Assignment#1 Computer Science

Q2. The origami is totally done and will be handled and discussed with the TA.

Q3.

Q4.

Q5.

def Fib (n)

if (n == 0)

return 0;

else if (n == 1)

return 1;

else

return fib(n - 1) + fib(n - 2);

Q6. " Bonus – Best case analysis in insertion sort "

As shown in Q3. A psoudocode for insertion sort

The difference in the best case analysis is that the program will NOT go through the while loop not at all as the array will be already sorted so the condition of ( A[wait -1]>original ) always fail .

So, T(n) would be = (c1 + c3 )*(n-1) which is time complexity of O(n).

Q7.

No.5 in the lab sheet:

Psoudocode:

Sum(n^2)

{

For i ← 1 to n

A[i] ← i * i ;

m ← length(A) ;

sum ← 0;

for i ← 1 to m

sum ← sum + A[i];

return sum;

}

No.8 in the lab sheet:

Psoudocode:

i ← 2 ;

while i > = 2

{ If i’s prime devisors are 2 OR 3 OR both

return i ;

}

** the code is not in the strict sense as it’s not terminating

Name : Mahmoud Mohamed Bahaa El Din Khedr

ID no. 201301069