Question

I need to find the minimum missing element from a sequence of non-negative integers.

ex: I have: 0 5 10 4 3 1

The missing element is 2.

In above sequence missing elements are 2 6 7 8 9 . The minimum among them is 2 so answer is 2.

Brute force . I will sort the sequence and get the minimum element in nlogn .I am looking for better solution. Any help ?

Answer 1

In ISO C99:

unsigned least_absent(unsigned seq_sz, unsigned seq[seq_sz])
{
   bool tab[seq_sz];
   memset(tab, 0, sizeof(tab));
   for(unsigned i=0; i<seq_sz; i++)
      if(seq[i] < seq_sz)
         tab[seq[i]] = true;
   for(unsigned i=0; i<seq_sz; i++)
      if(!tab[i])
         return i;
   return seq_sz;
}

This is O(n) time, O(n) memory.