Question

I am trying to understand the open addressing method. I refer to T. H. Cormen’s book on this topic, which states that deletion is difficult in open addressing. I am completely stuck at this paragraph:

Deletion from an open-address hash table is difficult. When we delete a key from slot i, we cannot simply mark that slot as empty by storing NIL in it. Doing so might make it impossible to retrieve any key k during whose insertion we had probed slot i and found it occupied.

I don’t understand this. Please explain it with some examples.

Answer 1

Assume hash(x) = hash(y) = hash(z) = i. And assume x was inserted first, then y and then z.

In open addressing: table[i] = x, table[i+1] = y, table[i+2] = z.

Now, assume you want to delete x, and set it back to NULL.

When later you will search for z, you will find that hash(z) = i and table[i] = NULL, and you will return a wrong answer: z is not in the table.

To overcome this, you need to set table[i] with a special marker indicating to the search function to keep looking at index i+1, because there might be element there which its hash is also i.