Time Complexity of linear search

Best Case

This case occurs when the key to be searched is the first element in the array.
So only 1 comparison is required.

Number of comparisons = 1

We say f(n) = O(g(n)) , if c1*g(n)<=f(n)<=c2*g(n) for all n>=n0 

Constants c1 and c2 are positive real numbers
n0 = non negative integer    
f(n),g(n) = non negative functions of non negative arguments                                               

Take g(n) = 1 and f(n) = 1

c1*1<=1<=c2*1

We know 0<=1<=1 ,so take c1=0,c2=1 and above condition is satisfied for all 
n>=1 (n0=1 here).

So,Time complexity of comparisons = O(1)

Time Complexity = O(1)

Worst Case

This case will occur if the key is not found or key is the last element of the array.
So,n comparisons are required.

Number of comparisons = n

We say f(n) = O(g(n)) , if c1*g(n)<=f(n)<=c2*g(n) for all n>=n0 

Constants c1 and c2 are positive real numbers
n0 = non negative integer    
f(n),g(n) = non negative functions of non negative arguments                                               

Take g(n) = n and f(n) = n

c1*n<=n<=c2*n

We know 0<=n<=n ,so take c1=0,c2=1 and above condition is satisfied for all 
n>=1 (n0=1 here).

So,Time complexity of comparisons = O(n)

Time Complexity = O(n)