problem solving

Question 1

well-defined problems

Answer 1

problems that are clear to understand and the solution has defined expectations.

Question 2

ill-defined problems

Answer 2

messy problems which are not clear how to solve.

Question 3

Stages of problem solving

Answer 3

1. Understand the problem
2. Devise a plan
3. carry out the plan
4. Review your work

Question 4

1. understand the problem

Answer 4

• do you have all the data?
• is the problem unsolvable?
• do you have to solve the whole problem?
• is it possible to divide the problem?

Question 5

2. Devise a plan

Answer 5

• are the patterns?
• can maths help?
• are the any similar problems that have already been solved?

Question 6

3. Carry out the plan

Answer 6

solve the problem continuously checking youre doing it right

Question 7

4. Review your work

Answer 7

• can the solution be improved?
• is any of the solution reusable?
• is it effectively solved?

Question 8

Why do algorithms help

Answer 8

• helps understand the problem
• executed more quickly
• possible to resort to trial and error

Question 9

problem recognition

Answer 9

The ability to recognize and acknowledge that an issue exists or that a situation needs attention in an existing process or program. The ability to define a problem and know exactly what it is.

Question 10

Computable

Answer 10

a problem is computable is we can come up with an algorithm that will solve every instance of the problem in a finite number of steps

Question 11

intractable problem

Answer 11

a problem which cannot be completely solved.

Question 12

problem decomposition

Answer 12

the process of taking a big problem and breaking it down into smaller problems until you fully explored the problems. Each of these smaller problems translate into one task which is more easily programmable as an individual module, function or procedure.

Question 13

Top-down Problem solving

Answer 13

an approach to solve a problem that involves breaking down the main problem into sub-problems.

Question 14

divide and conquer

Answer 14

a technique based around reducing the size of a problem with successive iterations. You look at a problem, apply some rules and discard any data that does not match then repeat the process with any information which is left. E.g. binary search.

Question 15

divide and conquer advantages

Answer 15

• efficient

- short runtime

Question 16

examples of solving problems using mathematical techniques

Answer 16

• estimating time

- estimating cost

Question 17

examples of messy problems that need humans to solve/help solve

Answer 17

• predicting the results of a race/ game
• planning shop layouts
• designing a new car

Question 18

5 methods of problem solving

Answer 18

1. enumeration
2. simulation
3. theoretical approach
4. trial and error
5. creative solution

Question 19

enumeration (method of problem solving)

Answer 19

Designing an algorithm that performs an exhaustive search

Question 20

enumeration example

Answer 20

find the solution to an anagram by testing every permutation of letters

Question 21

simulation (method of problem solving)

Answer 21

The process of designing a model of a real system in order to understand the behavior of the system, and to evaluate various strategies for its operation

Question 22

simulation examples

Answer 22

• Financial risk analysis
• Amusement park rides
• Population predications
• Managing inventory systems
• Queueing problems

Question 23

Theoretical approach (method of problem solving)

Answer 23

the problem be broken down into pure theory and be represented by mathematics

Question 24

Trial and error (method of problem solving)

Answer 24

If you don’t know how to solve a problem using trial and error may help the process/ completely solve the problem depending on its complexity.

Question 25

creative solution (method of problem solving)

Answer 25

Finding a solution to a problem which doesn’t follow the expected algorithms and rules but still provides an alternative solution

Question 26

abstraction

Answer 26

A way of managing complexity hiding some of the detail which is not neccessary and only representing what is important when solving the problem