Algorithms in C and states and graphs, Lecture notes of C programming

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EEE 11

Programming Fundamentals

Lecture 01: Problem Solving

What is a Problem?

◼ A new situation that presents some difficulty that one whishes to address ◼ “Whenever there is a gap between where you are now and where you want to be, and you don’t know how to find a way to cross that gap, you have a problem.”

• J. Hayes, The Computer Problem Solver , 1990

Understand the Problem

◼ Read the problem completely ◼ Try out examples ◼ Ask questions

▪ What would the result look like? ▪ What are the assumptions and constraints? ◼ Use diagrams and notations ◼ Restate the problem ◼ Avoid assumptions

Devise a Plan

◼ Establish subgoals ◼ Try to recognize something familiar

▪ Recognize patterns ▪ Use analogy ▪ Apply existing strategies ◼ Introduce external elements ◼ Take cases (validate the plan)

Look Back

◼ Be critical of your result ◼ Look for flaws in your solutions ◼ No deficiencies

▪ Use good test cases

Common Problem Solving

Techniques

◼ Work backwards ◼ Use existing models ◼ Solve by elimination ◼ Divide and conquer ◼ Recursion

Use Existing Models

◼ Most problems are just variations of existing problems ◼ Examples:

▪ Get the sum of all numbers from 1 to 100 ▪ Get the sum of all even numbers from 2 to 100

Solve by Elimination

◼ Remove invalid options ◼ Example:

▪ What is the largest prime number less than 100?

Recursion

◼ Find patterns that can be repeated

Computers as Problem Solving

Tools

◼ Computers follow instructions exactly

▪ Consistently applies the steps provided to it ▪ Can repeat as many times without getting tired ▪ Can perform tasks with speed and accuracy ◼ Limitations of Computers

▪ Limited input ▪ Processes digital data only ▪ Instructions have to be clear and concise

Algorithms

Pseudocodes and Flowcharts

Algorithms

◼ A problem solving method suitable for implementation as computer program* ◼ Procedures or formulas to solve a problem ◼ Key properties:

▪ Interpretable ▪ Finite set of instructions ▪ Recognizable end-state, end-point or result

*R. Sedgewick, Algorithms in C , 3 rd^. Ed., Addison-Wesley Publishing Company, Inc., 1998

Algorithms as Pseudocode

◼ Text-based representation of algorithms ◼ Notations from popular programming languages are used ◼ D0ne for human reading, not for machines ◼ No universal standard

Algorithms as Flowcharts

◼ Graphical representation ◼ Different shapes mean different things ◼ Flow of the algorithm is shown by arrows

Input/Output

Process

Decision

Start/Stop