Dynamic Programming, Greedy Algorithms

Dynamic Programming, Greedy Algorithms

This course is part of Foundations of Data Structures and Algorithms Specialization

Instructor: Sriram Sankaranarayanan

What you'll learn

Describe basic algorithm design techniques
Create divide and conquer, dynamic programming, and greedy algorithms
Understand intractable problems, P vs NP and the use of integer programming solvers to tackle some of these problems

Skills you'll gain

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Assessments

17 assignments

Taught in English

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This course is part of the Foundations of Data Structures and Algorithms Specialization

When you enroll in this course, you'll also be enrolled in this Specialization.

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There are 4 modules in this course

This course covers basic algorithm design techniques such as divide and conquer, dynamic programming, and greedy algorithms. It concludes with a brief introduction to intractability (NP-completeness) and using linear/integer programming solvers for solving optimization problems. We will also cover some advanced topics in data structures.

This course can be taken for academic credit as part of CU Boulder’s MS in Data Science or MS in Computer Science degrees offered on the Coursera platform. These fully accredited graduate degrees offer targeted courses, short 8-week sessions, and pay-as-you-go tuition. Admission is based on performance in three preliminary courses, not academic history. CU degrees on Coursera are ideal for recent graduates or working professionals. Learn more: MS in Data Science: https://roshoesn.top/degrees/master-of-science-data-science-boulder MS in Computer Science: https://coursera.org/degrees/ms-computer-science-boulder

We will formally cover divide and conquer algorithms as a design scheme and look at some divide and conquer algorithms we have encountered in the past. We will learn some divide and conquer algorithms for Integer Multiplication (Karatsuba’s Algorithm), Matrix Multiplication (Strassen’s Algorithm), Fast Fourier Transforms (FFTs), and Finding Closest Pair of Points.

What's included

9 videos13 readings5 assignments1 programming assignment1 discussion prompt

9 videosTotal 231 minutes

What Are Divide and Conquer Algorithms?7 minutesPreview module
Max Subarray Problem Using Divide and Conquer23 minutes
Karatsuba’s Multiplication Algorithm39 minutes
Master Method Revisited28 minutes
FFT Part 1: Introduction and Complex Numbers48 minutes
FFT Part 2: Definition and Interpretation of Discrete Fourier Transforms34 minutes
FFT Part 3: Divide and Conquer Algorithm for FFT22 minutes
Application # 1 : Fast Polynomial Multiplication using FFT 8 minutes
Application # 2: Data Analysis using FFT17 minutes

13 readingsTotal 130 minutes

Earn Academic Credit for Your Work! 10 minutes
Course Support10 minutes
Reading: Important Prerequisites10 minutes
Logistics: Textbook and Readings10 minutes
Important Specialization Information10 minutes
Overview of Module 110 minutes
CLRS Chapter 410 minutes
CLRS Chapter 4.110 minutes
Jupyter Notebook on Karatsuba's Algorithm10 minutes
CLRS Chapters 4.3 - 4.510 minutes
Basics of Complex Numbers10 minutes
Fourier Transforms10 minutes
Fast Fourier Transform10 minutes

5 assignmentsTotal 150 minutes

Max Subarray Problem30 minutes
Karatsuba's Multiplication Algorithm30 minutes
Master Method30 minutes
Complex Numbers and Roots of Unity30 minutes
FFT Algorithm and Applications30 minutes

1 programming assignmentTotal 180 minutes

Problem Set 1180 minutes

1 discussion promptTotal 10 minutes

Introduce Yourself!10 minutes

In this module, you will learn about dynamic programming as a design principle for algorithms. We will provide a step-by-step approach to formulating a problem as a dynamic program and solving these problems using memoization. We will cover dynamic programming for finding longest common subsequences, Knapsack problem and some interesting dynamic programming applications.

What's included

6 videos6 readings5 assignments1 programming assignment

6 videosTotal 131 minutes

Introduction to Dynamic Programming + Rod Cutting Problem30 minutesPreview module
Rod Cutting Problem: Memoization23 minutes
Coin Changing Problem12 minutes
Knapsack Problem29 minutes
When Optimal Substructure Fails10 minutes
Dynamic Programming: Longest Common Subsequence25 minutes

6 readingsTotal 60 minutes

Overview of Module 210 minutes
Rod Cutting Problem10 minutes
Memoization 10 minutes
Coin Changing Problem10 minutes
Jupyter Notebook10 minutes
CLRS Chapter 15.410 minutes

5 assignmentsTotal 150 minutes

Memoization 30 minutes
Coinchanging Problem30 minutes
Knapsack Problem30 minutes
Longest Common Subsequence30 minutes
Rod Cutting Problem and Recurrence30 minutes

1 programming assignmentTotal 180 minutes

Problem Set 2180 minutes

In this module, we will learn about greedy algorithms. We will understand the basic design principles for greedy algorithms and learn about a few algorithms for greedy scheduling and Huffman codes. We will also learn some interesting cases when being greedy provides a guaranteed approximation to the actual solution.

What's included

5 videos4 readings3 assignments1 programming assignment

5 videosTotal 102 minutes

Introduction to Greedy Algorithms20 minutesPreview module
Greedy Interval Scheduling23 minutes
Prefix Codes30 minutes
Huffman Codes11 minutes
Huffman Codes: Proof of Optimality 17 minutes

4 readingsTotal 40 minutes

Overview of Module 310 minutes
CLRS Chapter 1610 minutes
CLRS Chapters 16.1 and 16.210 minutes
CLRS Chapter 16.310 minutes

3 assignmentsTotal 90 minutes

Huffman Codes30 minutes
Greedy Algorithms30 minutes
Greedy Interval Scheduling30 minutes

1 programming assignmentTotal 180 minutes

Problem Set 3180 minutes

P vs NP, Examples such as Travelling Salesperson Problem, Vertex Cover, 3-Coloring and others; Integer Linear Programming and Translating Problems into Integer Programming.

What's included

9 videos5 readings4 assignments1 programming assignment

9 videosTotal 288 minutes

Decision Problems and Languages36 minutesPreview module
Polynomial Time Problems28 minutes
NP Definition29 minutes
NP Completeness and Reductions37 minutes
NP Complete Problems: Examples25 minutes
Computation and Physics30 minutes
Qubits and Operations37 minutes
Bell's Inequality21 minutes
Grover's Search Algorithm42 minutes

5 readingsTotal 50 minutes

Overview of Module 410 minutes
CLRS Chapter 34 10 minutes
CLRS chapter 34.110 minutes
CLRS Chapter 34.2 and 34.310 minutes
CLRS Chapter 34.510 minutes

4 assignmentsTotal 120 minutes

Decision Problems and Languages30 minutes
Polynomial Time and Certificates30 minutes
NP Completeness Problems30 minutes
NP Completeness Reductions30 minutes

1 programming assignmentTotal 180 minutes

Problem Set 4180 minutes

Instructor

Instructor ratings

4.6 (48 ratings)

Sriram Sankaranarayanan

University of Colorado Boulder

5 Courses75,839 learners

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University of Colorado Boulder

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Reviewed on Sep 21, 2021

Excellent. This course covers some difficult topics, but the lectures and homework assignments were superb and made them quite approachable.

Reviewed on Jul 23, 2022

Excellent course! I really learned alot and enjoyed all the challenges and topics in your course. Thank you so much!

Reviewed on Feb 9, 2023

I totally loved all the courses from this instructor. The content was rich, the programming assignments were instructive, and the whole course was so engaging.

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