Problem Solving CSC 1750 Spring 2009

References Sprankle, Maureen and Jim Hubbard, Problem Solving and Programming Concepts, Eighth Edition, Prentice Hall, Polya, George, How to Solve It, Second Edition, Doubleday Anchor Books, 1957

Types of Problems Algorithmic solutions Problems that can be solved with a series of actions Balancing checkbook, baking a cake Alphabetizing 10,000 names Heuristic solutions Problem solution requiring reasoning based on knowledge and experience, and a process of trial and error Solutions cannot be reached through a direct set of steps How to buy the best stock or expand the company Difficult to evaluate the solution

Types of Problems People are better at solving heuristic problems Artificial intelligence is the field of computer science that deals with heuristic problems Computers are better at solving complicated calculus problems or alphabetizing 10,000 names This class deals with algorithmic solutions

Problem Solving Steps Identify the problem Understand the problem Identify alternative ways to solve the problem Select the best way to solve the problem from the list of alternative solutions List instructions that enable you to solve the problem using selected solution Evaluate the solution

George Pólya's 1945, How to Solve It NameInformal Description Analogy Can you find a problem analogous to your problem and solve that? Generalization Can you find a problem more general than your problem? Induction Can you solve your problem by deriving a generalization from some examples? Variation of the Problem Can you vary or change your problem to create a new problem (or set of problems) whose solution(s) will help you solve your original problem? Auxiliary Problem Can you find a sub-problem or side problem whose solution will help you solve your problem? Here is a problem related to yours and solved before Can you find a problem related to yours that has already been solved and use that to solve your problem?

George Pólya's 1945, How to Solve It NameInformal Description SpecializationCan you find a problem more specialized? Decomposing and Recombining Can you decompose the problem and "recombine its elements in some new manner"? Working backward Can you start with the goal and work backwards to something you already know? Draw a FigureCan you draw a picture of the problem? Auxiliary Elements Can you add some new element to your problem to get closer to a solution?

Problem Solving Techniques Divide and conquer: break down a large, complex problem into smaller, solvable problems. Hill-climbing: attempting at every step to move closer to the goal situation. Means-end analysis: requires the setting of sub-goals based on the process of getting from the initial state to the goal state when solving the problem.

Problem Solving Techniques Trial-and-error: select a possible answer, apply it to the problem and, if it is not successful, select another possibility. Ends when a possibility yields a solution. Brainstorming: a group technique designed to generate a large number of ideas for the solution of a problem.