Problem Solving Methods

Class Objectives Learn to apply the problem solving process Learn techniques for error-free problem solving

Problem Solving Process Define and understand problem Gather information Generate potential methods and solutions. Refine and implement solution. Verify and test solution.

Define and Understand Understand what is being asked Describe input/output (I/O) what are you given knowns what are you trying to find unknowns Sketch the problem

Gather Information Collect necessary data List relevant equations/theories State all assumptions

Generate Solution Methods Apply theories and assumptions. Typically, there is more than one approach to solving a problem Work problem by hand using the potential solution methods Break problem into parts; scale it down; etc. e.g., if the problem was to calculate the average of 1000 numbers, work the problem by hand using, say, 10 numbers, in order to establish a method

Refine and Implement Evaluate solution methods. accuracy ease of implementation etc. Implement “best” solution.

Verify and Test Compare solution to the problem statement Is this what you were looking for? Does your answer make sense? Clearly identify the solution Sketch if appropriate

CHECK YOUR WORK!! Don’t stop at getting an answer!! Think about whether the answer makes physical sense. you are the instructor and you have to turn in final grades. In your haste, you calculate the average of Susie’s grades (100, 70, 90) to be 78 and give Susie a C...

Example State problem clearly: Given numeric student grades, determine grade distribution using regular grading scale. Describe I/O: Input: student numeric grades Output: numbers of A’s, B’s, C’s, etc.

Example (cont.) Gather data Grades: 91, 85, 82, 78, 76, 72, 65, 59, 94, 98 State theories and assumptions grade >= 90 is an A 90 > grade >= 80 is an B 80 > grade >= 70 is an C 70 > grade >= 60 is an D 60 > grade is an F

Example (cont.) Work the problem on a subset of the data: 91, 82, 78, 72, > 90, A’s = 1 82 > 80 and < 90, B’s = 1 78 > 70 and < 80, C’s = 1 72 > 70 and < 80, C’s = 2 59 >50 and < 60, F’s = 1 check your work!!

Example (cont.) Refine solution/implementation for each grade if grade >= 90 increment number of A’s by 1 if 90 > grade >= 80 increment number of B’s by 1 if 80 > grade >= 70 increment number of C’s by 1 if 70 > grade >= 60 increment number of D’s by 1 if grade < 60 increment number of F’s by 1 Output number of A’s, B’s, C’s, D’s, and F’s

Example (cont.) Test method and get the solution Grades: 91, 85, 82, 78, 76, 72, 65, 59, 94, 98 numA = 3, numB = 2, numC = 3, numD = 1, numF = 1 Is this correct?

Getting It Right The problem solving process may be an iterative process. If at first you don’t succeed (i.e., the algorithm test fails), try again… The more thorough you are at each step of the problem solving process, the more likely you are to get it right the first time!!

VCR Problem Statement You own a VCR that has two recording and playback speeds: 1) standard play (SP) and 2) extended play (EP). The speed in the EP mode is 1/3 the speed in the SP mode. At the SP setting, the video tapes you own can be used to record exactly 120 minutes of video. Develop an algorithm that specifies how long to record at SP speed, and how long to record at EP speed, given a program of known length.

Step 1: Understand the Problem You need to know how long to record at the EP speed and at SP speed so that the program fits exactly on a 120-minute tape. The EP mode does not have quality of resolution of the SP mode, so you want to record in the EP mode the minimum amount of time.

Exercise Turn off your computer monitor. As a TEAM, take 15 MINUTES to develop a solution to this problem