Output Stream:   The sum is 14  

Definition   A BINDING is an association from a name to an object (value).

Definition   An ENVIRONMENT is a set of bindings.

Problem A necklace is constructed from 20 Blue Beads and 14 Red Beads.   Each blue bead cost $ .22 while each red bead cost $ .33.   The cost of the thread is $ .14 per inch and 24 inches are required.   What is the total cost of the necklace?  

Definition   PROBLEM DECOMPOSITION is the problem solving strategy of decomposing a problem into a set of sub-problems,  solving each of the sub-problems,  and then composing a solution to the original problem from the solutions to the sub-problems.

Informal Solution Description To determine the total material cost (ie.   to solve the problem) we need only use Problem Decomposition and solve the following sub-problems;

• Find or determine the cost of the blue beads.
  
• Find or determine the cost of the red beads.
  
• Find the cost of the thread.
  

Sometimes problem decomposition is applied at many levels in solving a problem.   In this case we can apply it to solving each of the sub-problems.

• We can the find the blue bead cost by
  
  • Determining the # of blue beads
    
  • Determining the cost each blue bead
    
  • Multiplying the # of blue beads times the cost of each blue bead
    
• We can the find the red bead cost by
  
  • Determining the # of red beads
    
  • Determining the cost each red bead
    
  • Multiplying the # of red beads times the cost of each red bead
    
• We can the find the thread cost by
  
  • Determining the price per inch of thread
    
  • Determining the length of thread needed
    
  • Multiplying the price per inch times the length of the thread
    

Note that each of the problems labelled in the sub-points are trivial.  

REMARK We conceived of the solution in a ``top-down'' manner.  

REMARK When coding the solution we will have to type the Java in a ``bottom-up'' manner.  

REMARK Whenever you write programs in this class you must artfully name all values - within reason.  

- > NecklaceApp  

- >  

/ /Determine the cost of the Blue Beads   double costPerBlueBead = 0.22;   int nrBlueBeads = 20;   double blueBeadCost = costPerBlueBead * nrBlueBeads;     / /Determine the cost of the Red Beads   double costPerRedBead = 0.33;   int nrRedBeads = 14;   double redBeadCost = costPerRedBead * nrRedBeads;     / /Determine the cost of the thread   double costPerInchOfThread = 0.14;   double lengthOfThread = 24.0;   double costOfThread = costPerInchOfThread * lengthOfThread;     / /Solve the original problem by making use of the solutions   / /to the main sub-problems   double totalCost = blueBeadCost + redBeadCost + costOfThread;     / /Display the result   IO.print ( ``total cost of materials is:   ``);   IO.print (totalCost);   IO.println ();

 

The Environment - (bindings)
costPerBlueBead - > 0.22
nrBlueBeads - > 20
blueBeadCost - > 4.4
costPerRedBead - > 0.33
nrRedBeads - > 14
redBeadCost - > 4.62
costPerInchOfThread - > 0.14
lengthOfThread - > 24.0
costOfThread - > 3.36
totalCost - > 4.4 + 4.62 + 3.36 = 12.38