Finding the first n largest elements in an array

Question

I have got an array containing unique elements. I need to find out the first n largest elements in the array in the least complexity possible. The solution that I could thin

Answer 1

You can do this in O(n) if your elements are integers (or any integral type) within a range, i to k inclusive with k >= i. With this constraint, you can apply "bucket sort" to this.

The idea is quite simple. Allocate k - i + 1 buckets. Now, iterate through your collection and increment the bucket for that integer. Then, at the end, you can "recreate" the sorted list by creating as many integers that were found (i.e. the bucket number).

For example,

int collection[] = { 10, 4, 7, 1, 9, 0, 12 }; // maximum value to expect is 12, minimum is 0
int buckets[ 13 ] = { 0 };

for( int i = 0; i < 13; i++ )
{
      int n = collection[ i ];
      buckets[ n ]++;
}


// the first n largest elements (n = 4)

for( int j = 12; j >= 12 - 4; j-- )
{
      int n = buckets[ j ];

      while( n > 0 )
      {
           printf( "%d ", j );
           n--;
      }
}
printf( "\n" );