1. Recursive and Iterative Algorithms
1/17/2019
Debasis Mitra, FIT

2. What does the following algorithm do?
Algorithm what(n)
(1) x:=1; y:=1; z:=0;
(2) for int I:=1 to n-2 do
(3) z := x +y;
(4) y := x;
(5) x := z;
end for;
(6) return z;
End algorithm.
1/17/2019
Debasis Mitra, FIT

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.
1/17/2019
Debasis Mitra, FIT

4. Actually the recursion is working like:
Algorithm now-what(n)
(1) create stack;
(2) if n>1 then push(stack, n);
(3) int temp := 0;
(4) while stack not empty do
(5) int x := pop(stack);
(6) if x > 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.
1/17/2019
Debasis Mitra, FIT

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(2)
n-w(1)
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
1/17/2019
Debasis Mitra, FIT

6. Binary search recursive algorithm
Algorithm bin-search(sorted array A, index f, index l, key)
(1) If f = = l
(2) If key = = A[f] then return f
else return failure;
else
(3) int mid = (f + l)/2;
(4) if key > A[mid]
(5) return bin-search(A, mid+1, l);
(6) return bin-search(A, f, mid);
end if;
End algorithm.
Driver: bin-search (A, 1, n).
1/17/2019
Debasis Mitra, FIT

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 = = A[f] then return f
(8) else return failure;
else
(9) int mid := (f+l)/2;
(10) if key > A[mid] then
(11) push (stack, (mid+1, l));
(12) push (stack, (f, mid));
end if;
end while;
End algorithm.
1/17/2019
Debasis Mitra, FIT

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 > A[mid] then
(11) f := mid +1;
else
(12) l := mid;
end while;
(13)If key = = A[f] then return f
(14) else return failure;
End algorithm.
1/17/2019
Debasis Mitra, FIT