Problem Solving Basics

Problem Solving

• Problem solving consists of using generic or ad hoc methods, in an orderly manner, for finding solutions to problems.

Characteristics of Difficult Problems

• Intransparency (lack of clarity of the situation)

• Polytely (multiple goals)

• Complexity (large numbers of items, interrelations and decisions)

• Connectivity (hierarchy relation, communication relation, allocation relation)

• Heterogeneity

• Dynamics (time considerations)

Problem Solving Strategies

• Abstraction: solving the problem in a model of the system before applying it to the real system

• Analogy: using a solution that solves an analogous problem

• Brainstorming: suggesting a large number of solutions or ideas and combining and developing them until an optimum solution is found

• Divide and conquer: breaking down a large, complex problem into smaller, solvable problems

Problem Solving Strategies

• Hypothesis testing: assuming a possible explanation to the problem and trying to prove (or, in some contexts, disprove) the assumption

• Means-ends analysis: choosing an action at each step to move closer to the goal.

• Proof: try to prove that the problem cannot be solved. The point where the proof fails will be the starting point for solving it

Problem Solving Strategies

• Reduction: transforming the problem into another problem for which solutions exist

• Research: employing existing ideas or adapting existing solutions to similar problems

• Root cause analysis: identifying the cause of a problem

• Trial-and-error: testing possible solutions until the right one is found

Common barriers to problem solving

• Confirmation biased

- Confirmation bias is a tendency for people to favor information that confirms their preconceptions or hypotheses regardless of whether the information is true.

• Mental set

- mental set describes one's inclination to attempt to solve problems in such a way that has proved successful in previous experiences.

Common barriers to problem solving

• Unnecessary constraints-This occurs when the subject, trying to solve the problem subconsciously, places boundaries on the task at hand, which in turn forces him or her to strain to be more innovative in their thinking.• Irrelevant information- Irrelevant information is information presented within a problem that is unrelated or unimportant to the specific problem. Within the specific context of the problem, irrelevant information would serve no purpose in helping solve that particular problem.

Problem Solving in Computer Programming

• Different methods –

i) Flowchart

ii) Psedocode

iii) Algorithm

Flowchart

• Flowcharting is a graphical way of depicting a problem in terms of its inputs, outputs, and processes.

Example: finding the volume of a 3D object

Pseducode

• Pseudocode involves writing down all of the major steps you will use in the program as depicted in your flowchart.

• For the previous example in flowchart, the pseducode would be –

Another Example

• Pseducode-

Algorithm

• In computer science, an algorithm is a step-by-step procedure for calculations.

• Algorithms are used for calculation, data processing, and automated reasoning.

• Representations of algorithms can be classed into three accepted levels:

1. High-level description

2. Implementation description

3. Formal description

Ex.- Find the largest number in a list of numbers of random order.

• High-level description:

• If there are no numbers in the set then there is no highest number.

• Assume the first number in the set is the largest number in the set.

• For each remaining number in the set: if this number is larger than the current largest number, consider this number to be the largest number in the set.

• When there are no numbers left in the set to iterate over, consider the current largest number to be the largest number of the set.

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