that, given an array A of N integers, returns the smallest positive integer (greater than 0) that does not occur in A. java code example

Example: smallest positive integer not in array java

If the expected running time should be linear, you can't use a TreeSet, which sorts the input and therefore requires O(NlogN). Therefore you should use a HashSet, which requires O(N) time to add N elements.

Besides, you don't need 4 loops. It's sufficient to add all the positive input elements to a HashSet (first loop) and then find the first positive integer not in that Set (second loop).

int N = A.length;
Set<Integer> set = new HashSet<>();
for (int a : A) {
    if (a > 0) {
        set.add(a);
    }
}
for (int i = 1; i <= N + 1; i++) {
    if (!set.contains(i)) {
        return i;
    }
}