--Maximum Subarray: D&C solution

--Q:Maximum Subarray

-Maximum Subarray: Dynamic Programming Solution

--Maximum Subarray: Dynamic Programming Solution

--Q:Maximum Subarray DP solution

-Optimization Problems: Knapsack and Matrix Chain Multiplication

--Optimization Problems

--Q: Optimization Problems

-Steps of Dynamic Programming (1&2 Recursively Define Optimal Solutions)

--Steps 1&2 of Dynamic Programming

--Q:Steps of Dynamic Programming (1&2)

-Steps of Dynamic Programming (3&4 Compute Optimal Solutions)

--Steps 3&4 of Dynamic Programming

--Q:Steps of Dynamic Programming (3&4)

-Summary

--Summary

-Homework of Week 11

--Homework of Week 11

Combinatorics and Algorithms Design开设学校：清华大学

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