Outputting numbers within a range that are not in a list
Facetious answer: all the sizes involved are constant, so a straightforward algorithm for this will run in $O(1)$.

Serious answer: with such small numbers involved, getting too elaborate may just slow you down. Simplicity is your friend.

let found be an array [0..255]
found ← [false, false, false...]

for i ← [1..100]:
    value ← A[i]
    if found[value] is true:
        there was a repeat
    found[value] ← true

for j ← [0..255]:
    if found[value] is false:
        j was not in the list


This runs in $O(n+k)$ time and $O(k)$ space (where $n$ is the number of elements in the array and $k$ is the maximum size of those elements). I don't believe it's possible to do better.