lec31 - University at Buffalo · Selection vs Merge sort # comparisons are a good measure of work...

CSE 115Introduction to Computer Science I

Road map

▶︎ Review ◀

Linear vs Binary Search

Selection vs Merge Sort

Defining Custom Sorts

Empirical Demo

Music Rating App

index.html downloaded

myCode.js downloaded

Browser Navigates to

the app's [email protected]("/")# return static file:# index.html

HTTP Request for path "/"

User ServerThe Internet

@bottle.route("/myCode.js")# return static file:# myCode.js

HTTP Request for path "/myCode"

@bottle.route('/songs')# call get_songs() in the # ratings.py file

AJAX HTTP GET Request for path "/songs"

JSON formatted songs and ratings -Convert to HTML and set as the innerHTML of the songs div

Music Rating AppUser ServerThe Internet

@bottle.route('/add_song')# -read the new song# -call add_song from the# ratings.py file# -the song is appended to# songs.csv

AJAX HTTP POST Request for path

"/add_song"

User enters a new song and clicks button

Handle POST requests until the user leaves the site


@bottle.route('/rate_song')# -call rate_song from the# ratings.py file# -the rating is appended to# ratings.csv

AJAX HTTP POST Request for path

"/rate_song"User clicks a rating button


Music Rating App - Expansions

Prevent Multiple Ratings• Users can rate the same songs as many times as they can click

(or write a program to spam ratings)• Discussion: How would we prevent this?

Update Titles and Artists• If the user to add a song uses the wrong title/artist, it cannot be

updated later• Could make it so any user can edit these fields

Reviews• Add reviews to the ratings so users can share their opinions

instead of just numbers

Music Rating App - Expansions

Style• Add star ratings instead of displaying all ratings for each song• Add color and CSS

Sorting (module 4 foreshadow)• Sort the songs based on average rating, artist, or number of

ratings

Security (module 4 foreshadow)• This site is not secure!• Vulnerable to HTML/JavaScript injection• No encryption of HTTP requests• Preventing multiple ratings without compromising privacy

Road map

▶︎ Review ◀




Empirical Demo

Algorithms

An algorithm is

"a set of rules for solving a problem in a finite number of steps"

https://www.dictionary.com/browse/algorithm

Road mapExam return

Review

Algorithms

▶︎ Linear vs Binary Search ◀



Empirical Demo

Linear searchdef linearSearch(X, Z): for Y in X: if Y == Z: return True return False

Linear search

"AR" "BS" "BQ" "CD" "FW" "GM" "KD" "LP" … "JK"

def linearSearch(X, Z): for Y in X: if Y == Z: return True return False

0 1 2 3 4 5 6 7 … N-1

"KD"

IS "AR" == "KD"?



0 1 2 3 4 5 6 7 … N-1

"KD"

IS "BS" == "KD"?



0 1 2 3 4 5 6 7 … N-1

"KD"

IS "BQ" == "KD"?



0 1 2 3 4 5 6 7 … N-1

"KD"

IS "CD" == "KD"?



0 1 2 3 4 5 6 7 … N-1

"KD"

IS "FW" == "KD"?



0 1 2 3 4 5 6 7 … N-1

"KD"

IS "GM" == "KD"?



0 1 2 3 4 5 6 7 … N-1

"KD"

IS "KD" == "KD"?



0 1 2 3 4 5 6 7 … N-1

return True

"KD"

IS "KD" == "KD"?

Binary searchdef binarySearch(X, Z): left = 0 right = len(X) while (right - left) > 0: mid = (left + right)//2 if Z < X[mid]: right = mid elif Z > X[mid]: left = mid+1 else: return True return False

Binary search

def binarySearch(X, Z): left = 0 right = len(X) while (right - left) > 0: mid = (left + right)//2 if Z < X[mid]: right = mid elif Z > X[mid]: left = mid+1 else: return True return False


0 1 2 3 4 5 6 7 8

"KD"

"KD" > "FW"

Binary search



0 1 2 3 4 5 6 7 8

"KD"

"KD" == "KD"

Binary search



0 1 2 3 4 5 6 7 8

"KD"

"KD" == "KD"

return True

Linear vs Binary search # comparisons are a good measure of work

x == y comparison eliminates 1 item from consideration

If input has N items, in worst case we need to do N comparisons

x < y, x > y comparisons eliminate half of items from consideration

If input has N items, in worst case we need to do log2(N) comparisons

Road mapExam return

Review

Algorithms


▶︎ Selection vs Merge Sort ◀


Empirical Demo

SortingGiven a sequence of values that can be ordered, sorting involves rearranging these values so they go from smallest to largest (or largest to smallest).

Example:

[17, 93, 12, 44, 82, 81, 22, 73]

all mixed up

Sorting rearranges items:

[12, 17, 22, 44, 73, 81, 82, 93]

increasing smallest largest

Selection sortGiven a list of values, repeatedly select the smallest value and push it to the end of a list of sorted values.

Selection sortUNSORTED LIST [17, 93, 12, 44, 82, 81, 22, 73]

[] SORTED LIST


[] SORTED LIST

Smallest from unsorted is 12.


[] SORTED LIST

Remove 12 from unsorted.

Selection sortUNSORTED LIST [17, 93, 44, 82, 81, 22, 73]

[12] SORTED LIST

Add 12 to end of sorted.

Selection sortUNSORTED LIST [17, 93, 44, 82, 81, 22, 73]

[12] SORTED LIST


Selection sortUNSORTED LIST [ 93, 44, 82, 81, 22, 73]

[12] SORTED LIST


Selection sortUNSORTED LIST [93, 44, 82, 81, 22, 73]

[12, 17] SORTED LIST


Selection sortUNSORTED LIST [93, 44, 82, 81, 22, 73]



Selection sortUNSORTED LIST [93, 44, 82, 81, 73]




[12, 17, 22] SORTED LIST


Selection sortUNSORTED LIST [93, 82, 81, 73]




[12, 17, 22, 44] SORTED LIST


Selection sortUNSORTED LIST [93, 82, 81 ]

[12, 17, 22, 44] SORTED LIST


Selection sortUNSORTED LIST [93, 82, 81]

[12, 17, 22, 44, 73] SORTED LIST


Selection sortUNSORTED LIST [93, 82 ]

[12, 17, 22, 44, 73] SORTED LIST


Selection sortUNSORTED LIST [93, 82]

[12, 17, 22, 44, 73, 81] SORTED LIST


Selection sortUNSORTED LIST [93 ]

[12, 17, 22, 44, 73, 81] SORTED LIST


Selection sortUNSORTED LIST [93]

[12, 17, 22, 44, 73, 81, 82] SORTED LIST


Selection sortUNSORTED LIST [ ]

[12, 17, 22, 44, 73, 81, 82] SORTED LIST


Selection sortUNSORTED LIST []

[12, 17, 22, 44, 73, 81, 82, 93] SORTED LIST


Selection sortUNSORTED LIST []

[12, 17, 22, 44, 73, 81, 82, 93] SORTED LIST

Since the unsorted list is empty, we're done!

Selection sortdef removeSmallest(X): smallestIndex = 0 for Y in range(1,len(X)): if X[Y] < X[smallestIndex]: smallestIndex = Y return X.pop(smallestIndex)

def selectionSort(X): sorted = [] while len(X) > 0: sorted.push(removeSmallest(X)) return sorted

Merge sortGiven a list of values, split into in left and right partitions of roughly equal size. Sort each partition, then merge the two sorted partitions.

Merge sort basic idea

[17, 93, 12, 44, 82, 81, 22, 73]

Merge sort split into partitions

[17, 93, 12, 44, 82, 81, 22, 73]

[17, 93, 12, 44][82, 81, 22, 73]

Merge sort sort partitions

[17, 93, 12, 44, 82, 81, 22, 73]

[17, 93, 12, 44][82, 81, 22, 73]

.

.

.

[12, 17, 44, 93][22, 73, 81, 82]

Merge sort merge partitions

[17, 93, 12, 44, 82, 81, 22, 73]

[17, 93, 12, 44][82, 81, 22, 73]

.

.

.

[12, 17, 44, 93][22, 73, 81, 82]

[12, 17, 22, 44, 73, 81, 82, 93]

Merge sort merge partitions

[17, 93, 12, 44, 82, 81, 22, 73]

[17, 93, 12, 44][82, 81, 22, 73]

[17, 93][12, 44][82, 81][22, 73]

[17][93][12][44][82][81][22][73]

[17, 93][12, 44][81, 82][22, 73]

[12, 17, 44, 93][22, 73, 81, 82]

[12, 17, 22, 44, 73, 81, 82, 93]

Merge sortdef merge(X, L, M, R): temp = [] lp = L rp = M while lp < M and rp < R: if X[lp] < X[rp]: temp.append(X[lp]) lp = lp + 1 else: temp.append(X[rp]) rp = rp + 1 while lp < M: temp.append(X[lp]) lp = lp + 1 while rp < R: temp.append(X[rp]) rp = rp + 1 for i in range(L,R): X[i] = temp[i-L]

def mergeSortHelper(X, Left, Right): if Right - Left > 1 : Mid = (Left + Right) // 2 mergeSortHelper(X, Left, Mid) mergeSortHelper(X, Mid, Right) merge(X, Left, Mid, Right)

def mergeSort(X) : mergeSortHelper(X, 0, len(X)) return X

Selection vs Merge sort # comparisons are a good measure of work

If input has N items:

A complete sort requires roughly N2 x<y comparisons.

N2 grows quickly:

(2N)2 = 4 N2

Double input size quadruples work needed.

If input has N items:

A complete sort requires roughly N*log2(N) x<y comparisons.

N*log2(N) grows slowly:

(2N)*log2(2N) = 2N*(log2(2)+log2(N)) =2N*(1+log2(N))

Double input size a little more than doubles work needed.

For next time:Draw graphs (by hand) of N2 and N*log2(N) over range 100 to 100,000.

lec31 - University at Buffalo · Selection vs Merge sort # comparisons are a good measure of work...

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