Computer Science 15-110, Spring 2010
Class Notes:  Math and Random Methods

1. Math Constants
   1. PI
   2. E
2. Math Methods
   1. abs
   2. ceil
   3. exp
   4. floor
   5. log
   6. log10
   7. max
   8. min
   9. pow
   10. random
   11. round
   12. signum
   13. sqrt
   14. trigonometry methods
   15. Online Math API
3. Random Methods
   1. nextInt
   2. nextDouble
   3. nextBoolean
   4. setSeed
   5. Online Random API

Math and Random Methods

1. Math Constants
    
   1. PI

      class MyCode  {
        public static void main(String[] args) {
          System.out.println(Math.PI);
        }
      }

   2. E

      class MyCode  {
        public static void main(String[] args) {
          System.out.println(Math.E);
        }
      }

2. Math Methods
    
   1. abs

      class MyCode  {
        public static void main(String[] args) {
          System.out.println(Math.abs(5));
          System.out.println(Math.abs(-5));
          System.out.println(Math.abs(5.0));
          System.out.println(Math.abs(-5.0));
        }
      }

   2. ceil

      class MyCode  {
        public static void main(String[] args) {
          System.out.println(Math.ceil(2.01));
          System.out.println(Math.ceil(2.00));
          System.out.println(Math.ceil(1.99));
          System.out.println(Math.ceil(-2.01));
          System.out.println(Math.ceil(-2.00));
          System.out.println(Math.ceil(-1.99));
        }
      }

      A common mistake...

      class MyCode  {
        public static void main(String[] args) {
          int i = Math.ceil(3.5); // Error: will not compile!
        }
      }

   3. exp

      class MyCode  {
        public static void main(String[] args) {
          System.out.println(Math.E);
          System.out.println(Math.exp(1));
          System.out.println(Math.exp(0));
          System.out.println(Math.exp(2));
          System.out.println(Math.pow(Math.E, 2));
        }
      }

   4. floor

      class MyCode  {
        public static void main(String[] args) {
          System.out.println(Math.floor(2.01));
          System.out.println(Math.floor(2.00));
          System.out.println(Math.floor(1.99));
          System.out.println(Math.floor(-2.01));
          System.out.println(Math.floor(-2.00));
          System.out.println(Math.floor(-1.99));
        }
      }

   5. log

      class MyCode  {
        public static void main(String[] args) {
          double eSquared = Math.exp(2);
          double eCubed = Math.exp(3);
          System.out.println(Math.log(Math.E));
          System.out.println(Math.log(eSquared));
          System.out.println(Math.log(eCubed));
          System.out.println(Math.log(Math.exp(10)));
          System.out.println(Math.log(1));
          System.out.println(Math.log(0));  // doesn't crash!
          System.out.println(Math.log(-1)); // ditto (yet in a different way)
        }
      }

   6. log10

      class MyCode  {
        public static void main(String[] args) {
          System.out.println(Math.log10(0.001));
          System.out.println(Math.log10(0.1));
          System.out.println(Math.log10(10));
          System.out.println(Math.log10(1000));
        }
      }

   7. max

      class MyCode  {
        public static void main(String[] args) {
          System.out.println(Math.max(1, 2));
          System.out.println(Math.max(-1, -2));
          System.out.println(Math.max(1.0, 2.0));
          System.out.println(Math.max(1.0, 2));
        }
      }

      A common mistake...

      class MyCode  {
        public static void main(String[] args) {
          int i = Math.max(1,2,3); // Error: will not compile!
        }
      }

   8. min

      class MyCode  {
        public static void main(String[] args) {
          System.out.println(Math.min(1, 2));
          System.out.println(Math.min(-1, -2));
          System.out.println(Math.min(1.0, 2.0));
          System.out.println(Math.min(1.0, 2));
        }
      }

   9. pow

      class MyCode  {
        public static void main(String[] args) {
          System.out.println(Math.pow(2,3));
          System.out.println(Math.pow(2,2));
          System.out.println(Math.pow(2,1));
          System.out.println(Math.pow(2,0.5));
          System.out.println(Math.pow(2,0));
          System.out.println(Math.pow(2,-1));
        }
      }

      A common mistake...

      class MyCode  {
        public static void main(String[] args) {
          int i = Math.pow(2,3); // Error: will not compile!
          System.out.println(i);
        }
      }

   10. random

       class MyCode  {
         public static void main(String[] args) {
           System.out.println(Math.random());
           System.out.println(Math.random());
           System.out.println(Math.random());
           System.out.println(Math.random());
           System.out.println(Math.random());
         }
       }

   11. round

       class MyCode  {
         public static void main(String[] args) {
           System.out.println(Math.round(2.51));
           System.out.println(Math.round(2.50));
           System.out.println(Math.round(2.49));
           System.out.println(Math.round(-2.51));
           System.out.println(Math.round(-2.50)); // surprise?
           System.out.println(Math.round(-2.49));
         }
       }

       A common mistake...

       class MyCode  {
         public static void main(String[] args) {
           int i = Math.round(3.5); // Error: will not compile!
         }
       }

   12. signum

       class MyCode  {
         public static void main(String[] args) {
           System.out.println(Math.signum(42));
           System.out.println(Math.signum(0));
           System.out.println(Math.signum(-42));
         }
       }

   13. sqrt

       class MyCode  {
         public static void main(String[] args) {
           System.out.println(Math.sqrt(4));
           System.out.println(Math.sqrt(-4)); // surprise?
         }
       }

   14. trigonometry methods
       Note:  You are not responsible for the trigonometry methods (sin, cos, tan, asin, acos, atan, atan2, toDegrees, and toRadians), except those few methods which we will use (sparingly, and with clear explanations) when we cover graphics.
        
   15. Online Math API
       See:  http://java.sun.com/j2se/1.5.0/docs/api/java/lang/Math.html
        
3. Random Methods
    
   1. nextInt

      import java.util.Random;
      class MyCode  {
        public static void main(String[] args) {
          Random random = new Random();
          System.out.println(random.nextInt());
          System.out.println(random.nextInt());
          System.out.println(random.nextInt());
        }
      }

      Another Example:

      import java.util.Random;
      class MyCode  {
        public static void main(String[] args) {
          Random random = new Random();
          System.out.println("Randoms between about -2b and +2b:");
          for (int i=0; i<5; i++)
            System.out.println(random.nextInt());
          System.out.println();
          System.out.println("Randoms between 0 (inclusive) and 10 (exclusive):");
          for (int i=0; i<40; i++) {
            System.out.print(random.nextInt(10));
            System.out.print(" ");
          }
          System.out.println();
        }
      }

      A More Interesting Example (Odds of Rolling a 7):

      import java.util.Random;
      class MyCode  {
        public static void main(String[] args) {
          Random random = new Random();
          System.out.println("This program estimates the odds of rolling a 7 on two dice.");
          int rolls = 1000000;
          int sevens = 0;
          for (int roll=0; roll<rolls; roll++) {
            int die1 = 1 + random.nextInt(6);
            int die2 = 1 + random.nextInt(6);
            if ((die1 + die2) == 7)
              sevens++;
          }
          System.out.println("Odds = " + sevens + "/" + rolls + " = " + (100.0*sevens/rolls) + "%");
        }
      }

   2. nextDouble

      import java.util.Random;
      class MyCode  {
        public static void main(String[] args) {
          Random random = new Random();
          System.out.println(random.nextDouble());
          System.out.println(random.nextDouble());
          System.out.println(random.nextDouble());
        }
      }

      A More Interesting Example (Expected difference of two randoms in [0,1]):

      import java.util.Random;
      class MyCode  {
        public static void main(String[] args) {
          Random random = new Random();
          System.out.println("This program estimates the expected difference");
          System.out.println("between two random numbers between 0 and 1.");
          int attempts = 1000000;
          double sumOfDifferences = 0;
          for (int attempt=0; attempt<attempts; attempt++) {
            double d1 = random.nextDouble();
            double d2 = random.nextDouble();
            sumOfDifferences += Math.abs(d2 - d1);
          }
          System.out.println("Expected difference = " + (sumOfDifferences / attempts));
        }
      }

   3. nextBoolean

      import java.util.Random;
      class MyCode  {
        public static void main(String[] args) {
          Random random = new Random();
          System.out.println(random.nextBoolean());
          System.out.println(random.nextBoolean());
          System.out.println(random.nextBoolean());
        }
      }

      A More Interesting Example (Odds of Getting 1 Heads and 2 Tails):

      import java.util.Random;
      class MyCode  {
        public static void main(String[] args) {
          Random random = new Random();
          System.out.println("This program estimates the odds of flipping 3 coins");
          System.out.println("And getting exactly 1 heads and 2 tails.");
          int attempts = 1000000;
          int successes = 0;
          for (int attempt=0; attempt<attempts; attempt++) {
            boolean heads1 = random.nextBoolean();
            boolean heads2 = random.nextBoolean();
            boolean heads3 = random.nextBoolean();
            if ((heads1 && !heads2 && !heads3) ||
                (heads2 && !heads1 && !heads3) ||
                (heads3 && !heads1 && !heads2))
              successes++;
          }
          System.out.println("Odds = " + successes + "/" + attempts + " = " + (100.0*successes/attempts) + "%");
        }
      }

   4. setSeed

      import java.util.Random;
      class MyCode  {
        public static void main(String[] args) {
          Random random = new Random();
          System.out.println("These values change on each run:");
          System.out.println(random.nextInt(100));
          System.out.println(random.nextInt(100));
          System.out.println();
          System.out.println("But these values DO NOT CHANGE on each run:");
          System.out.println("(which is very handy for debugging!)");
          random.setSeed(42);
          System.out.println(random.nextInt(100));
          System.out.println(random.nextInt(100));
        }
      }

   5. Online Random API
      See:  http://java.sun.com/j2se/1.5.0/docs/api/java/util/Random.html

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