CS 46B - Lecture 20

Pre-class reading

• Section 16.4

Implementing a Hash Table

• Set implementation
• Adding, finding, removing an element must be fast
• Order doesn't matter
• Basic idea: put objects in an array
• Index computed from object

  buffer[index(obj)] = obj

• Finding duplicates is easy:

  if (buffer[index(obj)] != null) // obj already present

• Assumptions
  • Computing index(obj) is fast
  • No two objects occupy the same locations

Hash Functions

• Object class has a hashCode method
• Computes an integer for each object
• Override in your own class to be compatible with equals
• Hash code should depend on object contents
• Hash code should “spread around” objects into different numbers

Example: Hash code for String

final int HASH_MULTIPLIER = 31;
int h = 0;
for (int i = 0; i < s.length(); i++)
   h = HASH_MULTIPLIER * h + s.charAt(i); 

Lecture 20 Clicker Question 1

Trivia fact of the day: 'd' has code 100.

What is the hash code for the string "cab"?

1. 294
2. 98244
3. 97284
4. Something else

Implementing Hash Functions

• Form hash code of each instance variable that is compared in equals
• Combine these hash codes

public class Country
{
   public int hashCode()
   {
      int h1 = name.hashCode();
      int h2 = new Double(area).hashCode();
      final int HASH_MULTIPLIER = 31;
      int h = HASH_MULTIPLIER * h1 + h2;
      return h;
   }
}

Collisions

• index(obj) = Math.abs(obj.hashCode) % tableSize
• What if two objects occupy the same index?
• A collision
• Could move the colliding element somewhere else in the array
  • E.g. the next empty position
  • Gets complicated (Special Topic 16.2)
• Easier approach: Put all collisions in a linked list

Finding an Element

• Check whether obj is already present
• Compute index(obj) from hash code
• Look at all elements in bucket
• For each of them, call element.equals(obj)
• Until one of the calls returns true or you checked them all
• How efficient?
• Assume hashCode and equals is O(1)
• Assume buckets are short
  • When table gets too full, grow it
• Finding element is O(1)

Adding an Element

• Compute index(obj) from hash code
• Check if element is present in the bucket
• If any of them equals(obj), return
• Otherwise, add to bucket (as first element)
• O(1)+
• Removal is similar, also O(1)+
• Why +? If table gets too large/small, reallocate

Lecture 20 Clicker Question 2

Fred makes a hash table of Employee objects and defines an equals method

public boolean equals(Object other) { return id == ((Employee) other).id; }

But he forgets to implement a hashCode method for the Employee class What happens?

1. He gets a compile-time error
2. He gets a run-time exception
3. When adding multiple employee objects with the same ID, he sometimes ends up with more than one
4. When adding multiple employee objects with the same ID, he always ends up with more than one

Lecture 20 Clicker Question 3

Fred makes a hash table of Employee objects and defines a hashCode method

public int hashCode() { return id; }

But he forgets to implement an equals method for the Employee class What happens?

1. He gets a compile-time error
2. He gets a run-time exception
3. When adding multiple employee objects with the same ID, he sometimes ends up with more than one
4. When adding multiple employee objects with the same ID, he always ends up with more than one

Lecture 20 Clicker Question 4

Fred makes a hash table of Employee objects and defines a hashCode method

public int hashCode() { return id; }

and an equals method

public boolean equals(Employee other) { return id == other.id; }

But his hash table doesn't work right. What happens?

1. He gets a compile-time error
2. He gets a run-time exception
3. When adding multiple employee objects with the same ID, he sometimes ends up with more than one
4. When adding multiple employee objects with the same ID, he always ends up with more than one

Lecture 20 Clicker Question 5

Fred makes a hash table of Employee objects and defines an equals method

public boolean equals(Object other) { return id == ((Employee) other).id; }

and a hashCode method

public int hashCode() { return -1; }

What happens?

1. He gets a compile-time error
2. He gets a run-time exception
3. When adding multiple employee objects with the same ID, he sometimes ends up with more than one
4. The hash table works correctly, but its performance is disappointing

Iterating over a Hash Table

• Iterator has bucket index + reference to current element
• next advances to next element in current bucket
• or if there aren't any more, to first element in next bucket
• Assuming the table isn't too sparse, each call to next is O(1)

Lecture 20 Clicker Question 6

Suppose you have two hash tables, each with n elements. To find the elements that are in both tables, you iterate over the first table, and for each element, check whether it is contained in the second table. What is the big-Oh efficiency of this algorithm?

1. O(1)
2. O(1)+
3. O(n)
4. O(n²)