Post-9

• Review all of Module 10.

• Complete all in-class exercises in Module 10 from exercise 12 onwards to 42. Don't forget to upload these in BB.

• Self-check problems from Chapter 4 of the textbook: 1(a), 1(d), 1(h), 2, 12, 16, 24. These are on pages 289-295.

• Consider the array

     int[] A = {1, 2, 7, 9, 18, 29, 32, 41};
  

  The sequence of numbers in this array is always increasing. Similarly, the array

     int[] B = {38, 24, 18, 12, 8, 3};
  

  is a decreasing sequence of integers. We will call such arrays monotonic arrays. This property does not hold for the array

     int[] C = {1, 2, 7, 3, 18, 14, 32, 41};
  

  Here, after initially increasing numbers 1, 2, 7, the fourth one, 3, is less than 7. This array is neither always increasing nor always decreasing, and is therefore not monotonic. Write a program called CheckMonotonic.java that takes an array and prints either "Monotonic" nor "Not monotonic", depending on whether the array is monotonic. Test your program with the above three arrays.

• Consider points in the plane addressed by the usual (x,y) coordinates. When both x and y are integers, we'll call the point an integer point. Next, consider the point (3,1). Suppose we start a "walk" at this point and go East (rightwards) by one integer step. We would end up at the point (4,1). Then, from there, suppose we go North. We would end up at the point (4,2).

  We will use the numbers 1,2,3,4 to represent the four directions North, East, South, West. Then, the walk that that goes East, North, East, East, South, West is represented by the numbers 2,1,2,2,3,4.

  Here are the numbers in an array with the starting point (3,1):

    double x=3, y=1;
    double[] A = {2, 1, 2, 2, 3, 4};
  

  Clearly, after starting at (3,1) and following these "directions", we end up at (5,1).

  One can use DrawTool to depict this "integer walk":

  

  Write a program called IntegerWalk that takes a starting point and an array of "directions" like above and draws the walk. Test your program with the above data, and then get it working for this starting point and array:

    double x=1, y=9;
    double[] A  = {3,2,3,3,2,1,2,3,3,3,2,2,1,2,1,2,3,3,3,4,3};
  

  Note: although our points are actually integer values, we will use double variables (and arrays) for consistency with DrawTool.

• What is the longest possible integer walk that: (1) all the coordinates are within the bounds 1,...,9; (2) does not intersect itself? Write a program called LongestWalk.java that draws your longest walk using DrawTool. Of course, what you need to do is produce the starting point and "directions" array (as in the examples above) that create this walk.

• In an integer walk, we'll use the term segment to mean the line between two adjacent points on the walk. Thus, in the example above, there are six segments, the first being the one from (3,1) to (4,1). Now, given two different walks, we want to determine which line segments they have in common. Consider these two walks:

    double x1=3, y1=1;
    double[] A = {2, 1, 2, 2, 3, 4};
  
    double x2=5, y2=3;
    double[] B = {3, 2, 3, 2};
  

  When drawn in red and blue, we see that there are two segments in common:

  

  Write a program called CommonSegments to print out the common segments when given two integer walks (two starting points, and two direction arrays, as above). Your program should print out the common segments. For example, for the above two walks, the output should be

  2 segments:
   (5.0,2.0)-(6.0,2.0)
   (6.0,2.0)-(6.0,1.0)
  

  Test your program on both the small example above and the longer walks

    double x1=1, y1=9;
    double[] A  = {3,2,3,3,2,1,2,3,3,3,2,2,1,2,1,2,3,3,3,4,3};
  
    double x2=2, y2=2;
    double[] B  = {1,2,1,2,3,2,1,2,2,2,2,1,1,4,4,4,1,1,2};
  

• Don't forget your reflection exercise!

Recommended, but not required:
This week, to reflect the upcoming break, we'll explore computers and movies.

• Which famous movie made in the 1960's made the computer a villain? What was the iconic name of the computer?
• See this article on computers in movies.
• You've heard the term pixel. What is a pixel? See this video from Discovery that explains.
• Then, read this article to learn how computer animation works.