Sorting Lecture

8/3/2019 Sorting Lecture

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SortingAPS105: Computer Fundamentals

Jason Anderson

Dept. of Electrical and Computer Engineering

Faculty of Applied Science and Engineering

University of Toronto


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Sorting

Phonebook useless if names

were not in alphabetical(sorted) order


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Why Sorting?

Sorting used in many computer programs: iPod sorts songs based on title or artist.

Facebook sorts friends in alphabetical order.

Facebook gives you the most-recent status. Excel spreadsheet can sort column by values.

Online dating: sort dating matches based on

how close by they live. Youtube sorts based on popularity.

.


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Sorting Objective

Given: list of items (numbers, names, etc). Want to put the items sorted order.

Alpha order

Largest-to-smallest Smallest-to-largest

Darkest colour to lightest colour

Sometimes there are so many items, weneed computers help to do the sorting!


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What is an Algorithm?

Set of steps for completing a task.

You have already been designing

algorithms in this class. You already use algorithms all the time inyour daily life!


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Algorithm for Baking a Cake

Cream the butter. Mix the dry ingredients

separately.

Combine the dry and wetingredients.

Mix until smooth.

Put into baking pan.

Bake for 30 mins at 350 F. Is cake done?

If yes, remove from oven.

If no, bake for another 5 minutes.


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Algorithm Efficiency

Washer, dryer take 30 mins each. Have one load of light clothes, one load

dark clothes.

Algorithm 1:2 pm : Light clothes into

washer

2:30 pm: Light clothesinto dryer

3 pm: Darks into washer3:30 pm: Darks into dryer

Algorithm 2:2 pm: Light clothes into

washer

2:30 pm: Light clothesinto dryer AND

Darks into washer3 pm: Darks into dryer

All done at 4 pm! All done at 3:30 pm!


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Sorting Algorithms

Sequence of steps computer takes forgetting items into the right (sorted) order.

Many different sorting algorithms invented:

But they have different efficiencies! Some take more steps to get things into the right

order.

Some work better for different types of items.

Want fast sorting algorithms:

Sort GTA phonebook with 6 million names.


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Sorting Algorithms

Research on sorting algorithms: Started in 1950s

Still active today

(new algorithm invented in 2004)! Well discuss three classic sorting

approaches today:

Bubble sort Insertion sort

Quicksort


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Bubble Sort

Walk through the list of numbers,comparing two items at a time. Swap the two items if theyre out of order.

The biggest item bubbles up to the top.

Walk the list of numbers several times untilcompletely sorted!


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Bubble Sort

Sort Children from Shortest to Tallest


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Bubble Sort


Look at first two children andswap them, if necessary.


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Bubble Sort


Look at NEXT two children andswap them, if necessary.


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Bubble Sort




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Bubble Sort




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Bubble Sort




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Bubble Sort


Look at LAST two children andswap them, if necessary.


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Bubble Sort


Look at LAST two children andswap them, if necessary.


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Bubble Sort


Look at FIRST two children andswap them, if necessary.


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Bubble Sort




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Bubble Sort




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Bubble Sort




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Bubble Sort




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Bubble Sort


We dont need to look at the last TWO, as in each pass

the biggest bubbles up to the top spot.


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Bubble Sort




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Bubble Sort




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Bubble Sort


We dont need to look at these TWO, as in each pass



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Bubble Sort


We dont need to look at these TWO, as in each pass


Since we didnt make ANY swaps in this pass,

were DONE!


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Bubble Sort

How many comparisons?

Sort 1000 items: 1st pass: 999 comparisons/swaps

2nd pass: 998 comparisons/swaps

999th pass: 1 comparison/swap

Sort n items:

(n-1)*(n-2)/2 comparison/swaps


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Insertion Sort

Like sorting playing cards in hand: Draw a first card card is sorted.

Draw second card compare with first card.

Draw third card compare with two cards.

Draw nth

card

compare with n-1 cards. Can speed-up using property that hand is

kept sorted.


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Quicksort

Invented in 1962 by C. Hoare.

Much more efficient than previousalgorithms. Fewer steps needed to get items into order.

Still widely used today.

Uses recursion.


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Recursion

Containssmaller

version ofsame picture


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Recursion in Computing

Task is broken down into smaller/easiertasks solved in a similar way.

Ends when we hit a BASE/END case.


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Recursion in Computing

Task is broken down into smaller/easiertasks solved in a similar way.

Ends when we hit a BASE/END case.

Invest $1000 at 8% interest. How much do I have in 3 years?

Cash(3 years) = Cash(2 years) + 8% x Cash(2 years)

Cash(2 years) = Cash(1 years) + 8% x Cash(1 years)

Cash(1 year) = Cash(0 years) + 8% x Cash(0 years) Cash(0 years) = $1000.00

Cash(3 years) = $1259.71!


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Quicksort Core Action

Want to sort 10 cards:

6 3 9 0 2 1 7 4 5 8

Choose a pivot card: 6


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Walk along the cards and partition the cardsinto two groups: Cards smaller than the pivot. Cards larger than the pivot.

4 3 5 0 2 1 7 8 9 76

Left partition Right partition

Pivot card is where

it should be!Left partition is all less than 6,

but is still unsorted!


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Now take the left partition & repeat action!

4 3 5 0 2 1


Partition the left partition:

2 3 1 0 2 54

Pivot is in its

correct place


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Likewise, take the right partition andrepeat the process.

8 9 7


Partition the right partition:

7 9 98


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Quicksort Overview

Pivot and partition the left and right half.


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Quicksort Overview


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Quicksort Overview


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Quicksort Overview


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Quicksort Overview


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Quicksort Overview

Continue until the pieces are so smallthere is nothing to do! SORTED


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Nitty Gritty Details

How do we do the partitioning?

6 3 9 0 2 1 7 4 5 8

6

LOW HIGH

Consider two arrows LOW and HIGH.


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6 3 9 0 2 1 7 4 5 8

6

LOW HIGH

Consider two arrows LOW and HIGH. HIGH will march LEFT until it finds a

number less than PIVOT.


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6 3 9 0 2 1 7 4 5 8

6

LOW HIGH

Consider two arrows LOW and HIGH. HIGH marches LEFT until it finds a number

less than PIVOT.


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6 3 9 0 2 1 7 4 5 8

6

LOW HIGH

The number at HIGH is moved to theposition LOW.


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5 3 9 0 2 1 7 4 5 8

6

LOW HIGH

The number at HIGH is moved to theposition LOW.


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5 3 9 0 2 1 7 4 5 8

6

LOW HIGH

LOW marches RIGHT until it finds anumber greater than PIVOT


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5 3 9 0 2 1 7 4 5 8

6

LOW HIGH

LOW marches RIGHT until it finds anumber greater than PIVOT


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5 3 9 0 2 1 7 4 5 8

6

LOW HIGH

The number at position LOW is moved toposition HIGH.


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5 3 9 0 2 1 7 4 9 8

6

LOW HIGH



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5 3 9 0 2 1 7 4 9 8

6

LOW HIGH

HIGH marches left until it finds a numberless than PIVOT.


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5 3 9 0 2 1 7 4 9 8

6

LOW HIGH

HIGH marches left until it finds a numberless than PIVOT.


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5 3 9 0 2 1 7 4 9 8

6

LOW HIGH

The number at position HIGH is moved toposition LOW.


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5 3 4 0 2 1 7 4 9 8

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LOW HIGH

The number at position HIGH is moved toposition LOW.


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5 3 4 0 2 1 7 4 9 8

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LOW HIGH

LOW marches right until it finds a numberlarger than PIVOT.


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5 3 4 0 2 1 7 4 9 8

6

LOW HIGH

LOW marches right until it finds a numberlarger than PIVOT.


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5 3 4 0 2 1 7 4 9 8

6

LOW HIGH



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5 3 4 0 2 1 7 7 9 8

6

LOW HIGH



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5 3 4 0 2 1 7 7 9 8

6

LOW HIGH

HIGH marches LEFT until it aligns withLOW.


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5 3 4 0 2 1 7 7 9 8

6

LOW HIGH

HIGH marches LEFT until it aligns withLOW.


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5 3 4 0 2 1 7 7 9 8

6

LOW HIGH

The PIVOT is inserted at the positionLOW/HIGH.


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5 3 4 0 2 1 7 7 9 8

6

LOW HIGH


6


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5 3 4 0 2 1 7 7 9 8

6

LOW HIGH


6

PARTI

TIONINGCO

MPLETE!

Quicksort


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Quicksort

How many comparisons/swaps?

Sort 1000 items:1000 items

Quicksort


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Quicksort



~500 items ~500 items

Quicksort


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Quicksort




~250 items ~250 items ~250 items ~250 items

Quicksort


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Quicksort How many comparisons/swaps?



~250 items ~250 items ~250 items ~250 items

~1 item ~1 item ~1 item ~1 item ~1 item~1 item. . . . .

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Comparing Algorithms

To sort 1000 times: Quicksort requires ~10,000 comparisons

(on average).

Bubble sort may require ~500,000comparisons.

Insertion sort may require ~500,000

comparisons.


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Sorting Summary

Sorting: key part of many computer programs!! Algorithm: set of steps for completing a task.

Different algorithms for same task may have

different efficiencies! Talked about three sorting algorithms: Bubble sort, Insertion Sort and Quicksort

Bubble sort and insertion sort are simple to

build, but need manysteps to sort the list. Quicksort is more complex to build,

sorts list muchfaster.

Sorting Lecture

Documents

Transcript of Sorting Lecture