1 Today’s Objectives Announcements Hand in Homework 4 – no late assignments accepted! No email submissions! The final exam will be on 1-May at 7 p.m

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Today’s Objectives

Announcements• Hand in Homework 4 – no late assignments accepted! No email submissions!• The final exam will be on 1-May at 7 p.m. in D201 – No alternate times, no makeup exam• Quiz 4 will be next week, 24-Apr

– Some simple Java, for example, write a Java statement that uses a public method of a class

– Know about using an ArrayList to store tree data

– Know how to draw a picture of a binary search tree if I give you a list of data to insert into it

– Know about separate chaining and open address collision resolution

– Know the runtime efficiencies of sorting algorithms that we’ve studied

Student presentations Maps and hash tables – (from last week’s slides)

• Map ADT• Hash function and hash code• Collision handling• Ordered search tables and binary search

Sorting• Bubble sort• Selection sort• Insertion sort

Week 14

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Sorting

Bubble Sort Selection Sort Insertion Sort

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Sorting

Arranging data into ascending or descending order

Influences the speed and complexity of algorithms that use the data, e.g. searching

Many algorithms – many implementations• Bubble sort• Selection sort• Insertion sort• Shell sort• Quick sort

Sorting (Knuth, 1–5)

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Sorting

Some uses of sorting:

• Grouping equal items in a collection

• Matching data in more than one file

• Speeding up the process of searching for data


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Sorting Algorithms

Two general types:

• For internal sorting – all data is kept in memory

• For external sorting – some of the data is stored on external media


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Two Important Measuresof Sorting Efficiency

1. Running time• The most important measure of efficiency• Compare number of comparisons to number of elements (n)• Less important measure: number of swaps

2. Space• Amount of extra memory used is also important• Sorting in place

– Instead of transferring elements out of a sequence and then back into it, we just re-arrange them

– Uses a constant amount of memory

– More efficient space usage

Sorting (Sedgewick, 270–271; Dale, 586)

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Bubble Sort

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Bubble Sort

One way to sort elements stored in a linear sequence

Easy to understand

In each loop through the sequence, each successive pair of elements is compared

If the first element is larger than the second, they are swapped

Sequence (Goodrich 2004, 235–237)

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Bubble Sort

abcdej j+1


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Bubble Sort

abcde

abcedj j+1


j j+1

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Bubble Sort

abcde

abced

abecdj j+1


j j+1

j j+1

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Bubble Sort

abcde

abced

abecd

aebcdj j+1


j j+1

j j+1

j j+1

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Bubble Sort

abcde

abced

abecd

aebcd

eabcdSorted

First pass throughouter loopi = 0


j j+1

j j+1

j j+1

j j+1

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Bubble Sort

abcde

abced

abecd

aebcd

eabcdSorted


j j+1

j j+1

j j+1

j j+1

First pass throughouter loopi = 0

for(int i=0;i<A.size()-1;++i){ for (int j=0; j<A.size()-(i+1);++j){

}}

for(int i=0;i<A.size()-1;++i){ for (int j=0; j<A.size()-(i+1);++j){

}}

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Bubble Sort

eabcd

eabdc

eadbc

edabc

Second pass throughouter loopi = 1

Sorted


j j+1

j j+1

j j+1

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Bubble Sort

edabc

edacb

edcab

Third pass throughouter loopi = 2

Sorted


j j+1

j j+1

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Bubble Sort

edcab

edcba

Fourth pass throughouter loopi = 3

Sorted


j j+1

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Bubble Sort Algorithm

import java.util.*;public class DemoSorting {

public static void bubbleSort(ArrayList<Integer> A){ for (int i=0; i<A.size()-1; ++i){ for (int j=0; j<A.size()-(i+1); ++j){ if (A.get(j) > A.get(j+1)){ Collections.swap(A, j, j+1); } } } }

public static void main(String[] args) { ArrayList<Integer> A = new ArrayList<Integer>(); A.add(6274); A.add(4892); A.add(2843); A.add(9523); A.add(1892); bubbleSort(A); for(Integer i : A) System.out.print(i + " "); } }}

What is the Big-Oh?


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Sorting in Place – Selection SortSorting

The main idea:• We find the smallest element and put it in the first position.• Then we find the next smallest element and put it in the second position.• Continue this way until the entire collection is sorted.

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Sorting in Place – Selection Sort

18929523284348926274

Unsorted

Sorting

62749523284348921892

Sorted

62749523489228431892

62749523489228431892

95236274489228431892

The main idea:• We find the smallest element and put it in the first position.• Then we find the next smallest element and put it in the second position.• Continue this way until the entire collection is sorted.

Unsorted array

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Selection Sort

import java.util.*;public class Main {

public static void selectionSort(ArrayList<Integer> A){ for (int i=0; i<A.size()-1; ++i){ int minIndex = i; for (int j=i+1; j<A.size(); ++j) if (A.get(j) < A.get(minIndex)) minIndex = j; Collections.swap(A, i, minIndex); } } public static void main(String[] args) { ArrayList<Integer> A = new ArrayList<Integer>(); A.add(6274); A.add(4892); A.add(2843); A.add(9523); A.add(1892); selectionSort(A); for(Integer i : A) System.out.print(i + " "); }}

Sorting (Sedgewick, 273)

What’s the Big-Oh?

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Sorting in Place – Insertion SortSorting (Sedgewick, 274; Bentley, 115–116)

The main idea:• Examine the elements one at a time• Insert each into its proper order among the elements already examined

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Sorting in Place – Insertion Sort

18929523284348926274

Unsorted

Sorting (Sedgewick, 274; Bentley, 115–116)

18929523284348926274

Sorted

18929523284362744892

18929523627448922843

18929523627448922843

95236274489228431892

The main idea:• Examine the elements one at a time• Insert each into its proper order among the elements already examined

Unsorted array

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Insertion Sort

import java.util.*;public class Main {

public static void insertionSort(ArrayList<Integer> A){ for( int i=1; i<A.size(); ++i ) for( int j=i; j>0 && A.get(j-1)>A.get(j); --j ){ Collections.swap(A, j, j-1); } } public static void main(String[] args) { ArrayList<Integer> A = new ArrayList<Integer>(); A.add(6274); A.add(4892); A.add(2843); A.add(9523); A.add(1892); insertionSort(A); for(Integer i : A) System.out.print(i + " "); }}

Sorting (Bentley, 115–116)

What’s the Big-Oh?

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Stable Sorting

Items that have equal key values are kept in their original order


Second sort – with the state as a keyFirst sort – with the city as a keyUnsorted

San Francisco, CADetroit, MIAustin, TX

Los Angeles, CAAnn Arbor, MIDetroit, MI

Austin, TXMonterey, CADallas, TX

Detroit, MILos Angeles, CASan Francisco, CA

Ann Arbor, MIHouston, TXSan Antonio, TX

San Antonio, TXSan Francisco, CASacramento, CA

Houston, TXSan Antonio, TXLos Angeles, CA

Dallas, TXSacramento, CAAnn Arbor, MI

Sacramento, CADallas, TXMonterey, CA

Monterey, CAAustin, TXHouston, TX

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Sorting Algorithms

So far, we’ve studied:

Sorting

O(n)O(n2)Insertion sort

O(n2)O(n2)Selection sort

O(n2)O(n2)Bubble sort

Best caseefficiencyWorst case efficiencyAlgorithm

Next• Shell sort• Quick sort

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Sorting Demos

Race Demo:Bubble Sort vs. Heap Sort vs. Quick Sort

Animated Sorting Web Sites:http://www.cosc.canterbury.ac.nz/people/mukundan/dsal/appldsal.html

http://www.cs.ubc.ca/spider/harrison/Java/sorting-demo.html

http://cg.scs.carleton.ca/~morin/misc/sortalg/

Sorting

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References

Bentley, J., Programming Pearls, Second Edition. Boston: Addison-Wesley, 2000.

Dale, N., C++ Plus Data Structures. Boston: Jones and Bartlett Publishers, 2003.

Gilberg, R. F. and B. A. Forouzan, Data Structures, A Pseudocode Approach with C. Boston: PWS Publishing Company, 1998.

Goodrich, M. T., D. Mounts, and R. Tamassia, Data Structures and Algorithms in C++. Hoboken, NJ: John Wiley & Sons, Inc., 2004.

Goodrich, M. T. and R. Tamassia, Data Structures and Algorithms in Java. Hoboken, NJ: John Wiley & Sons, Inc., 2006.

Knuth, D. E., The Art of Computer Programming, Second Edition, Volume 3 / Sorting and Searching. Boston: Addison-Wesley, 1998.

Sedgewick, R., Algorithms in C++, Third Edition. Boston: Addison-Wesley, 1998.

Documents

1 Today’s Objectives Announcements Hand in Homework 4 – no late assignments accepted! No email submissions! The final exam will be on 1-May at 7 p.m