Question

Determine the basic operation(s) in the following algorithm and then analyze its performance

     for i = 1 to n do
     {

}

for j = i to n do
     x++;

for j = 1 to i do
     y++;

Answer 1

Number of times each line runs in the code 
for i = 1 to n do   -> (n+1)
{                   -> 1
}                   -> 1

for j = i to n do   -> (n+1)
     x++;           -> (n)
for j = 1 to i do   -> n(n+1)
     y++;           -> n(n)


Total time complexity 
= (n+1)+1+1+(n+1)+n+n(n+1)+n(n)
= 2(n+1)+2+n+n(n+1+n)
= 2(n+1)+2+n+n(2n+1)
= 2n+2+2+n+2n^2+n
= 4n+4+2n^2
= O(n^2)