Download Recursion

Chapter 6:
Repetition
Continued
Validity Checks
What’s weak about the following code?
do
{
s1 = JOptionPane.showInputDialog (“Enter a
number: ”);
idNum = Integer.parseInt(s1);
}
While (idNum < 100 || idNum > 1999);
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Alternative Code
do
{
s1 = JOptionPane.showInputDialog (“Enter a number: ”);
idNum = Integer.parseInt(s1);
if (idNum < 100 || idNum > 1999)
JOptionPane.showMessageDialog(null, “Error bla bla bla”,
JOptionPane.ERROR_MESSAGE);
else
break; // a valid id num was entered
} while (true); // expression is always true
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Recursion
• It is possible for a method to call itself
• Methods that call themselves are referred to as:
– Self-referential methods
– Recursive methods
• Direct recursion
– A method invokes itself
• Indirect or mutual recursion
– A method can invoke a second method, which in turn
invokes the first method
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Mathematical Recursion
• The recursive concept is that the solution to a
problem can be stated in terms of “simple”
versions of itself
• Factorial of number n:
– Denoted as n!, where n is a positive integer
1! = 1
n! = n * (n * 1)! for n > 1
5
Mathematical Recursion
(continued)
• General considerations that must be specified
include:
– What is the first case?
– How is the nth case related to the (n - 1) case?
6
Pseudocode for Method
factorial
If n = 1
factorial = n
Else
factorial = n * factorial(n - 1)
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Recursive Example
public class Recursive
{
public static void main(String[] ags)
{
int n = 3;
long result;
result = factorial(n);
System.out.println("The factorial of " + n + " is " + result);
}
public static long factorial(int n)
{
if (n == 1)
return (n);
else
return (n * factorial(n-1));
}
}
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How the Computation Is
Performed
• A Java method can call itself due to:
– Java’s allocation of new memory locations for all
method arguments and local variables as each method is
called
• The allocation is made dynamically in a memory
area referred to as the stack
• The stack is memory used for rapidly storing and
retrieving data
9
Recursion Versus Iteration
• The recursive method can be applied to any
problem in which the solution is represented in
terms of solutions to simpler versions of the same
problem
• Recursive methods can always be written in a nonrecursive manner using an iterative solution
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Recursion Versus Iteration
(continued)
• If a problem solution can be expressed iteratively
or recursively with equal ease, the iterative
solution is preferable because it:
– Executes faster
– Uses less memory
• There are times when recursive solutions are
preferable
– Some problems are easier to visualize using a recursive
algorithm
– Sometimes a recursive solution provides a much
simpler solution
11
Applications: Random
Numbers and Simulations
• Random numbers
– Series of numbers whose order cannot be predicted
– Hard to find in practice
• Pseudorandom numbers
– Sufficiently random for task at hand
• Java compilers provide general-purpose method
for creating random numbers
– Defined in the Math class
– Named random()
12
public class RandomNumbers
{
public static void main(String[] args)
{
double randValue;
int i;
for (i = 1; i <= 10; i++)
{
randValue = Math.random();
System.out.println(randValue);
}
}
}
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Scaling
• A method for adjusting random numbers produced
by a random number generator to reside within
ranges, such as 1 to 100
– Accomplished using the expression:
(int) (Math.random() * N)
14
Simulations
• Common use of random numbers:
– Simulate events rather than going through time and
expense of constructing a real-life experiment
• Coin Toss Simulation
– Use random number generator to simulate coin tosses
• Elevator Simulation
– Simulate the operation of an elevator
15
Common Programming Errors
• Creating a loop that is “off by one”
• Repetition statements should not test for equality
when testing floating-point (real-values) operands
• Placing a semicolon at the end of either a while or
for loop’s parentheses
• Using commas to separate items in a for statement
instead of the required semicolons
• Omitting a final semicolon from a do-while
statement
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Summary
• A section of repeating code is referred to as a loop
– Types of loops:
• while
• for
• do-while
• A while statement checks a condition before any
other statement in a loop
17
Summary (continued)
• A for statement is extremely useful in creating
loops that must be executed a fixed number of
times
• A do-while statement checks its expression at the
end of the loop
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