Problem Solving & Program Design

Tom Kelliher, CS 102

Feb. 19, 1999

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Outline

1. Problem Solving.

2. Program Design: structural elements.

3. Examples.

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Structural elements of JavaScript, I/O.

Problem Solving

The process of transforming the description of a problem into the solution of that problem by using our knowledge of the problem domain and by relying on our ability to select and use appropriate problem-solving strategies, techniques, and tools.

A few problem examples:

1. Calculating a tip.
2. Double checking a grocery receipt.
3. A web browser.

Problem Analysis

Details to be determined:

• Inputs/Outputs, their form, their media.
• Special constraints or conditions. (Realtime processing.)
• Computational formulas, equations.

Algorithm Design and Representation

Algorithm:

A sequence of a finite number of steps arranged in a specific logical order which, when executed, produces the solution for a problem.

An algorithm must satisfy the following requirements:

1. Input --- usually required.
2. Output.
3. Unambiguousness --- computers don't accept ambiguity.
4. Generality --- solves a class of problems.
5. Correctness --- correctly solve the given problem.
6. Finiteness --- termination.
7. Efficiency --- recognition of finite computing resources: CPU cycles, memory.

Pseudocode:

A semiformal, English-like language with a limited vocabulary that can be used to design and describe algorithms.

• Meta-programming language.
• Algorithm representation.

Pseudocode Structural Elements

C. Bohm and G. Jacopini proved in 1966 than pseudocode required only three structural elements

The Sequence Control Structure

A series of steps or statements that are executed in the order they are written in an algorithm.

Example:

name = prompt("What is your name?", "");
document.write("Hello " + name + "!<br><br>");
age = prompt(name + ", how old are you?", "");
birthYear = currentYear - age - 1;

Statements terminate with a ;.

{/} pair grouping for constructing a compound statement:

{
   amountDue = overDue + currentBilling + penalty;
   document.write("You owe: " + amountDue);
}

The Selection Control Structure

The alternatives of two courses of action only one of which is taken depending on the outcome of a condition, which is either true or false.

if (condition)
   then_statement;
else
   else_statement;

Structure of then_part, else_part:

• A single statement.
• A set of statements enclosed by {/}.

if (payment is overdue)
{
   amountDue = pastDue + currentBilling + penalty;
   document.write("You owe: " + amountDue);
}
else
   document.write("You owe: " + currentBilling);

Alternative nested if-else structure element: else_if

if (grade < 60)
   document.write("F");
else if (grade < 70)
   document.write("D");
else if (grade < 80)
   document.write("C");
else if (grade < 90)
   document.write("B");
else
   document.write("A");

The Repetition Control Structure

Specifies a block of one or more statements that are repeatedly executed until a condition is satisfied.

while (condition)
   loop_statement;

sum = 0;
while (there are input numbers to sum)
{
   number = prompt("Next number: ", "");
   sum = sum + number;
}
document.write("The sum is: " + sum);

Example Problems

1. Design an algorithm that keeps reading numbers until the user enters a zero value, and outputs the sum of the numbers.
2. Design an algorithm that keeps reading positive numbers until the user enters a zero value, and determines and outputs the largest number.
3. Design an algorithm that reads an arbitrary number of numbers and outputs their arithmetic average.