Finding data fast

• You know that searching for a key in an unsorted array or a linked list has time cost O(N) average case
  
• You know that searching for a key in a sorted array or a balanced search tree or a randomized search tree or a skip list has time cost O(logN) average case
  
• Is it possible to do better?...
  
• Consider searching for a key k in an array a . If we somehow knew that, if key k is in the array, it would be at index i , we could do a find on k with one array access: a[i]
• This would be O(1), ignoring any memory hierarchy effects
  
• Of course it may be unreasonable to just "know" the index for key k . But suppose we could compute the index for k in time O(1). Then we could still do a search with time cost O(1)!
  
• Hashing and hash tables are ways of trying to make this simple idea a reality
• ... and it turns out that with good design it is definitely possible to get O(1) average case find, insert, and delete time costs, and good space costs too