How to tell if an array is a permutation in O(n)?

Question

Input: A read-only array of N elements containing integer values from 1 to N (some integer values can appear more than once!). And a memory zone of a fixed<

Answer 1

Java solution below answers question partly. Time complexity I believe is O(n). (This belief based on the fact that solution doesn't contains nested loops.) About memory -- not sure. Question appears first on relevant requests in google, so it probably can be useful for somebody.

public static boolean isPermutation(int[] array) {   
    boolean result = true;
    array = removeDuplicates(array);
    int startValue = 1;
    for (int i = 0; i < array.length; i++) {
        if (startValue + i  != array[i]){
            return false;
        }
    }
    return result;
}
public static int[] removeDuplicates(int[] input){
    Arrays.sort(input);
    List result = new ArrayList();
    int current = input[0];
    boolean found = false;

    for (int i = 0; i < input.length; i++) {
        if (current == input[i] && !found) {
            found = true;
        } else if (current != input[i]) {
            result.add(current);
            current = input[i];
            found = false;
        }
    }
    result.add(current);
    int[] array = new int[result.size()];
    for (int i = 0; i < array.length ; i ++){
        array[i] = result.get(i);
    }
    return array;
}
public static void main (String ... args){
    int[] input = new int[] { 4,2,3,4,1};
    System.out.println(isPermutation(input));
    //output true
    input = new int[] { 4,2,4,1};
    System.out.println(isPermutation(input));
    //output false
}