Remove duplicates from array in linear time and without extra arrays

Question

We have an array and it is unsorted. We know the range is [0,n].

We want to remove duplicates but we cannot use extra arrays and it must run in linear time.

Any ideas? Just to clarify, this is not for homework!

Answer 1

If the integers are limited 0 to n, you can move through the array, placing numbers by their indices. Every time you replace a number, take the value that used to be there and move it to where it should be. For instance, let's say we have an array of size 8:

-----------------
|3|6|3|4|5|1|7|7|
-----------------
 S

Where S is our starting point, and we'll use C to keep track of our "current" index below. We start with index 0, and move 3 to the 3 index spot, where 4 is. Save 4 in a temp var.

-----------------
|X|6|3|3|5|1|7|7|   Saved 4 
-----------------  
 S     C

We then put 4 in the index 4, saving what used to be there, 5.

-----------------
|X|6|3|3|4|1|7|7|   Saved 5
-----------------
 S       C

Keep going

-----------------
|X|6|3|3|4|5|7|7|   Saved 1
-----------------
 S         C

-----------------
|X|1|3|3|4|5|7|7|   Saved 6
-----------------
 S C

-----------------
|X|1|3|3|4|5|6|7|   Saved 7    
-----------------
 S           C 

When we try to replace 7, we see a conflict, so we simply don't place it. We then continue from the starting index S, increment it by 1:

-----------------
|X|1|3|3|4|5|6|7| 
-----------------  
   S           

1 is fine here, 3 needs to move

-----------------
|X|1|X|3|4|5|6|7|
-----------------
     S

But 3 is a duplicate, so we throw it away and keep iterating through the rest of the array.

So basically, we move each entry at most 1 time, and iterate through the entire array. That's O(2n) = O(n)

Answer 2

Assume int a[n] is an array of integers in the range [0,n-1]. Note that this differs slightly from the stated problem, but I make this assumption to make clear how the algorithm works. The algorithm can be patched up to work for integers in the range [0,n].

for (int i=0; i<n; i++)
{
    if (a[i] != i)
    {
         j = a[i];
         k = a[j];
         a[j] = j;  // Swap a[j] and a[i]
         a[i] = k;
     }
 }

 for (int i=0; i<n; i++)
 {
     if (a[i] == i)
     {
        printf("%d\n", i);
     }
 }

Answer 3

    void printRepeating(int arr[], int size)
{
  int i;
  printf("The repeating elements are: \n");
  for(i = 0; i < size; i++)
  {
    if(arr[abs(arr[i])] >= 0)
      arr[abs(arr[i])] = -arr[abs(arr[i])];
    else
      printf(" %d ", abs(arr[i]));
  }
}

Answer 4

Walk through the array assign array[array[i]] = -array[array[i]]; if not negative; if its already negative then its duplicate, this will work since all values are within 0 and n.

Answer 5

Extending @Joel Lee's code for completion.

#include <iostream>
void remove_duplicates(int *a, int size)
{
  int i, j, k;
  bool swap = true;

   while(swap){
    swap = false;
    for (i=0; i<size; i++){
        if(a[i] != i && a[i] != a[a[i]]){
            j = a[i];
            k = a[j];
            a[i] = k;
            a[j] = j;
            swap = true;      
        }

    }
    }
}

int main()
{
    int i;
    //int array[8] = {3,6,3,4,5,1,7,7};
    int array[8] = {7,4,6,3,5,4,6,2};

    remove_duplicates(array, sizeof(array)/sizeof(int));

    for (int i=0; i<8; i++)
        if(array[i] == i)
            std::cout << array[i] << " ";

    return 0;
}

Answer 6

Can you sort? Sort with Radix Sort - http://en.wikipedia.org/wiki/Radix_sort with complexity O(arraySize) for given case and then remove duplicates from sorted array O(arraySize).

Answer 7

With ES6 I think this can be solved with only a few lines reducing the array into an object and then using object.keys to get array without duplicates. This probably takes more memory. I'm not sure.

I did it like this:

var obj = array.reduce(function (acc, elem) {
      acc[elem] = true;
      return acc;
    },{});
var uniqueArray = Object.keys(obj);

This has the added bonus (or disadvantage) of sorting the array. It works with strings too.

Answer 8

Use the array a a container with negative sign as an indicator, this will corrupt the input though.