Simple Java soution. Scored 100/100 in correctness and performance.
public int solution(int[] A) {
int smallestMissingInteger = 1;
if (A.length == 0) {
return smallestMissingInteger;
}
Set set = new HashSet();
for (int i = 0; i < A.length; i++) {
if (A[i] > 0) {
set.add(A[i]);
}
}
while (set.contains(smallestMissingInteger)) {
smallestMissingInteger++;
}
return smallestMissingInteger;
}