15.1. File Input/Output and matrixes

In this chapter we will develop a program that reads and writes files, parses input, and demonstrates the matrix class. We will also implement a data structure called Set that expands automatically as you add elements.

Aside from demonstrating all these features, the real purpose of the program is to generate a two-dimensional table of the distances between cities in the United States. The output is a matrix that looks like this:

Atlanta 0
Chicago 700     0
Boston  1100    1000    0
Dallas  800     900     1750    0
Denver  1450    1000    2000    800     0
Detroit 750     300     800     1150    1300    0
Orlando 400     1150    1300    1100    1900    1200    0
Phoenix 1850    1750    2650    1000    800     2000    2100    0
Seattle 2650    2000    3000    2150    1350    2300    3100    1450    0
        Atlanta Chicago Boston  Dallas  Denver  Detroit Orlando Phoenix Seattle

The diagonal elements are all zero because that is the distance from a city to itself. Also, because the distance from A to B is the same as the distance from B to A, there is no need to print the top half of the matrix.

Q-1: Why aren’t we filling in every value in our table, who are we leaving blank space above the diagonal of 0’s?

• Because we only need the half of the dataset contained by the triangle.
• Incorrect! All of the data above the 0 diagonal is a mirror image of the triangle! So, the triangle contains the whole dataset.
• Because triangles are the most effective shape to use when presenting data to others.
• Incorrect! Triangles do look cool, but they aren't necessarily the most effective shape to use when presenting data.
• Because matrices are triangles.
• Incorrect! This triangle is PART OF an apmatrix.
• Because the triangle contains the entire dataset.
• Correct! The triangle contains all data points with no repeat data. If we included all datapoints, the would just be repeats of the points we already have.

Q-2: Based on how it is used to create the above table, what do you think a matrix is?

• a geometric shape
• Incorrect! A matrix is not a geometric shape, although they ARE rectangles.
• a two-dimensional vector
• Correct!
• a material in which something develops
• Incorrect! This is a definition for matrix, but not in the programming sense.
• a mold used to shape things
• Incorrect! This is a definition for matrix, but not in the programming sense.

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