Linear search

Linear search is a searching algorithm. It sequentially checks every element in an array until it finds the required value or all the elements of the array is checked. Worst case complexity is $$O(n)$$ and best case is $$O(1)$$.

Pseudo-code
A is an array of size n and k is the value we want to find.

linearSearch (A, n, k) 1. for i from 1 to N 2.    if A[i] = k 3.         return i 4. return NOT-FOUND

Recursive:

linearSearch (A, n, k, i) 1. if i > n 2.    return NOT-FOUND 3. if A[i] = k 4.    return i 5. return linearSearch (A, n, k, i+1)

Optimizations
A small improvement can be made. At line 1 we are checking $$n+1$$ times if we have gone past the last index of the array A? At line 2 we are checking $$n$$ times if index i has the value we are searching for.

linearSearch (A, n, k) 1. Store the value of A[n] in variable last 2. Replace the value of A[n] with k 3. Set i = 1 4. while (A[i] != k) 5.    i++; 6. Restore the value of A[i] from variable last 7. if(i < n OR a[n] = k) 8.    return i 9. return NOT-FOUND