Question

I need to write an algorithm of sorting the array of size [0..N-1], that is filled with the values of the range [0..N-1]. Values in the array can not be repeated. The sorting should work in a linear time, and I allowed to use only some additional variable.

plz comment the code i wrote. As far as I guess the worst time is 2*N. Is is still a linear time? Is it possible to make is faster?

public int sort(){
    int i  = 0;             
    while (i < n){
        if (a[i] != i)      
            switchElements(a[i], a[a[i]]);                  
        else
            i++;                    
    }
    return count;
}

additional 1
I really need to sort the array, cause sorting is only the part of the task. The full task is to find is there a duplicate values in array, in a linear time, and no additional variables.

Answer 1

In order to detect duplicates you can extend that logic further, forcing the values into their respective spots.

public int sort(){
    int i  = 0;             
    while (i < n){
        while (a[i] != a[a[i]])      
            switchElements(a[i], a[a[i]]);                  
        ++i;                    
    }
    return count;
}

and in the end, if for any i, i and A[i] do not match that would indicate a repetition!
Overall it would be still O(N) procedure.

For more details refer to following post:
Finding duplicates in O(n) time and O(1) space