Recursion

Report
Programming With Java
ICS201
Chapter 11
Recursion
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Programming With Java
ICS201
Recursive Methods
o A recursive method is a method that calls itself directly
or indirectly.
o A recursive method has two major steps:
1.recursive step in which the method calls itself
2.base step which specifies a case with a known
solution
o The method should select one of two steps based on a
criteria:
Example:
recursive step: fact(n) = n * fact(n-1)
base step: fact(0) = 1
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Programming With Java
ICS201
Constructing Recursion
o To construct a recursive algorithm you have to find out:
1.Recursive step
2.Base step
o A selection structure is then used to determine which
step to take.
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Programming With Java
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General Algorithm
if (stopping condition) then
solve simple problem (base)
else
use recursion to solve smaller problem
combine solutions from smaller problem
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Programming With Java
ICS201
Recursive Methods
0!
n!
3!
2!
1!
=
=
=
=
=
1 (By Definition!)
n x (n – 1) ! If n >
3 x 2!
2 x 1!
1 x 0!
0!
=
1
1!
2!
3!
=
=
=
1 x 0!
2 x 1!
3 x 2!
(Base Case!)
= 1x1=1
= 2x1=2
= 3x2=6
0
Programming With Java
ICS201
Recursive Methods
•
•
recursive step: fact(n) = n * fact(n-1)
base step: fact(0) = 1
fact(4) = 4 * fact(3)
= 4 * (3 * fact(2))
= 4 * (3 * (2 * fact(1)))
= 4 * (3 * (2 * (1 * fact(0))))
= 4 * (3 * (2 * (1 * 1)))
= 4 * (3 * (2 * 1))
= 4 * (3 * 2)
=4*6
= 24
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Programming With Java
ICS201
Recursive Factorial Method
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Programming With Java
ICS201
Recursive Factorial Method
public static int fact(int num)
{
if (num = = 0)
return 1;
else
return num * fact(num – 1);
}
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Programming With Java
ICS201
Fibonacci numbers
n
0
1
2
3
4
5
6
7
8
9
10
11
Fib(n)
0
1
1
2
3
5
8
13
21
34
55
89
public int fib(int n) {
if(n <= 1) {
return n;
} else {
return fib(n - 1) + fib(n - 2);
}
}
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Programming With Java
ICS201
Convert from decimal to binary
This method converts an integer number to its binary
equivalent.
Base step:
dec2bin(n) = n if n is 0 or 1
Recursive step:
dec2bin(n) = dec2bin (n/2) , (n mod 2)
Algorithm dec2bin(n):
If n < 2
else
Print n
dec2bin(n / 2)
Print n mod 2
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Programming With Java
ICS201
Example (Recursion)
class Method {
public static void dec2bin( int n){
if ( n < 2 )
System.out.print( n );
else {
dec2bin( n / 2 );
System.out.print( n % 2 );
}
}
}
class Dec2Bin{
public static void main(String [] arg){
int i=10;
dec2bin(i);
}
}
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Output:
1010
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Programming With Java
ICS201
Example (iterative)
public static void dec2bin(int n){
String binary ="";
while ( n >= 1 )
{
binary = n%2 + binary;
n /= 2;
}
System.out.print(binary);
}
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Programming With Java
ICS201
Recursion or Iteration?


Two ways to solve particular problem:

Iteration

Recursion
Iterative control structures use looping to
repeat a set of statements.

Tradeoffs between two options:

Sometimes recursive solution is easier.

Recursive solution is often slower.
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Programming With Java
ICS201
Exercise
1. Write a recursive method to find the greatest common
divisor (GCD) of two integer n and m.
2. Write a recursive method to find Xn given the double X
and the integer n.
3. Consider a Boolean array b filled with Boolean values.
Write a recursive method boolean allTrue() that returns
true if all values are true and returns false otherwise.
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