Decision Maths

1
Decision Maths

• Lesson 13 Search Algorithms

2
Search Algorithms

• There are many situations where we need to search
  for specific things.
• An example is when you look someone up in a phone
  book.
• You have been using an algorithm without
  realising it.
• We are now going to look at different search
  algorithms.

3
Search Algorithms

• In your pairs get one person to think of a number
  between 1 and 99, keeping it secret.
• The other person needs to ask questions which
  have a yes or no answer to locate that number.
• What is the min/max and average number of
  questions that need to be answered to locate the
  number?
• Can you describe an efficient algorithm?
• Min 1
• Max 98
• Best method is to half known range each time.

4
Linear Search Algorithm

• This is the easiest of the search algorithms.
• You basically search each item in the list till
  you find the one that satisfies your criteria.
• There is no restriction on the data and it can be
  in any order.
• This is however the least efficient search
  algorithm.
• Especially if the item you are searching for is
  not on the list.
• Imagine trying to locate someones details from
  the phone book if you only know their telephone
  number.
• It is usually worth ordering the data to suit
  your needs.
• Give some examples of sorting methods that you
  have seen.
• How would you locate a name in the phone book.
• How would you find a library book
• How would you locate your name in the school
  register.

5
Search Algorithms

• Phone books are ordered alphabetically on the
  first letter of surname then second then third
  etc.
• benn
• carl
• caroline
• cherice
• Library books can be categorised, then ordered by
  the author, then the book title.
• Class lists, by year, by tutor, alphabetical.

6
Indexed Sequential Search Algorithm

• The data are first ordered and then subdivided.
• An extra list or index is created using the first
  or last item in the subdivision
• In the same way as the examples on the last
  slide.
• This method is used in phone books and
  dictionaries.
• The index appears at the top corner of the page.
• If you are searching for horse in the
  dictionary you first flick through the pages to
  locate H, then you would perform a linear
  search on that page.

7
Binary Search Algorithm

• Used to search and locate a specific item in a
  list.
• The list must be in alphabetical or numerical
  order.
• The algorithm hinges around the middle item of a
  sub list.
• The middle item is defined as 0.5(n1n2)
• Where n1 is the first item in the sub list and n2
  is the last.

8
Binary Search Algorithm

• Locate the names below in the list shown.
• a) Dixon
• b) Davy
• 1) Abbot
• 2) Brown
• 3) Carr
• 4) Casson
• 5) Cater
• 6) Daniel
• 7) Dixon
• 8) Domb
• 9) Fox
• 10) Gough
• 11) Hampton

Iteration 1
Middle 1 ( 1 11) 6th
2
Daniel
9
Binary Search Algorithm
2nd Iteration
Middle 1 ( 7 11) 9th
7) Dixon
2
8) Domb
9) Fox
Fox
10) Gough
11) Hampton
Dixon is before Fox
3rd Iteration
Middle 1 ( 7 8) 7.5th 8th
2
7) Dixon
Domb
8) Domb
Dixon is before Domb
10
Binary Search Algorithm
4th Iteration
7) Dixon
Middle 1 ( 7 7) 7th
2
Dixon
Found Dixon and it is in the 7th position
11
Binary Search Algorithm
Locate the names
1st Iteration
a) Dixon
b) Davy
Middle 1 ( 1 11) 6th
1) Abbot
2
2) Brown
3) Carr
Daniel
4) Casson
5) Cater
6) Daniel
7) Dixon
8) Domb
Davy is after Daniel
9) Fox
10) Gough
11) Hampton
12
Binary Search Algorithm
2nd Iteration
Middle 1 ( 7 11) 9th
7) Dixon
2
8) Domb
9) Fox
Fox
10) Gough
11) Hampton
Davy is before Fox
3rd Iteration
Middle 1 ( 7 8) 7.5th 8th
2
7) Dixon
Domb
8) Domb
Davy is before Domb
13
Binary Search Algorithm
4th Iteration
7) Dixon
Middle 1 ( 7 7) 7th
2
Dixon
List has expired so Davy is not on the list
14
Binary Search Algorithm

• The Algorithm proceeds most smoothly when the
  number of data items is 3, 7, 15, 31, 63.
• Can you see why?
• The sequence has nth term 2n-1
• Each sub list is always odd and part of the same
  sequence, so when you add one and half it works
  perfectly.
• In some cases it can be beneficial to add a dummy
  item to make the list up to 2n -1.

15
Binary Search Algorithm

• Questions
• Locate James in the following lists
• 1) Andrea 1) Adam
• 2) Bill 2) Benn
• 3) Robert 3) James
• 4) Peter 4) Katie
• 5) Claire 5) Lou
• 6) Polly 6) Pamela
• 7) Nick
• 8) Caroline