What is the computational complexity of the following code s

What is the computational complexity of the following code snippet? In other words, how many times will the instruction, \"x = x + 1\" be executed? for I = 1 to n for j = 1 to n x = x + 1 Suppose an algorithm will search for a member x in a list of number starting from the start of the list and iterating thought the list until the end of the list. What is the best-case algorithm?

Solution

1) the statement x=x+1 will run n*n times.

This is because,

for i=1 to n ---> when i=1
  for j=1 to n ----> this will run n times
   x= x+1

For every value of i, j will continue to run from 1 to n.

hence the statement executes n*n times.

2) For a list , say, list = [ 1, 4, 7, 9, 10, 11, 16 ]

The algorithm will search from the beginning of the list to the end of the list.

Hence the best case input x would be the first value in the list.

3) Taking the same above mentioned as an example, the worst case input x would be the last value in the list.