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Problem Solving Patterns
Programming Principles and Problem Solving Patterns
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Goal Directed Planning
Metatext on Goal Directed Planing

Goal directed planning is a "procedurally flavored" form of the problem solving strategy of problem decomposition.  

Problem-- Perimeter of the Figure

The squares in the following figure are congruent. Their collective area is187.32units. What is the perimeter of the figure?  

    

Definition of goal directed planning

Goal directed planning is the problem solving strategy of

  1. identifying a goal (initially the "ultimate" goal)
  2. determining what information is required to achieve that goal
  3. establishing as subgoals the problems of securing the information required to achieve the ultimate goal
  4. "recursively" applying this same approach to the various subgoals which are nontrivial.
Note-- an informal solution the Necklace Problem

How might one proceed to solve the Perimeter Problem? Perhaps by working backwards from the goal to established facts!That is, by proceding along a "solution path" which is created by means of a goal directed planning.
  • To determine the figure's perimeter, we need to know the length of each external line segment as well as the number of external line segments.
  • To determine the number of external line segments, we will count.
  • We can determine the length of each external line segment, if we know the area of each small square.
  • We can determine the area of each small square from the total area of the figure and the number of small squares.
  • To determine the area of the figure, we recall the problem statement.
  • To determine the number of small squares, we count.
Note-- a programming approach for the problem

We can construct a program to solve the problem by simply recording an observation or expressing a computation for each of the "subproblems" identified in the goal directed planning session. In doing so, we will work, roughly speaking, from the facts towards the goal. That is, we will
  1. Record the number of small squares.
  2. Record the total area of the figure.
  3. Compute the area of one small square.
  4. Compute the area of one small square.
  5. Record the number of external line segments.
  6. Compute the figure's perimenter.
Java program PerimeterOfFigureApp
Program which features problem decomposition.


// REQUIRED PACKAGES
   import blue.io.*;

// APPLICATION CLASS
   class PerimeterOfFigureApp
   {
      static public void main (String args[])
      {
      // Solve the problem
         int nrSmallSquares = 15;
         double totalArea = 187.32;
         double smallSquareArea = ( totalArea / nrSmallSquares );
         double smallSquareSide = Math.sqrt(smallSquareArea);
         int nrExternalSegments = 20;
         double perimeter = ( smallSquareSide * nrExternalSegments );

      // Print the result
         IO.print("The perimeter of the figure is ");
         IO.print(perimeter);
         IO.println(" units.");
      }
   }
 

Java specification of some java.lang.Math functionality
The Math   class of the java.lang package provides lots of functionality for performing numeric processing, only a very small fraction of which is presented at this time.

  1. Math.PI
    This expression denotes the classic Greek constant defined as the ratio of the circumference of a circle to its diameter.  

  2. Math.sqrt(<double> )--><double>
    Return the square root of the given number.

  3. Math.pow(<double> ,<double> )--><double>
    Return the first number raised to the power of the second number.
Example numeric processing

In the program previous program we employed

   Math.sqrt(smallSquareArea)

to compute the square root of the small square area. We might write

   Math.PI * Math.pow(15,2)

to compute the area of a circle of radius15.  

Note-- named constants

It is useful to name constants in certain situations. The naming of domain specific values and various classic values tends to enhance program integrity, to promote readability, and to facilitate maintenance tasks.  

Java specification of named constants
A constant can be viewed as a static variable of some type which cannot be rebound once it is introduced.

The following sort of statement can be placed just prior to the definition of the first method in a class.

  • staticfinal<Type> Identifier=<Expression>
    The variable introduced is bound to the value of the expression in such a way that it cannot be rebound to another value.
 

Java program AreaOfCircleApp
Imagine that you know nothing about the java.lang.Math class. The following program illustrates how you might name your own constant called PI . The program simply reads a real number corresponding to the diameter of a circle and displays the area of the circle.


// REQUIRED PACKAGES
   import blue.io.*;

// APPLICATION CLASS
   class AreaOfCircleApp
   {
      static final double PI = 3.14;

      static public void main (String args[])
      {
      // Read the diameter
         IO.print("Please enter the diameter:  ");
         double diameter = IO.read_double();
 
      // Compute and print the area
         double radius = diameter / 2.0;
         double area = PI * ( radius * radius );
         IO.print("The area is:  ");
         IO.print(area);
         IO.println(" square units.");
      }
   }
 

Note-- typing convention for constants

Constants are conventionally written in all capital letters.