Example: Solution of Quadratic Equations

1
Example Solution of Quadratic Equations

• We want to solve for
  real values of x, for given values of a, b, and
  c.
• The value of x can be determined from the
  well-known formula
• Depending on the value of the discriminantwe
  have 3 cases
• two real values for x
• one real value for x
• no real values for x

2
Flow diagram
b2 4ac gt 0
True
False
b2 4ac lt 0
False
True
x1 b/2a
No solutions
3
Flow diagram, version 2
d b2 4ac
False
True
d gt 0
d lt 0
False
True
x1 b/2a
No solutions
4
Structure of nested if statements

• discriminant b b - 4.0 a c
• if ( discriminant gt 0 )
• // We have two real solutions
  
• else
• if ( discriminant lt 0 )
• // We have no real solutions.
• else
• // We have one real solution.

5
Adding the Complex case

• Suppose we now want to solve
  for real or complex values of x, for given
  values of a, b, and c.
• In this case, we can still use the formula
• but when we have we will need to be careful to
  avoid taking a square root of a negative number.
• If we take the square root of the absolute value
  of the discriminant, we have the complex
  coefficient

6
Flow diagram
d b2 4ac
False
d gt 0
True
d lt 0
True
False
x1 b/2a
7
Testing for Equality withFloating Point Values

• Because of the possibility of round-off error,
  testing for equality (or inequality) of float or
  double values is NOT recommended.
• Instead, test that the value is close enough to
  the desired value by using a tolerance value, and
  checking that the absolute value of the
  difference is less than the tolerance
• double EPSILON 1.0e-10
• double x
• ...
• if ( x 37.0 ) // not recommended
• ...
• if ( Math.abs( x 37.0 ) lt EPSILON ) // better

8
The switch statement

• Allows for multi-way branches
• You can only use case statements when the test is
  on an integer, Boolean, or character variable.
• Idea
• List various cases for specific values of the
  tested variable, plus one default case for when
  there is no match.
• Provide a statement block for each case.
• You MUST end each statement block with break or
  the program will go to the next following case.

9
The switch statement
true
case 1
statement block 1
break
false
true
case 2
statement block 2
break
false
true
case n
statement block n
break
false
defaultstatement block
10
Example

• System.out.println(Enter an integer from 1 to 3
  )
• int a Keyboard.readInt()
• switch( a )
• case 1
• System.out.println(You entered a 1.)
• break
• case 2
• System.out.println(You entered a 2.)
• break
• case 3
• System.out.println(You entered a 3.)
• break

11
Missing break statement
true
case 1
statement block 1
false
true
case 2
statement block 2
break
false
true
case n
statement block n
break
false
defaultstatement block