Recursive and Iterative Algorithms

1
Recursive and Iterative Algorithms
2
What does the following algorithm do?

• Algorithm what(n)
• (1) x1 y1 z0
• (2) for int I1 to n-2 do
• (3) z x y
• (4) y x
• (5) x z
• end for
• (6) return z
• End algorithm.

3
Now this Algorithm?

• Algorithm now-what(n)
• (1) if n 1 or 0 then return 1
• (2) else
• (3) return now-what(n-1) now-what(n-2)
• (4) end if
• End algorithm.

4
Actually the recursion is working like

• Algorithm now-what(n)
• (1) create stack
• (2) if ngt1 then push(stack, n)
• (3) int temp 0
• (4) while stack not empty do
• (5) int x pop(stack)
• (6) if x gt 1 then
• (7) push (stack, x-1)
• (8) push (stack, x-2)
• else
• (9) temp temp 1
• end if
• end while
• (10) return temp
• End algorithm.

5
Recursion tree for recursive Fibonacci number
calculation sample
n-w(4)
n-w(2)
n-w(3)
n-w(0)
n-w(1)
n-w(1)
n-w(2)
n-w(1)
n-w(0)
n-w(4) n-w(1) n-w(0) n-w(1)
n-w(1) n-w(0) 5
6
Binary search recursive algorithm

• Algorithm bin-search(sorted array A, index f,
  index l, key)
• (1) If f l
• (2) If key Af then return f
• else return failure
• else
• (3) int mid (f l)/2
• (4) if key gt Amid
• (5) return bin-search(A, mid1, l)
• else
• (6) return bin-search(A, f, mid)
• end if
• end if
• End algorithm.
• Driver bin-search (A, 1, n).

7
Binary Search iterative algorithm stack-based

• Algorithm bin-search(sorted array A, key)
• (1) create stack int f 1 int l
  size_of(A)
• (3)push(stack, (f, l))
• (4) while stack not empty do
• (5) (f, l) pop(stack)
• (6) if f l then
• (7) if key Af then return f
• (8) else return failure
• else
• (9) int mid (fl)/2
• (10) if key gt Amid then
• (11) push (stack, (mid1, l))
• else
• (12) push (stack, (f, mid))
• end if
• end while
• End algorithm.

8
Binary Search iterative algorithm non-stack
based

• Algorithm bin-search(sorted array A, key)
• (1) int f 1 int l size_of(A)
• (2) While f ? l do
• (3) int mid (f l)/2
• (4) if key gt Amid then
• (11) f mid 1
• else
• (12) l mid
• end while
• (13)If key Af then return f
• (14) else return failure
• End algorithm.