Conditional%20assignment

1
Conditional assignment

• if ((x2)0)
• y x/2
• else
• y (x1)/2
• Same as
• y ((x2)0) ? x/2 (x1)/2

2
Euclids division algorithm

• A fast way to compute the greatest common divisor
  of two numbers a and b
• Algorithm (this is not a program)
• Divide b by a, assign a to b and the remainder to
  a loop until a is zero. The value of b at this
  point is the gcd.
• Assumes a is less than b
• Main observation gcd (a, b) gcd (a, b-a)

3
GCD

• class gcd
• public static void main (String arg)
• int a 40, b 24, r, gcd
• if ((a0) (b0))
• gcd (a gt b) ? a b
• else if (a lt b)
• while (a!0)
• r ba
• b a
• a r
• gcd b
• // next slide

4
GCD

• else
• while (b!0)
• r ab
• a b
• b r
• gcd a
• System.out.println(GCD gcd)

5
Sorting three numbers

• class sortThree
• public static void main(String arg)
• int x 2, y 5, z 1
• int max, mid, min
• if ((x gt y) (x gt z))
• max x
• if (y gt z)
• mid y
• min z
• else
• mid z
• min y
• // next slide

6
Sorting three numbers

• else
• if (y gt z)
• max y
• if (x gt z)
• mid x
• min z
• else
• mid z
• min x
• else // the remaining two
  permutations
• // end else
• // end main
• // end class

7
Integer index

• class integerIndex
• public static void main(String arg)
• int n 3
• double x 3.14, y 1.0
• int m n
• if (n lt 0)
• x 1/x
• m -n
• while (m gt 0)
• y x
• m--
• System.out.println(x to the power
  n is y)

8
Positive Decimal to Binary

• class positiveDecimalToBinary
• public static void main(String arg)
• int n 34, y0, polyTerm 1
• if (n lt 0)
• System.out.println(Sorry, cannot
  handle negative integers today!)
• else
• while (n gt 0)
• y (polyTerm(n2))
• n / 2
• polyTerm 10
• System.out.println(Required binary
  y)

9
Primality testing

• class primalityTestSlow
• public static void main (String arg)
• int n 42, d
• if (n lt 1)
• System.out.println(n is not a
  prime.)
• else
• for (d2 dltn/2 d)
• if ((nd)0)
• System.out.println(n is
  not a prime.)
• break
• if (d gt n/2)
• System.out.println(n is a
  prime.)

10
Primality testing

• class primalityTestLittleBetter
• public static void main (String arg)
• int n 42, d
• if (n lt 1)
• System.out.println(n is not a
  prime.)
• else
• for (d2 ddltn d)
• if ((nd)0)
• System.out.println(n is
  not a prime.)
• break
• if (dd gt n)
• System.out.println(n is a
  prime.)