UTPA STEM/CBI Courses/Computer Science/Algorithm Design

Course Title: Computer Science

Lecture Topic: Algorithm Desigm

Instructor: Bin Fu

Institution: University of Texas - Pan American

Backwards Design

Course Objectives

• Primary Objectives- By the next class period students will be able to:
  • Understand the basic dynamic programming method
  • Find the recursion for dynamic programming
  • Find the right order to build up the table for dynamic programming
  • Solve a knapsack problem with dynamic programming

• Sub Objectives- The objectives will require that students be able to:
  • Input of data
  • Implementation
  • Performance
  • Complexity analysis

• Difficulties- Students may have difficulty:
  • Identifying the recursion for dynamic programming, and the hardship to build up the table.

• Real-World Contexts- There are many ways that students can use this material in the real-world, such as:
  • A knapsack problem has many interesting applications. It is one of the classical NP-hard problems.

Model of Knowledge

• Concept Map
  • Recursion
  • Dynamic Programming
  • Greedy Method
  • Approximation
  • NP-completeness

• Content Priorities
  • Enduring Understanding
    • Recursion
    • Dynamic Programming
    • Greedy Method
    • Approximation
  • Important to Do and Know
    • Find the size of sub-problems
    • Determine the size of the table of dynamic programming
    • Finding an accurate approximation
  • Worth Being Familiar with
    • Memory allocation
    • Complexity analysis
    • Approximation

Assessment of Learning

• Formative Assessment
  • In Class (groups)
    • Give an example to the students and ask them solve it with dynamic programming method.
  • Homework (individual)
    • Ask them to solve the Knapsack problem with dynamic programming method.
• Summative Assessment
  • Try to solve more problems with dynamic programming method.

Legacy Cycle

OBJECTIVE

By the next class period, students will be able to:

• Be efficient in finding a recursion for solving a computational problem.

The objectives will require that students be able to:

• Effectively shrink a computational problem.

THE CHALLENGE

How to handle the exponential number of cases in a knapsack problem.

GENERATE IDEAS

When the size of a knapsack is not too large, using a table to save the sum of subsets is better than trying all subsets.

MULTIPLE PERSPECTIVES

NP-hardness.

The methods of algorithm design depend on problems.

Each method can be applied to a specific class of problems.

RESEARCH & REVISE

Find new method to attack the problem with large Knapsack.

TEST YOUR METTLE

Implement the method with dynamic programming.

GO PUBLIC

Post software implementation over internet.

Pre-Lesson Quiz

1. What is recursion?
2. What is the limitation of divide and conquer in solving a knapsack problem?
3. What is computational time for brute force method in solving a knapsack problem?

Test Your Mettle Quiz

1. What is the computational complexity of dynamic programming method for solving a knapsack problem?
2. Apply the method to the longest common sequence problem.