Problem Solving

What is a Problem?

• An ambiguous situation not clearly showing how to reach the goal.

Given Initial

Situation

DesiredGoal

SituationWhat can I do to move from A to B?

What is Problem Solving?

• Moving from an initial situation, a given, to a desired target situation, a goal, using a set of resources and imposing specific constraints.

• Given: An initial situation.• Goal: A desired outcome.• Resources: things that can be used to reach a

goal.• Constraints: Specific conditions.

Understanding the problem

• The first stage of problem solving is to understand the problem.

• Understanding a problem means turning an ill defined problem into a well defined problem, without any ambiguity.

• To solve the problem you must have knowledge of the problem domain.

Components of a well defined problem

1. A clearly defined initial situation, given.2. A clearly defined goal.3. Set of resources and constraints.4. Ownership.

Constraints

• Rules, regulations and guidelines about what you are allowed to do in solving a particular problem.

• Constraints are what you can do or can not do. • Some other kind of constraints are available

time, available equipment and software.

Ownership

• You must be committed to use your knowledge, skill and energies to solve the problem.

Reason for a problem remaining unsolved.

• Ownership is not made clear. • In team working problem tasks are delegated

to individual members of a team. Sometime it is not made clear who is doing what, so problem does not get solved.

Example

• You are at a river that you want to cross with all your goods.• Your goods are a chicken, a bag of grain and your dog, Rover.• You have to cross the river in your rowing boat and can bring

only one passenger with you at a time, the chicken , the bag of grain or the dog.

• You can not leave the chicken alone with bag of grain as chicken will eat grain.

• You can not leave the chicken alone with the dog as Rover will eat the chicken.

• However you know that Rover does not eat the grain.• How do you get everything across the river intact?

Problem

• Initial situation: you , chicken, bag of grain, dog on one bank of river with rowing boat.

• Resources: Rowing boat and your knowledge and skill.

• Constraints: bring only one passenger at a time, cant leave chicken alone with bag of grain or dog.

• Goal: you with your goods on opposite river bank.• Ownership: you will be involved in planning the

solution and carrying it out.

Solution

• Take the chicken leave it on other side of river.• Take Rover and leave him on other side and

take the chicken back with you,• Leave the chicken where you started. Take the

bag of grain on other side, leave it with Rover.• Go back and fetch the chicken. And take it

with you on other side.

Challenging your Assumptions

• It is an important fact of problem solving that how you have assumed your problem. Your assumptions are either true or not.

• Sometime people assume constraint that are not true.

• You can challenge your assumptions by lateral thinking.

Defining Boundaries

• Establishing the limits or rules about what can and can not be done when solving a problem.

• A boundary is a form of constraints.• It is vital that you understand the constraint

clearly what are constraints and what you can do or can not do.

Lateral Thinking

• It is used to challenge assumptions, establish facts and rules and define the boundaries of problem solving.

Pattern of lateral thinking

Be consiously aware that we need to add facts to those we start with.• Ask question. Who sets the puzzles. Answer must be

yes or no.• Identify the assumptions. Separate the facts we

established from that we have not established but assumed unconsiously.

• Make new proposed facts from putting together other facts.

I

Planning a solution.

• A strategy can be thought of as a plan or a possible approach to solve a problem.

Plan of action

• You must determine plan of action• What strategies will you apply?• What resources will you use?• How will you use the resources?• In what order will you use the resources?• Are your resources adequate for the task?

Top down strategy

• Breaking big problem into smaller problems, that are easier to work on.

• Each of the smaller problems can be worked on independently.

• It is also called dived and conquer or functional decomposition.

Module

• A self contained entity that results when a problem is divided into sub-problems.

• Each module corresponds to a sub problem.

Stepwise refinement

• The process of breaking a problem down through successive steps into smaller problems.

• Structure table: An intended, numbered list of steps produced by stepwise refinement.,