Grokking Algorithms

Chapter 5
 
 
I
 
 
Hash tables
As a reminder, there’s a big difference between O(
n
) and O(log 
n
) time! 
Suppose you could look through 10 lines of the book per second. Here’s 
how long simple search and binary search would take you.
You already know that binary search is darn fast. But as a cashier, 
looking things up in a book is a pain, even if the book is sorted. You can 
feel the customer steaming up as you search for items in the book. What 
you really need is a buddy who has all the names and prices memorized. 
Then you don’t need to look up anything: you ask her, and she tells you 
the answer instantly.

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75
Hash tables
Your buddy Maggie can give you the price in O(1) time for any item, no 
matter how big the book is. She’s even faster than binary search.
What a wonderful person! How do you get a “Maggie”?
Let’s put on our data structure hats. You know two data structures so 
far: arrays and lists (I won’t talk about stacks because you can’t really 
“search” for something in a stack). You could implement this book as
an array.
Each item in the array is really two items: one is the name of a kind of 
produce, and the other is the price. If you sort this array by name, you 
can run binary search on it to find the price of an item. So you can find 
items in O(log 
n
) time. But you want to find items in O(1) time. That is, 
you want to make a “Maggie.” That’s where hash functions come in.

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76
Chapter 5
 
 
I
 
 
Hash tables
Hash functions
A hash function is a function where you put in a string
1
and you get 
back a number.
In technical terminology, we’d say that a hash function “maps strings 
to numbers.” You might think there’s no discernable pattern to what 
number you get out when you put a string in. But there are some 
requirements for a hash function:
• It needs to be consistent. For example, suppose you put in “apple” and 
get back “4”. Every time you put in “apple”, you should get “4” back. 
Without this, your hash table won’t work.
• It should map different words to different numbers. For example, a 
hash function is no good if it always returns “1” for any word you put 
in. In the best case, every different word should map to a different 
number.
So a hash function maps strings to numbers. What is that good for? 
Well, you can use it to make your “Maggie”!
Start with an empty array:
You’ll store all of your prices in this array. Let’s add the price of an apple. 
Feed “apple” into the hash function.