Lecture Notes on 3 Jul 2013

// Illustration of labeled break
int sum = 0;
loop1: for (int i = 0; i < 10; i++)
{
  loop2: for (int j = 0; j < 10; j++)
  {
    for (int k = 0; k < 10; k++)
    {
      sum = sum + i * j * k;
      if (sum > 50)
      {
        break loop1;
      }
    }
  }
}

// Program to print the nth Fibonacci term
import java.util.*;

public class Fib
{
  public static void main (String[] args)
  {
    Scanner sc = new Scanner (System.in);
    System.out.print ("Enter Fibonacci term: ");
    int n = sc.nextInt();
    if ((n == 0) || (n == 1))
    {
      System.out.println (n);
    }
    else
    {
      int f1 = 0;
      int f2 = 1;
      int f = f1 + f2;
      for (int i = 0; i < n - 2; i++)
      {
        f1 = f2;
	f2 = f;
	f = f1 + f2;
      }
      System.out.println (f);
    }
  }
}


// Program to compute Pythagorean triplets less than 100
public class Triples
{
  public static void main (String[] args)
  {
    for (int c = 100; c >= 2; c--)
    {
      for (int b = c - 1; b >= 1; b--)
      {
        for (int a = b; a >= 1; a --)
	{
          if ((a * a + b * b) == c * c)
	  {
            System.out.println (a + ", " + b + ", " + c);
	  }
	}
      }
    }
  }
}

// Program to compute the longest Collatz sequence less than a million
import java.util.*;

public class Collatz
{
  public static void main (String[] args)
  {
    int maxSeqLength = 0;
    int maxN = 1;
    for (int i = 2; i < 1000000; i++)
    {
      int seqLength = 1;
      int n = i;
      while (n > 1)
      {
        if (n % 2 == 0)
          n = n / 2;
        else
          n = 3 * n + 1;
        seqLength++;
      }
      if (seqLength > maxSeqLength)
      {
        maxSeqLength = seqLength;
        maxN = i;
      }
    }
    System.out.println ("Max sequence length: " + maxSeqLength);
    System.out.println ("Number with max sequence length: " + maxN);
  }
}