Cosc236/recursion1 Recursion Recursive method calls itself Recursion frequently occurs in...
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cosc236/recursion 1 Recursion • Recursive method calls itself • Recursion frequently occurs in mathematics • Recursive definition – 2 parts • base part (basis) • recursive part (inductive part)
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Transcript of Cosc236/recursion1 Recursion Recursive method calls itself Recursion frequently occurs in...
cosc236/recursion 1
Recursion
• Recursive method calls itself
• Recursion frequently occurs in mathematics
• Recursive definition – 2 parts
• base part (basis)
• recursive part (inductive part)
cosc175/recursion 2
Recursion
• Base part– states one or more cases that satisfy the definition
– No base->infinite recursion
• recursive part – states how to apply the definition to satisfy other cases
– with repeated applications, reduces to base
• implicitly: nothing else satisfies the definition
cosc175/recursion 3
Power
public static int power(int x, int n)
{
if (n == 0)
return 1; //base case
else
return x * power(x,n-1); // recursive case
}
cosc175/recursion 4
Power
public static int power(int x, int n)
{ // n >= 0
if (n < 0)
throw new IllegalArgumentException(“negative exponent”);
else if (n == 0)
return 1; //base case
else
return x * power(x,n-1); // recursive case
}
cosc175/recursion 5
Factorial
• n! • 0! = 0• 1! = 1• For n > = 1, n! = n * (n-1)!• Exa:
– 6! = 6 * 5!– 6 * 5 * 4!– 6 * 5 * 4 * 3!– 6 * 5 * 4 * 3 * 2!– 6 * 5 * 4 * 3 * 2 * 1
cosc175/recursion 6
Factorial – N!N! = N * (N-1)!
public static int factorial(int n)
// n >= 0
{
if (n == 0)
return 0;
else if (n == 1)
return 1;
else
return n * factorial(n – 1);
}
cosc175/recursion 7
Recursive methods
• Recursive method - invokes itself directly or indirectly– direct recursion - method is invoked by a
statement in its own body– indirect recursion - one method initiates a
sequence of method invocations that eventually invokes the original
• A->B->C->A
cosc175/recursion 8
Why use Recursion?• Any loop can be rewritten using recursion
• Recursion requires more memory
• Recursion more complex
• Some problems are naturally recursive
• Recursive solution may be shorter
• Recursive solution may be more efficient– Quicksort, dynamic memory
• not every recursion can be replaced by a loop
cosc175/recursion 9
Recursion
• When a method is invoked - activated
• activation frame - collection of information maintained by the run-time system(environment)– current contents of local automatic variables– current contents of all formal parameters– return address– pushed on stack
cosc175/recursion 10
public static void echoReversed(){ String s= console.next();
char c = (char)s.charAt(0);if (c == '\n')
System.out.println(); else { echoReversed();
System.out.print(b); }}
cosc175/recursion 11
Infinite Recursionno base condition
public static void infRec()
{
if (<Condition>)
{
infRec();
<Body>
}
}
cosc175/recursion 12
Factorial(loop version)
public static int loopFactorial (int n){ int i; int fact = 1;
for (i = 1; i <= n; i++) fact = fact * i; return fact;}
cosc175/recursion 13
When to Use Recursion
• If the problem is stated recursively
• if recursive algorithm is less complex than recursive algorithm
• if recursive algorithm and nonrecursive algorithm are of similar complexity - nonrecursive is probably more efficient
Examplepublic static int mystery (int number)
{
if (number == 0)
return number;
else
return (number + mystery (number – 1);
}
1. Identify the base case
2. Identify the general case
3. What is the result of mystery(0)
4. What is the result of mystery(5);
cosc175/recursion 14
Examplepublic static void mystery (char param1, char param2)
{
if (param1 != param2)
{
param1++;
param2--;
mystery(param1, param2);
System.out.println(param1);
System.out.println(param2);
}
}
1. Show all output resulting from the following invocation : Mystery('A','G');
2. Under what circumstances does Mystery result in infinite recursion?
cosc175/recursion 15
public static mystery(int n)
{
if (n <= 1)
System.out.println(n);
else
{
mystery(n/2);
System.out.println(“, “ + n);
}
}
cosc175/recursion 16
mystery(1);mystery(2);mystery(3);mystery(4);mystery(16);mystery(30);
