Question

Update the following algorithm so that it reduced from Θ(n) to Θ(1)

     sum = 0;
     for i = 1 to n do

sum = sum + i;

Answer 1

Code lines and number of times each line runs
sum = 0;            -> 1 time
for i = 1 to n do   -> n+1 times
    sum = sum + i;  -> n times
    
Time complexity = Θ(n)

This code is calculating sum fo numbers from 1 to n.
We can do same with single line

sum = n*(n+1)/2

So, This code runs Θ(1) time.  
    

sum = n*(n+1)/2