Intro to Sorting
Intro to Computer Science
CS1510
Dr. Sarah Diesburg
Last Time
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We looked at two basic algorithms for
searching
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Linear search
Binary search
Linear search was the easiest to write
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But perhaps not the best from a complexity
standpoint
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Last Time
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Big “O” measures how badly the problem
grows as the data set grows
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Study of complexity of algorithms
Worst case of linear search was N, where N is the
number of comparisons that we need to perform
Double the number of items in list, double the
amount of time needed to complete the search in
the worst case
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Last Time
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The binary search was another solution that
incurred less comparisons in the worst case
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Only works on sorted list
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Binary Search
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Binary search algorithm
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Try the guess at middle index of the range
If the value we are searching for is higher than
number at the index, then adjust your low range
bound to be your guess+1
If the value we are searching for is lower than
number at the index, then adjust your high range
bound to be your guess-1
Repeat
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Binary Search
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What is the worst-case scenario of the binary
search?
Thinking of a number between 1 and 100
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7 guesses in total – why?
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1 guesses – cut down to 50 possibilities
2 guesses – cut down to 25
3 guesses – cut down to 12
4 guesses – cut down to 6
5 guesses – cut down to 3
6 guesses – cut down to 1
7 guesses – to figure out if last guess is right
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Binary Search
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What is the complexity of a binary search?
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Big O value of log2 N
This is “log base 2”
log2(100) = x
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What is this saying?
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Binary Search
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What is the complexity of a binary search?
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Big O value of log2 N
This is “log base 2”
log2(100) = x
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What is this saying?
2x = 100
Go “to the next power” when not exact
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Binary Search
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How does that relate to our binary search?
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Let’s say there are 16 items in our list. What is
the worst case number of guesses? 32? 34? 64?
One million?
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Binary Search
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How does that relate to our binary search?
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Let’s say there are 16 items in our list. What is
the worst case number of guesses? 32? 34? 64?
One million?
One million is about 20 guesses
2^10 = 1024
One million is 1000 squared, so twice as much
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Searching
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So which kind of search would amazon.com
use to search their databases?
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Demo
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binarySearch() on different types of lists
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Ordered
Odd
Reverse
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Demo
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binarySearch() on different types of lists
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Ordered
Odd
Reverse
The reverse list doesn’t work because the list
needs to be sorted in ascending order.
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How do we sort?
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Group Time!
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Let’s get into 4 big groups
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Put the cards in order
You can only look at two cards at a time
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Sorting Methods
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Insertion Sort
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Two chunks of data (sorted and unsorted)
Go through unsorted data and insert it in order
into sorted pile
As humans, if we could look at all cards at once,
we would probably perform an insertion sort
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Sorting Methods
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Bubble Sort
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Higher cards “bubble” to the top
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Compare two cards
Move the higher card to the top
Pick out another card
Repeat
After each run, one more high card is in order
Lower cards slowly “bubble” to the bottom
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Sorting Methods
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Selection Sort
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Find smallest card by
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Comparing two cards at a time
Saving out the current smallest card
Repeat until reach end of pile
Put smallest card in sorted pile
Repeat
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Sorting
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Humans will tend to want to fan out all the
cards and scan them
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With 13 cards, this works
But what if I gave you 10,000 student ID cards?
Computers can only compare a finite number
of cards together at a time
Let’s start to think about how long each of
these will take in the worst case
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Big O (Worst Case)
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Selection sort
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First pass – compare 13 cards and set aside
lowest
Second pass – compare 12 cards and set aside
lowest
Etc….
How many passes do I make? – 13
N^2 = 169 but actually 91
As you double your data, you quadruple your
time.
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