Hashing

• Review: Hash Functions
• Review: Hash Tables

Set < Hash >

• Hash Structure
• T = type of elements in Set
• s = number of elements in set = size of Set
• h = hash function for T
• B = Vector of Lists
• b = number of buckets = size of Vector
• Hash Search Algorithm
1. t = search value
2. Calculate hash_value = h(t.key)
3. Calculate index = hash_value % b
4. Search B[index] for t
5. Returns [index, List::Iterator]
• Set::Includes(t):
  
  1. [i,I] = Hash Search
  2. if (I.Valid() && t == *I) t = *I
  3. (alternate) return SetIterator(i,I)
• Set::Insert(t):
1. [i,I] = Hash Search
2. if (!I.Valid() || t != *I) B[i].Insert(I,t)
3. else *I = t;
• Set::Remove(t):
  
  1. [i,I] = Hash Search
  2. B[i].Remove(I)
• Expected Runtime = O(average search time for List)
  = O(average size of B[index])
  = O(size of set / number of buckets)
  = O(s/b)
• Expected Runspace = O(s + b)
• When O(s) = O(b): Runtime = O(1) and Runspace = O(s)

Set::Iterator < Hash >

• Data
• Interface: Bidirectional Iterator
• Set::Begin()
• Iterator::++()
• Amortized runtime O(b/(s+1))