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Lecture 6, Mon 01/27

Hashing

Hashing

• The ability to address unique key values in an array whose size may be smaller than the set of possible key values.
• Generally, keys are unique values that identify some record of information.
  • In order to put data (value) in the appropriate place in the collection, a hash function is required.
    • The hash function outputs a position in the collection based on the key value
    • Hash function outputs should be uniformly distributed
      • Or else all data would try to be stored in the same index.
    • For example, if you have array of 100 elements, a simple hash function could be:
      • key % 100 = [0-99]

• Hashing is very efficient for searching for data in an array.
  • Recall binary search: O(log n) search time (if elements are sorted).
  • Linear search: O(n) search time.
  • Hash Table search: O(1) average search time in unsorted order.
    • Hash Table searching provides instant access to an element in an array since the hash function computes the index where the data is stored.

Collisions

• It’s possible that two elements may be indexed to the same location.
  • This is known as collisions

Open-address Hashing

• Collisions are resolved by placing the item in the next open spot in the array.
• For example, if a record is hashed to position i and data already exists in that index, then check the next available spot i+1, i+2, etc.
  • Known as linear probing
  • What is a problem with this mechanism?
    • Delayed Insertion – inserting an item in a crowded hash table takes time since it must look for an empty spot.
      • Elements are inserted farther away from their actual hashed index.
    • Clustering – When different keys are hashed to the same index, there may be groups of data records grouped in the same place.

Double Hashing

• Technique that uses a 2nd hash function when resolving a collision.
  • If a hash function index results in a collision, then use the 2nd hash function to determine how far to step in the array to look for an empty slot.
  • Helps reduce the clustering effect.
• Problems
  • If hash2 function is large, there is a possibility that we will go out of bounds.
  • Depending on the table size and hash2, it is possible that the index won’t be uniformly distributed.

Chained Hashing

• The biggest problem to open-address hashing is
  • If the table is full, no more elements can be added.
  • Similar to a vector, it could expand the capacity “under-the-hood” when needed, but…
    • All elements will probably have to be rehashed
    • New capacity shouldn’t be wasteful (too big) or too small
• Chained hashing (chaining)
  • If a collision occurs, then we store a series of data records in a list that the index in the hash table references.
  • Linked Lists are a common collection to store collided data records.

std::map vs std::unordered_map

• The underlying structure of an std::map is implemented with a balanced tree structure.
  • Useful if you care about the ordering of keys.
• std::unordered_map is used similarly to std::map, but the std::unordered_map is implemented with hash tables.
  • Notice the std::unsorted_map’s key / value pairs are not printed in sorted order by keys, but std::map’s keys are.
  • Hash Tables have a better average case performance (O(1)), but data order is not guaranteed when traversing the structure with iterators.

	unordered_map		map
	Average	Worst-Case	Average	Worst-Case
Lookup	O(1)	O(n)	O(log n)	O(log n)
Deletion	O(1)	O(n)	O(log n)	O(log n)