CSC300: Homework (MySecondHomework)

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Read chapter 2 of Core Java for the Impatient.
Skim section 1.3 of Algorithms

Read the subsection on Linked Lists, starting around page 142.
Do the homework assigned on d2l.

One of the problems is to convert mickey mouse:

to mickey moose:

This is an example of a Fractal also known as a Recursive drawing

file:MySecondHomework.java [source] [doc-public] [doc-private]

package algs11;

import java.util.Arrays;
import stdlib.*;

/**
 * This is a skeleton file for your homework. Edit the sections marked TODO. You
 * may add new functions. You may also edit the function "main" to test your
 * code.
 *
 * You must not add static variables. You MAY add static functions, just not
 * static variables.
 *
 * It is okay to add functions, such as
 *
 * <pre>
 *     public static double sumHelper (double[] list, int i, double sumSoFar) {
 * </pre>
 *
 * but it is NOT okay to add static variables, such as
 *
 * <pre>
 * public static int x;
 * </pre>
 *
 * As for homework 1, you must not change the declaration of any method.
 * 
 * You can edit the main function all you want. I will not run your main
 * function when grading.
 */
public class MySecondHomework {

  /**
   * As a model, here is a minValue function, both iteratively and recursively
   */
  /** iterative version */
  public static double minValueI (double[] list) {
    double result = list[0];
    int i = 1;
    while (i < list.length) {
      if (list[i] < result) result = list[i];
      i = i + 1;
    }
    return result;
  }

  /** recursive version */
  public static double minValue (double[] list) {
    return minValueHelper (list, 1, list[0]);
  }
  private static double minValueHelper (double[] list, int i, double result) {
    if (i < list.length) {
      if (list[i] < result) result = list[i];
      result = minValueHelper (list, i + 1, result);
    }
    return result;
  }

  /**
   * PROBLEM 1: Translate the following sum function from iterative to
   * recursive.
   *
   * You should write a helper method. You may not use any "fields" to solve
   * this problem (a field is a variable that is declared "outside" of the
   * function declaration --- either before or after).
   */
  public static double sumI (double[] a) {
    double result = 0.0;
    int i = 0;
    while (i < a.length) {
      result = result + a[i];
      i = i + 1;
    }
    return result;
  }
  public static double sum (double[] a) {
    // TODO
    return StdRandom.uniform ();
  }

  /**
   * PROBLEM 2: Do the same translation for this in-place reverse function
   *
   * You should write a helper method. You may not use any "fields" to solve
   * this problem (a field is a variable that is declared "outside" of the
   * function declaration --- either before or after).
   */
  public static void reverseI (double[] a) {
    int hi = a.length - 1;
    int lo = 0;
    while (lo < hi) {
      double loVal = a[lo];
      double hiVal = a[hi];
      a[hi] = loVal;
      a[lo] = hiVal;
      lo = lo + 1;
      hi = hi - 1;
    }
  }
  public static void reverse (double[] a) {
    // TODO
  }

  /**
   * PROBLEM 3: The following function draws mickey mouse, if you call it like
   * this from main:
   *
   * <pre>
   * draw (.5, .5, .25);
   * </pre>
   *
   * Change the code to draw mickey moose instead. Your solution should be
   * recursive.
   * 
   * Before picture:
   * http://fpl.cs.depaul.edu/jriely/ds1/images/MickeyMouse.png After picture:
   * http://fpl.cs.depaul.edu/jriely/ds1/images/MickeyMoose.png
   *
   * You may not use any "fields" to solve this problem (a field is a variable
   * that is declared "outside" of the function declaration --- either before
   * or after).
   */
  public static void draw (double centerX, double centerY, double radius) {
    // TODO 
    if (radius < .0005) return;

    StdDraw.setPenColor (StdDraw.LIGHT_GRAY);
    StdDraw.filledCircle (centerX, centerY, radius);
    StdDraw.setPenColor (StdDraw.BLACK);
    StdDraw.circle (centerX, centerY, radius);

    double change = radius * 0.90;

    StdDraw.setPenColor (StdDraw.LIGHT_GRAY);
    StdDraw.filledCircle (centerX + change, centerY + change, radius / 2);
    StdDraw.setPenColor (StdDraw.BLACK);
    StdDraw.circle (centerX + change, centerY + change, radius / 2);

    StdDraw.setPenColor (StdDraw.LIGHT_GRAY);
    StdDraw.filledCircle (centerX - change, centerY + change, radius / 2);
    StdDraw.setPenColor (StdDraw.BLACK);
    StdDraw.circle (centerX - change, centerY + change, radius / 2);
  }

  /**
   * PROBLEM 4: Run runTerribleLoop for one hour. You can stop the program
   * using the red "stop" square in eclipse. Fill in the OUTPUT line below
   * with the numbers you saw LAST --- edit the line, replacing the two ...
   * with what you saw:
   *
   * OUTPUT: terribleFibonacci(...)=... // TODO
   *
   * Comment: the code uses "long" variables, which are like "int", but
   * bigger. It's because fibonacci numbers get really big really fast.
   */
  public static void runTerribleLoop () {
    for (int N = 0; N < 100; N++)
      StdOut.format ("terribleFibonacci(%2d)=%d\n", N, terribleFibonacci (N));
  }
  public static long terribleFibonacci (int n) {
    if (n <= 1) return n;
    return terribleFibonacci (n - 1) + terribleFibonacci (n - 2);
  }

  /**
   * PROBLEM 5: The implementation of terribleFibonacci is TERRIBLE! Write a
   * more efficient version of fibonacci. Do not change runFibonacciLoop or
   * runFibonacciSomeValues.
   *
   * To make fibonacci run faster, you want it so that each call to
   * fibonacci(n) computes the fibonacci numbers between 0 and n once, not
   * over and over again.
   *
   * Comment: You will want to use a local variable of type "long" rather than
   * type "int", for the reasons discussed above.
   *
   * Comment: At some point, your fibonacci numbers might become negative.
   * This is normal and expected.
   * http://en.wikipedia.org/wiki/Integer_overflow We discuss this at length
   * in our systems classes.
   *
   * You may not use any "fields" to solve this problem (a field is a variable
   * that is declared "outside" of the function declaration --- either before
   * or after).
   * 
   * You may use a loop on this problem.
   * You do not need to use recursion.
   */
  public static void runFibonacciLoop () {
    for (int N = 0; N < 100; N++)
      StdOut.format ("fibonacci(%2d)=%d\n", N, fibonacci (N));
  }
  public static long fibonacci (int n) {
    return 0; // TODO
  }

  /**
   * A test program, using private helper functions.  See below.
   * To make typing tests a little easier, I've written a function to convert strings to arrays.  See below.
   * You can modify this -- it is not graded.
   */
  public static void main (String[] args) {
    testSum ("11 21 81 -41 51 61");
    testSum ("11 21 81 -41 51");
    testSum ("11 21 81 -41");
    testSum ("11 21 81");
    testSum ("11 21");
    testSum ("11");
    testSum ("");

    testReverse ("11 21 81 -41 51 61");
    testReverse ("11 21 81 -41 51");
    testReverse ("11 21 81 -41");
    testReverse ("11 21 81");
    testReverse ("11 21");
    testReverse ("11");
    testReverse ("");

    testFibonacci (0, 0);
    testFibonacci (1, 1);
    testFibonacci (1, 2);
    testFibonacci (2, 3);
    testFibonacci (21, 8);
    testFibonacci (233, 13);
    testFibonacci (75025, 25);
    testFibonacci (             1_836_311_903L, 46);
    testFibonacci (             2_971_215_073L, 47);
    testFibonacci (       308_061_521_170_129L, 71); 
    testFibonacci (       498_454_011_879_264L, 72);
    testFibonacci ( 7_540_113_804_746_346_429L, 92);
    testFibonacci (-6_246_583_658_587_674_878L, 93);
    testFibonacci (  -813_251_414_217_914_645L, 376);
    StdOut.println ("Finished tests");

    draw (.5, .5, .25);

    // TODO: uncomment these temporarily when you want to see the output of your Fibonacci functions
    //runTerribleLoop (); 
    //runFibonacciLoop();   
  }
  
  /*
   * A main function for debugging -- change the name to "main" to run it (and
   * rename the existing main method to something else). Change the test as
   * appropriate.
   */
  public static void main1 (String[] args) {
    Trace.drawStepsOfMethod ("minValueI");
    Trace.drawStepsOfMethod ("minValue");
    Trace.drawStepsOfMethod ("minValueHelper");
    Trace.run ();
    testMinValue ("11 21 9 31 41");
  }

  /* Test functions --- lot's of similar code! */
  private static void testSum (String list) {
    double[] aList = doublesFromString (list);
    double expected = sumI (aList);
    double actual = sum (aList);
    if (! Arrays.equals (aList, doublesFromString (list))) {
      StdOut.format ("Failed sum([%s]): Array modified\n", list);
    }
    if (expected != actual) {
      StdOut.format ("Failed sum([%s]): Expecting (%.1f) Actual (%.1f)\n", list, expected, actual);
    }
  }
  private static void testMinValue (String list) {
    double[] aList = doublesFromString (list);
    double expected = minValueI (aList);
    double actual = minValue (aList);
    if (! Arrays.equals (aList, doublesFromString (list))) {
      StdOut.format ("Failed minValue([%s]): Array modified\n", list);
    }
    if (expected != actual) {
      StdOut.format ("Failed minValue([%s]): Expecting (%.1f) Actual (%.1f)\n", list, expected, actual);
    }
  }
  private static void testReverse (String list) {
    double[] expected = doublesFromString (list);
    reverseI (expected);
    double[] actual = doublesFromString (list);
    reverse (actual);
    // != does not do what we want on arrays
    if (! Arrays.equals (expected, actual)) {
      StdOut.format ("Failed reverse([%s]): Expecting (%s) Actual (%s)\n", list, Arrays.toString (expected), Arrays.toString (actual));
    }
  }
  private static void testFibonacci (long expected, int n) {
    long actual = fibonacci (n);
    if (expected != actual) {
      StdOut.format ("Failed fibonacci(%d): Expecting (%d) Actual (%d)\n", n, expected, actual);
    }
  }

  /* A utility function to create an array of doubles from a string. */
  // The string should include a list of numbers, separated by single spaces.
  private static double[] doublesFromString (String s) {
    if ("".equals (s)) return new double [0]; // empty array is a special case
    String[] nums = s.split (" ");
    double[] result = new double[nums.length];
    for (int i = nums.length-1; i >= 0; i--) {
      try { 
        result[i] = Double.parseDouble (nums[i]); 
      } catch (NumberFormatException e) { 
        throw new IllegalArgumentException (String.format ("Bad argument \"%s\": could not parse \"%s\" as a double", s, nums[i]));
      }
    }
    return result;
  }
}

Revised: 2008/03/17 13:01