Week11.pptx

7/27/2019 Week11.pptx

1/42

CS1010: Programming Methodologyhttp://www.comp.nus.edu.sg/~cs1010/
http://www.comp.nus.edu.sg/~cs1101/http://www.comp.nus.edu.sg/~cs1101/

7/27/2019 Week11.pptx

2/42

Week 11: Searching and Sorting

Objectives: Understand the basic searching algorithms and

sorting algorithms

Introduce the concept of complexity analysis

(informally)

Implement the searching and sorting algorithms

using arrays.

Reference: Chapter 6 Arrays

Lesson 6.7

CS1010 (AY2011/2 Semester 1) Week11 - 2

7/27/2019 Week11.pptx

3/42

Week 11: Outline (1/2)

0. Week 10 Strings Exercise 4: Counting the

Exercise 5: Find Elements

Command-line Arguments

1. Introduction

2. Searching

3. Linear Search (Demo #1)

4. Exercise #1: Compatible Teammate

5. Binary Search


7/27/2019 Week11.pptx

4/42

Week 11: Outline (2/2)

6. Sorting

7. Selection Sort (Demo #2)

8. Bubble Sort (Demo #3)

9. More Sorting Algorithms10. Animated Sorting Algorithms

11. Exercise #2 (take-home): Module Sorting


7/27/2019 Week11.pptx

5/42

Week 10: 9. Ex4 (take-home): Countingthe (1/2) Write a program Week10_CountThe.c to count the

number of times the appears in users input.

The program ends when the user enters an empty

string.

The string the may be entered with leading or/and

trailing spaces, may contain uppercase or lowercase

letter, or may be part of a longer word.

You may assume that each string entered by the usercontains at most 30 characters.

Hint: Use the strstr() function and other appropriate

function(s).

Week10 - 5CS1010 (AY2011/2 Semester 1)

7/27/2019 Week11.pptx

6/42

Week 10: 9. Ex4 (take-home): Countingthe (1/2) A sample run:

Enter strings, each with

7/27/2019 Week11.pptx

7/42

Week 10: 10. Exercise #5: Find Elements

Write a program Week10_FindElements.c that breaks acompound into its elemental components, assuming that each

element name begins with an uppercase letter.

(If you are interested in the element period table, you may refer

to: http://www.webelements.com/)

You may assume that each compound is at most 10 characterslong, and each element is at most 3 characters.

Hint: Use strcpy and strncpy.

Sample run:Enter a compound: H2ZrCO4

The elements are:H2ZrCO4

http://www.webelements.com/http://www.webelements.com/

7/27/2019 Week11.pptx

8/42

Week 10: 11. Command-line Arguments (1/2)

So far, our main function header looks like this:int main(void)

We can pass arguments to a program when we run it:

a.out water "ice cream" 34+7

Add two parameters in the main function header:

int main(int argc, char *argv[])

Parameterargcstands for argument count

Parameterargvstands for argument vector. It is an array of

pointers to strings.

argv[0] is the name of the executable file (sometimes also

called the command)

You can name them anything, but the names argc and argv

are commonly used.


7/27/2019 Week11.pptx

9/42

#include int main(int argc, char *argv[]){

int count;printf ("This program was called with \%s\\n, argv[0]);if (argc > 1)

for (count = 1; count < argc; count++)

printf("argv[%d] = %s\n", count, argv[count]);else

printf("The command had no argument.\n");

return 0;}


Week 10: 11. Command-line Arguments (2/2)

gcc Week10_CommandLineArgs.c

a.out water "ice cream" 34+7This program was called with "a.out"argv[1] = waterargv[2] = ice creamargv[3] = 34+7

Week10_CommandLineArgs.c

7/27/2019 Week11.pptx

10/42

You have accumulated quite a bit of basic programmingexperience by now.

Today, we will study some simple yet useful classical

algorithms which find their place in many CS applications

Searching for some data amid very large collection of data

Sorting very large collection of data according to some order

We will begin with an algorithm (idea), and show how the

algorithm is transformed into a C program

(implementation).

This brings back (reminds you) our very first lecture: the

importance of beginning with an algorithm.


1. Introduction

7/27/2019 Week11.pptx

11/42

Searching is a common task that we carry out withoutmuch thought everyday.

Searching for a location in a map

Searching for the contact of a particular person

Searching for a nice picture for your project report Searching for a research paper required in your course.

In this lecture, you will learn how to search for an item

(sometimes called a search key) in an array.


2. Searching (1/2)

7/27/2019 Week11.pptx

12/42

Problem statement:Given a list (collection of data) and a search key X, return the

position of X in the list if it exists.

For simplicity, we shall assume there are no duplicate values in

the list. We will count the number of comparisons the algorithms

make to analyze their performance.

The ideal searching algorithm will make the least possible

number of comparisons to locate the desired data.

We will introduce worst-case scenario.

(This topic is called analysis of algorithms, which will be formally

introduced in CS1020. Here, we will give an informal introduction just for

an appreciation.)


2. Searching (2/2)

7/27/2019 Week11.pptx

13/42

Also known as Sequential Search

Idea: Search the list from one end to the other end in linear

progression.

Algorithm


// Search for key in list A with n items

linear_search(A, n, key)

{

for i = 0 to n-1

if Ai is key then report i}

87 12 51 9 24 63

Example: Search for 24in this list

no no no no yes!

Question: What to report if key is not found?

Aim for a clean design

3. Linear Search

7/27/2019 Week11.pptx

14/42

If the list is an array, how would youimplement the Linear Search algorithm?


// To search for key in arr using linear search// Return index if found; otherwise return -1

int linearSearch(int arr[], int size, int key){int i;for (i=0; i

7/27/2019 Week11.pptx

15/42

We use the number of comparisons here as a roughmeasurement.

Analysis is done for best case, average case, and worstcase. We will focus on the worst case.

For an array with n elements, in the worst case,

What is the number of comparisons in our linear_searchalgorithm?

Under what circumstances do we encounter the worst case?


3. Linear Search: Performance

7/27/2019 Week11.pptx

16/42

Problem: Given three arrays: The first array contains theplayers names. The second array stores the players ages

corresponding to the entries in the first array. The third array

contains the gender information for each player corresponding

to the entries in the first array.

Your task is to accept as input a players name and find acompatible teammate for this player. A compatible teammate

is one who is of the same age but opposite sex.

Analysis:

Inputs: char player_name[STR_LENGTH+1];char names[MAX_PLAYER][STR_LENGTH+1];

int ages[MAX_PLAYER];

char genders[MAX_PLAYER];


4. Exercise #1: Compatible Teammate (1/3)

7/27/2019 Week11.pptx

17/42


Sample run:

Given an incomplete program Week11_TeamMate.c,

complete the program by filling in the search_teammate()

function.

Enter 5 players info:Alvin 23 MByron 21 MMay 19 FJune 21 F

Jupiter 22 MThe list of players are:Name Age GenderAlvin 23 MByron 21 MMay 19 FJune 21 FJupiter 22 M

Enter a player's name: ByronByrons compatible teammate is June.

Enter a player's name:AlvinSorry, we cannot find a teammate forAlvin!

or

Enter a player's name: John

No such player John.

or

4. Exercise #1: Compatible Teammate (2/3)

7/27/2019 Week11.pptx

18/42


int main(void) {char names[MAX_PLAYER][STR_LENGTH+1];

int ages[MAX_PLAYER];char genders[MAX_PLAYER];char player_name[STR_LENGTH+1];int i, result;

printf("Enter %dplayers' info:\n", MAX_PLAYER);for (i=0; i

7/27/2019 Week11.pptx

19/42

5. Binary Search (1/6)

You are going to witness a radically different approach,one that has become the basis of many well-knownalgorithms.

The idea is simple and fantastic, but applied on the

searching problem, it has this pre-condition that the listmust be sorted before-hand.

How the data is organized (in this case, sorted) usuallyaffects how we choose/design an algorithm to accessthem.

In other words, sometimes (actually, very often) we seekout new way to organize the data so that we can processthem more efficiency.


7/27/2019 Week11.pptx

20/42


The algorithm Look for the key in the middle position of the list. Either of the

following 2 cases happens:

If the key is smaller than the middle element, then discard the

right half of the list and repeat the process.

If the key is greater than the middle element, then discard the

left half of the list and repeat the process.

Terminating condition: when the key is found, or when all

elements have been discarded


7/27/2019 Week11.pptx

21/42


Example: Search for key = 23


5 12 17 23 38 44 77 84 90

[0] [1] [2] [3] [4] [5] [6] [7] [8]array

1. low = 0, high = 8, mid = (0+8)/2 = 4

2. low = 0, high = 3, mid = (0+3)/2 = 13. low = 2, high = 3, mid = (2+3)/2 = 2

4. low = 3, high = 3, mid = (3+3)/2 = 3

Found!

Return 3

7/27/2019 Week11.pptx

22/42


In binary search, each step eliminates the problem size(array size) by half.

The problem size gets reduced to 1 very quickly (see next slide)

This is a simple yet powerful strategy, of halving the

solution space in each step Which lab exercise employs similar strategy?

Such strategy, a special case ofdivide-and-conquerparadigm, can be naturally implemented using recursion

(a topic we have just covered last week) At the moment, we will stick to repetition (loop)

You can write the recursion version by yourself after class.


7/27/2019 Week11.pptx

23/42

5. Binary Search (5/6): Performance

Worst-case analysis


Array size

n

Linear Search

(ncomparisons)

Binary search

(log2ncomparisons)

100 100 7

1,000 1,000 10

10,000 10,000 14

100,000 100,000 ?

1,000,000 1,000,000 ?

109 109 ?

7/27/2019 Week11.pptx

24/42

// To search for key in sorted arr using binary search// Return index if found; otherwise return -1int binarySearch(int arr[], int size, int key){

int low = 0, high = size 1, mid = (low + high)/2;

}

binary_search.c

5. Binary Search (6/6): Code

Using iteration. (We will discuss the recursive version in discussionsession.)


7/27/2019 Week11.pptx

25/42

6. Sorting (1/2) Sorting is any process of arranging items in some

sequence and/or in different sets Wikipedia.

Sorting is important because once a set of items is sorted,

many problems (such as searching) become easy. Searching can be speeded up.

Determining whether the items in a set are all unique. Finding the median item in the set.

etc.


7/27/2019 Week11.pptx

26/42

6. Sorting (2/2)

Problem statement:Given a list ofn items, arrange the items into ascending

order.

We will implement the list as an integer array.

We will introduce two basic sort algorithms.

We will count the number of comparisons the algorithms

make to analyze their performance.

The ideal sorting algorithm will make the least possible number of

comparisons to arrange data in a designated order.

We will compare the algorithms by analyzing theirworst-

case performance.


7/27/2019 Week11.pptx

27/42

7. Selection Sort (1/3)


The algorithmStep 1: Find the smallest element in the list (find_min)

Step 2: Swap this smallest element with the element in the first

position. (Now, the smallest element is in the right place.)

Step 3: Repeat steps 1 and 2 with the list having one fewerelement (i.e. the smallest element just found and placed is

discarded from further processing).

7/27/2019 Week11.pptx

28/42



n = 9

23 17 5 90 12 44 38 84 77

[0] [1] [2] [3] [4] [5] [6] [7] [8]array

1st pass:

first min

5 17 23 90 12 44 38 84 772nd pass:

first min

5 12 23 90 17 44 38 84 773rd pass:

first min

5 12 17 90 23 44 38 84 774th pass:

first min

7/27/2019 Week11.pptx

29/42



n = 9

5 12 17 23 90 44 38 84 775th pass:

first min

5 12 17 23 38 44 90 84 776th pass:

first min

5 12 17 23 38 44 90 84 777th pass:

first min

5 12 17 23 38 44 77 84 908th pass:

first min

5 12 17 23 38 44 77 84 90Final array:

Q: How many passes for

an array with n elements?

7/27/2019 Week11.pptx

30/42

7. Demo #2: Selection Sort


// To sort arr in increasing order

voidselectionSort(int arr[], int size){

int i, start_index, min_index, temp;

for (start_index = 0; start_index < size-1; start_index++){

// each iteration of the for loop is one pass

// find the index of minimum elementmin_index = start_index;for (i = start_index+1; i < size; i++)

if (arr[i] < arr[min_index])min_index = i;

// swap minimum element with element at start_indextemp = arr[start_index];arr[start_index] = arr[min_index];arr[min_index] = temp;

}}

See selection_sort.c for full program

7/27/2019 Week11.pptx

31/42

7. Selection Sort: Performance We choose the number of comparisons as our basis of analysis.

Comparisons of array elements occur in the inner loop, where theminimum element is determined.

Assuming an array with n elements. Table below shows the numberof comparisons for each pass.

The total number of comparisons is calculated in the formula below.

Such an algorithm is call an n2 algorithm, orquadratic algorithm, interms of running time complexity.


Pass #comparisons

1 n 1

2 n 2

3 n 3

n 1 1

7/27/2019 Week11.pptx

32/42

8. Bubble Sort

Selection sort makes one exchange at the end of eachpass.

What if we make more than one exchange during each

pass?

The key idea of the bubble sort is to make pairwise

comparisons and exchange the positions of the pair if

they are out of order.


7/27/2019 Week11.pptx

33/42

8. One Pass of Bubble Sort0 1 2 3 4 5 6 7 8

23 17 5 90 12 44 38 84 77

17 23 5 90 12 44 38 84 77

17 5 23 90 12 44 38 84 77

17 5 23 12 90 44 38 84 77

17 5 23 12 44 90 38 84 77

17 5 23 12 44 38 90 84 77

17 5 23 12 44 38 84 90 77

17 5 23 12 44 38 84 77 90

exchange

ok

exchange

exchange

exchange

exchange

exchange

exchange


Done!Q: Is the array sorted?Q: What did we achieve?

7/27/2019 Week11.pptx

34/42

8. Demo #3: Bubble Sort


// To sort arr in increasing order

voidbubbleSort(int arr[], int size){

int i, limit, temp;

for (limit = size-2; limit >= 0; limit--){

// limit is where the inner loop variable i should end

for (i=0; i arr[i+1]) // swap arr[i] with arr[i+1]{

temp = arr[i];

arr[i] = arr[i+1];arr[i+1] = temp;}

}}

}

See bubble_sort.c for full program

Can we improved on this?

Will discuss on Friday.

7/27/2019 Week11.pptx

35/42

8. Bubble Sort Performance Bubble sort, like selection sort, requires n 1 passes for an array

with n elements.

The comparisons occur in the inner loop. The number of

comparisons in each pass is given in the table below.

The total number of comparisons is calculated in the formulabelow.

Like selection sort, bubble sort is also an n2 algorithm, orquadratic algorithm, in terms of running time complexity.


Pass #comparisons

1 n 1

2 n 2

3 n 3

n 1 1

7/27/2019 Week11.pptx

36/42

8. Bubble Sort: Enhanced version

It is possible to enhance bubble sort algorithm to reduce

the number of passes.

Suppose that in a certain pass, no swap is needed. This

implies that the array is already sorted, and hence the

algorithm may terminate without going on to the nextpass.

You will write this enhanced version for your discussion

session.


7/27/2019 Week11.pptx

37/42

9. More Sorting Algorithms

What we have introduced are 2 basic sort algorithms.Together with the Insertion Sort algorithm, these 3

algorithms are the simplest.

However, they are very slow, as their running time

complexity is quadratic.

Faster sorting algorithms exist and are topics in more

advanced modules such as CS1020.


7/27/2019 Week11.pptx

38/42

10. Animated Sorting Algorithms

There are a number of animated sorting algorithms on

the Internet

Here are two sites:

http://www.sorting-algorithms.com/

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

http://www.sorting-algorithms.com/http://www.cs.ubc.ca/~harrison/Java/sorting-demo.htmlhttp://www.cs.ubc.ca/~harrison/Java/sorting-demo.htmlhttp://www.cs.ubc.ca/~harrison/Java/sorting-demo.htmlhttp://www.cs.ubc.ca/~harrison/Java/sorting-demo.htmlhttp://www.sorting-algorithms.com/http://www.sorting-algorithms.com/http://www.sorting-algorithms.com/

7/27/2019 Week11.pptx

39/42

11. Exercise #2 (take-home): Module Sorting Write a program Week11_ModuleSorting.c: Given two arrays

with 10 elements: one containing the code of the modules, andthe other containing the number of students enrolled in that

module. Sort the modules according to the number of students

enrolled in that module, using Selection Sort, Bubble Sort, or

Insertion Sort (to be discussed at next lecture).

Sample run:


Enter module codes and students enrolled:CS1010 292CS1234 178CS1010E 358CS2102 260

IS1103 215IS2104 93IS1112 100GEK1511 83IT2002 51MA1101S 123

Sorted by student enrolment:IT2002 51GEK1511 83IS2104 93

IS1112 100MA1101S 123CS1234 178IS1103 215CS2102 260CS1010 292CS1010E 358

7/27/2019 Week11.pptx

40/42

Summary for Today

Searching algorithms Linear (sequential) search

Binary search

Basic sorting algorithms Selection sort

Bubble sort


7/27/2019 Week11.pptx

41/42

Announcements/Things-to-do

Revise Chapter 6: Numeric Arrays Lesson 6.7

PE2 this Saturday

29 October 2011, Saturday

See module website for details

Next weeks lecture:

Structures: Chapter 8

Lessons 8.1 8.5


7/27/2019 Week11.pptx

42/42

End of File

Date post:	14-Apr-2018
Category:	Documents
Upload:	minh-tieu
View:	221 times
Download:	0 times

Week11.pptx

Documents