1. Hash Tables: Associative Containers with Constant Time Operations --- On Average
Consider the problem of computing the frequency of words in a text file . . .

2. This is this and that is that, said Carl.
Hash Tables: Associative Containers with Constant Time Operations --- On Average
Consider the problem of computing the frequency of words in a text file . . .
This is this and that is that, said Carl.
Carl 1
that 2 is 2
said 1
this 2
and 1

3. This is this and that is that, said Carl. Strings Frequency
Hash Tables: Associative Containers with Constant Time Operations --- On Average
This is this and that is that, said Carl.
Strings
Frequency 1 2 3 4 5
‘this’ 6
Hash Table

4. This is this and that is that, said Carl. Strings Frequency
Hash Tables: Associative Containers with Constant Time Operations --- On Average
This is this and that is that, said Carl.
Strings
Frequency 1
h is a hash
function 2 3 4 h 5
‘this’ 6
Hash Table

5. This is this and that is that, said Carl. Strings Frequency
Hash Tables: Associative Containers with Constant Time Operations --- On Average
This is this and that is that, said Carl.
Strings
Frequency 1 2 3 4
Initialize the
frequency h 5 1
‘this’ 6
Hash Table

6. This is this and that is that, said Carl. Strings Frequency
Hash Tables: Associative Containers with Constant Time Operations --- On Average
This is this and that is that, said Carl.
Strings
Frequency 1
Another
word 2
‘is’ 3 4 5 1
‘this’ 6
Hash Table

7. This is this and that is that, said Carl. Strings Frequency
Hash Tables: Associative Containers with Constant Time Operations --- On Average
This is this and that is that, said Carl.
Strings
Frequency 1 2 h
‘is’ 3 4 5 1
‘this’ 6
Hash Table

8. This is this and that is that, said Carl. Strings Frequency
Hash Tables: Associative Containers with Constant Time Operations --- On Average
This is this and that is that, said Carl.
Strings
Frequency 1 2 h
‘is’ 3 1 4 5 1
‘this’ 6
Hash Table

9. This is this and that is that, said Carl. Strings Frequency
Hash Tables: Associative Containers with Constant Time Operations --- On Average
This is this and that is that, said Carl.
Strings
Frequency 1 2
‘is’ 3 1 4
Another
‘this’ 5 1
‘this’ 6
Hash Table

10. This is this and that is that, said Carl. Strings Frequency
Hash Tables: Associative Containers with Constant Time Operations --- On Average
This is this and that is that, said Carl.
Strings
Frequency 1 2
‘is’ 3 1 4 h 5 1
‘this’ 6
Hash Table

11. This is this and that is that, said Carl. Strings Frequency
Hash Tables: Associative Containers with Constant Time Operations --- On Average
This is this and that is that, said Carl.
Strings
Frequency 1 2
‘is’ 3 1 4
Increment the
frequency h 5 2
‘this’ 6
Hash Table

12. This is this and that is that, said Carl. Strings Frequency
Hash Tables: Associative Containers with Constant Time Operations --- On Average
This is this and that is that, said Carl.
Strings
Frequency
Another
word
‘and’ 1 2
‘is’ 3 1 4 5 2
‘this’ 6
Hash Table

13. This is this and that is that, said Carl. Strings Frequency
Hash Tables: Associative Containers with Constant Time Operations --- On Average
This is this and that is that, said Carl.
Strings
Frequency
‘and’ 1 2
‘is’ h 3 1 4 5 2
‘this’ 6
Hash Table

14. This is this and that is that, said Carl. Strings Frequency
Hash Tables: Associative Containers with Constant Time Operations --- On Average
This is this and that is that, said Carl.
Strings
Frequency
‘and’ 1 2
‘is’ h 3 1 4 5 2
‘this’ 6 1
Hash Table

15. This is this and that is that, said Carl. Strings Frequency
Hash Tables: Associative Containers with Constant Time Operations --- On Average
This is this and that is that, said Carl.
Strings
Frequency
‘and’ 1 2
‘is’ 3 1 4
‘that’ 5 2
‘this’ 6 1
Hash Table

16. This is this and that is that, said Carl. Strings Frequency
Hash Tables: Associative Containers with Constant Time Operations --- On Average
This is this and that is that, said Carl.
Strings
Frequency
‘and’ 1 2 h
‘is’ 3 1 4
‘that’ 5 2
‘this’ 6 1
Hash Table

17. This is this and that is that, said Carl. Strings Frequency
Hash Tables: Associative Containers with Constant Time Operations --- On Average
This is this and that is that, said Carl.
Strings
Frequency
‘and’ 1 2 1 h
‘is’ 3 1 4
‘that’ 5 2
‘this’ 6 1
Hash Table

18. This is this and that is that, said Carl. Strings Frequency
Hash Tables: Associative Containers with Constant Time Operations --- On Average
This is this and that is that, said Carl.
Strings
Frequency
‘and’ 1 2 1
Another
‘is’
‘is’ 3 1 4
‘that’ 5 2
‘this’ 6 1
Hash Table

19. This is this and that is that, said Carl. Strings Frequency
Hash Tables: Associative Containers with Constant Time Operations --- On Average
This is this and that is that, said Carl.
Strings
Frequency
‘and’ 1 2 1 h
‘is’ 3 1 4
‘that’ 5 2
‘this’ 6 1
Hash Table

20. This is this and that is that, said Carl. Strings Frequency
Hash Tables: Associative Containers with Constant Time Operations --- On Average
This is this and that is that, said Carl.
Strings
Frequency
‘and’ 1 2 1 h
‘is’
Increment the
frequency 3 2 4
‘that’ 5 2
‘this’ 6 1
Hash Table

21. This is this and that is that, said Carl. Strings Frequency
Hash Tables: Associative Containers with Constant Time Operations --- On Average
This is this and that is that, said Carl.
Strings
Frequency
‘and’ 1 2 1
‘is’ 3 2
Another
‘that’ 4
‘that’ 5 2
‘this’ 6 1
Hash Table

22. This is this and that is that, said Carl. Strings Frequency
Hash Tables: Associative Containers with Constant Time Operations --- On Average
This is this and that is that, said Carl.
Strings
Frequency
‘and’ 1 2 1 h
‘is’ 3 2 4
‘that’ 5 2
‘this’ 6 1
Hash Table

23. This is this and that is that, said Carl. Strings Frequency
Hash Tables: Associative Containers with Constant Time Operations --- On Average
This is this and that is that, said Carl.
Strings
Frequency
‘and’ 1
Increment the
frequency 2 2 h
‘is’ 3 2 4
‘that’ 5 2
‘this’ 6 1
Hash Table

24. This is this and that is that, said Carl. Strings Frequency
Hash Tables: Associative Containers with Constant Time Operations --- On Average
This is this and that is that, said Carl.
Strings
Frequency
‘and’ 1 2 2
‘is’ 3 2
Another
word
‘said’ 4
‘that’ 5 2
‘this’ 6 1
Hash Table

25. This is this and that is that, said Carl. Strings Frequency
Hash Tables: Associative Containers with Constant Time Operations --- On Average
This is this and that is that, said Carl.
Strings
Frequency
‘and’ 1 2 2 h
‘is’ 3 2
Collision!
Another
word
‘said’ 4
‘that’ 5 2
‘this’ 6 1
Hash Table

26. This is this and that is that, said Carl. Strings Frequency
Hash Tables: Associative Containers with Constant Time Operations --- On Average
This is this and that is that, said Carl.
Strings
Frequency
‘and’ 1 2 2
‘is’ 3 2
Collision!
Another
word
‘said’ 4
‘that’ 5 2
‘this’ 6 1
Hash Table

27. How can collisions be resolved?
This is this and that is that, said Carl.
Strings
Frequency
‘and’ 1 2 2
‘is’ 3 2
Another
word
‘said’ 4
‘that’ 5 2
‘this’ 6 1
Hash Table

28. How can collisions be resolved?
First of all, store the keys in the table. . .
Strings
Frequency
‘and’ 1 2 2
‘is’ 3 2
Another
word
‘said’ 4
‘that’ 5 2
‘this’ 6 1
Hash Table

29. How can collisions be resolved?
First of all, store the keys in the table. . .
Strings
Key
Frequency
‘and’ 1 2
that 2
‘is’ 3 is 2
Another
word
‘said’ 4
‘that’ 5
this 2
‘this’ 6
and 1
Hash Table

30. Collision is detected if HashTable[h(word)].Key  word
Strings
Key
Frequency
‘and’ 1 2
that 2
‘is’ 3 is 2
word =
‘said’ 4
‘that’ 5
this 2
‘this’ 6
and 1
Hash Table

31. Collision is detected if HashTable[h(word)].Key  word
e.g., HashTable[h(‘said’)].Key = ‘is’  ‘said’
Strings
Key
Frequency
‘and’ 1 2
that 2
‘is’ 3 is 2
word =
‘said’ 4
‘that’ 5
this 2
‘this’ 6
and 1
Hash Table

32. Consider h(word) to be just the starting position for searching the table for word.
Strings
Key
Frequency
‘and’ 1 2
that 2
‘is’ 3 is 2
word =
‘said’ 4
‘that’ 5
this 2
‘this’ 6
and 1
Hash Table

33. Consider h(word) to be just the starting position for searching the table for word.
E.g., start the search for ‘said’ at position 3, since h(‘said’) = 3.
Strings
Key
Frequency
‘and’ 1 2
that 2
‘is’ 3 is 2
word =
‘said’ 4
‘that’ 5
this 2
‘this’ 6
and 1
Hash Table

34. Continue search by going through some sequence of positions.
Strings
Key
Frequency
‘and’ 1 2
that 2
‘is’ 3 is 2
word =
‘said’ 4
‘that’ 5
this 2
‘this’ 6
and 1
Hash Table

35. Continue search by going through some sequence of positions.
E.g, h(word), h(word) + 1, h(word) + 2, . . .
Strings
Key
Frequency
‘and’ 1 2
that 2
‘is’ 3 is 2
word =
‘said’ 4
‘that’ 5
this 2
‘this’ 6
and 1
Hash Table

36. Continue search by going through some sequence of positions.
E.g, h(word), h(word) + 1, h(word) + 2, . . .
Strings
Key
Frequency
‘and’ 1 2
that 2
‘is’ 3 is 2
word =
‘said’ 4
‘that’ 5
this 2
‘this’ 6
and 1
Hash Table

37. Continue search by going through some sequence of positions.
E.g, h(word), h(word) + 1, h(word) + 2, . . .
Strings
Key
Frequency
‘and’ 1 2
that 2
‘is’ 3 is 2
word =
‘said’
Empty slot, so put it there 4
‘that’ 5
this 2
‘this’ 6
and 1
Hash Table

38. Continue search by going through some sequence of positions.
E.g, h(word), h(word) + 1, h(word) + 2, . . .
Strings
Key
Frequency
‘and’ 1 2
that 2
‘is’ 3 is 2
word =
‘said’
Empty slot, so put it there 4
said
‘that’ 5
this 2
‘this’ 6
and 1
Hash Table

39. Continue search by going through some sequence of positions.
E.g, h(word), h(word) + 1, h(word) + 2, . . .
Strings
Key
Frequency
‘and’ 1 2
that 2
‘is’ 3 is 2
word =
‘said’
And initialize frequency 4
said 1
‘that’ 5
this 2
‘this’ 6
and 1
Hash Table

40. Continue search by going through some sequence of positions.
E.g, h(word), h(word) + 1, h(word) + 2, . . .
Strings
Key
Frequency
‘and’
word =
‘carl’ 1 2
that 2
‘is’ 3 is 2
‘said’ 4
said 1
‘that’ 5
this 2
‘this’ 6
and 1
Hash Table

41. Continue search by going through some sequence of positions.
E.g, h(word), h(word) + 1, h(word) + 2, . . .
Strings
Key
Frequency
‘and’
word =
‘carl’ 1 2
that 2
‘is’ 3 is 2
‘said’ 4
said 1
‘that’ 5
this 2
‘this’ 6
and 1
Hash Table

42. Continue search by going through some sequence of positions.
E.g, h(word), h(word) + 1, h(word) + 2, . . .
Strings
Key
Frequency
‘and’
word =
‘carl’ 1 2
that 2
‘is’ 3 is 2
‘said’ 4
said 1
‘that’ 5
this 2
‘this’ 6
and 1
Hash Table

43. Continue search by going through some sequence of positions.
E.g, h(word), h(word) + 1, h(word) + 2, h(word) + 3, . . .
Strings
Key
Frequency
‘and’
word =
‘carl’ 1 2
that 2
‘is’ 3 is 2
‘said’ 4
said 1
‘that’ 5
this 2
‘this’ 6
and 1
Hash Table

44. Continue search by going through some sequence of positions.
E.g, h(word), h(word) + 1, h(word) + 2, h(word) + 3, 0, 1, . . .
Strings
Key
Frequency
‘and’
Wrap around
word =
‘carl’ 1 2
that 2
‘is’ 3 is 2
‘said’ 4
said 1
‘that’ 5
this 2
‘this’ 6
and 1
Hash Table

45. Continue search by going through some sequence of positions.
E.g, h(word), h(word) + 1, h(word) + 2, h(word) + 3, 0, 1, . . .
Strings
Key
Frequency
‘and’
Empty slot, so insert it here
word =
‘carl’ 1 2
that 2
‘is’ 3 is 2
‘said’ 4
said 1
‘that’ 5
this 2
‘this’ 6
and 1
Hash Table

46. Continue search by going through some sequence of positions.
E.g, h(word), h(word) + 1, h(word) + 2, h(word) + 3, 0, 1, . . .
Strings
Key
Frequency
‘and’
carl
word =
‘carl’ 1 2
that 2
‘is’ 3 is 2
‘said’ 4
said 1
‘that’ 5
this 2
‘this’ 6
and 1
Hash Table

47. Continue search by going through some sequence of positions.
E.g, h(word), h(word) + 1, h(word) + 2, h(word) + 3, 0, 1, . . .
Strings
Key
Frequency
‘and’
And initialize frequency
carl 1
word =
‘carl’ 1 2
that 2
‘is’ 3 is 2
‘said’ 4
said 1
‘that’ 5
this 2
‘this’ 6
and 1
Hash Table

48. } Strings Key Frequency
Continue search by going through some sequence of positions.
E.g, h(word), h(word) + 1, h(word) + 2, h(word) + 3, 0, 1, . . .
This method
of collision
resolution is
called . . . }
Strings
Key
Frequency
‘and’
carl 1
word =
‘carl’ 1 2
that 2
‘is’ 3 is 2
‘said’ 4
said 1
‘that’ 5
this 2
‘this’ 6
and 1
Hash Table

49. } Strings Key Frequency
Continue search by going through some sequence of positions.
E.g, h(word), h(word) + 1, h(word) + 2, h(word) + 3, 0, 1, . . .
“linear probing”
(one form of
“open
addressing”) }
Strings
Key
Frequency
‘and’
carl 1
word =
‘carl’ 1 2
that 2
‘is’ 3 is 2
‘said’ 4
said 1
‘that’ 5
this 2
‘this’ 6
and 1
Hash Table