Open Addressing - Example Pseudo Code

Example Pseudo Code

The following pseudocode is an implementation of an open addressing hash table with linear probing and single-slot stepping, a common approach that is effective if the hash function is good. Each of the lookup, set and remove functions use a common internal function find_slot to locate the array slot that either does or should contain a given key.

record pair { key, value } var pair array slot function find_slot(key) i := hash(key) modulo num_slots // search until we either find the key, or find an empty slot. while ( (slot is occupied) and ( slot.key ≠ key ) ) do i := (i + 1) modulo num_slots repeat return i function lookup(key) i := find_slot(key) if slot is occupied // key is in table return slot.value else // key is not in table return not found function set(key, value) i := find_slot(key) if slot is occupied slot.value := value else if the table is almost full rebuild the table larger (note 1) i := find_slot(key) slot.key := key slot.value := value

Another example showing open addressing technique. Presented function is converting each part(4) of an internet protocol address, where NOT, XOR, OR and AND are bitwise operations and << and >> are left and right logical shifts:

// key_1,key_2,key_3,key_4 are following 3-digit numbers - parts of ip address xxx.xxx.xxx.xxx function ip(key parts) j := 1 do key := (key_2 << 2) key := (key + (key_3 << 7)) key := key + (j OR key_4 >> 2) * (key_4) * (j + key_1) XOR j key := key AND _prime_ // _prime_ is a prime number j := (j+1) while collision return key

note 1

Rebuilding the table requires allocating a larger array and recursively using the set operation to insert all the elements of the old array into the new larger array. It is common to increase the array size exponentially, for example by doubling the old array size.

function remove(key) i := find_slot(key) if slot is unoccupied return // key is not in the table j := i loop mark slot as unoccupied r2: (note 2) j := (j+1) modulo num_slots if slot is unoccupied exit loop k := hash(slot.key) modulo num_slots // k lies cyclically in ]i,j] // | i.k.j | // |....j i.k.| or |.k..j i...| if ( (i<=j) ? ((i

note 2

For all records in a cluster, there must be no vacant slots between their natural hash position and their current position (else lookups will terminate before finding the record). At this point in the pseudocode, i is a vacant slot that might be invalidating this property for subsequent records in the cluster. j is such a subsequent record. k is the raw hash where the record at j would naturally land in the hash table if there were no collisions. This test is asking if the record at j is invalidly positioned with respect to the required properties of a cluster now that i is vacant.

Another technique for removal is simply to mark the slot as deleted. However this eventually requires rebuilding the table simply to remove deleted records. The methods above provide O(1) updating and removal of existing records, with occasional rebuilding if the high water mark of the table size grows.

The O(1) remove method above is only possible in linearly probed hash tables with single-slot stepping. In the case where many records are to be deleted in one operation, marking the slots for deletion and later rebuilding may be more efficient.