List Comprehension, Dictionaries &Benchmark Analysis

Prakash Gautaminfo@prakashgautam.com.nphttps://prakashgautam.com.np/6cs008

Agenda

➔ List Comprehension➔ Benchmark Analysis➔ Dictionaries

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List Comprehension

➔ Explicitly write the whole thing

➔ Write a loop to create it

Squares = [0,1,4,9,16,25,36,49,64,81,100]

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Squares = []for i in range(11)

Squares.append(i*i)

List Comprehension

➔ Write a loop to create it

➔ Write a List Comprehension

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Squares = []for i in range(11)

Squares.append(i*i)

Squares = [i*i for i in range(11)]

List Comprehension

➔ Write a List Comprehension

➔ List Comprehension is a concise description of list➔ List Comprehension is a shorthand for a loop

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Squares = [i*i for i in range(11)]

List Comprehension

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[expression for item in list if conditional]

for item in list: if conditional:

expression

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1. List of Squares

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Squares = [i**2 for i in range(1,101)]print(Squares)

Squares = []for i in range(1,101):

Squares.append(i**2)print(Squares)

2. Remainders of 5

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Remainder5 = [i**2%5 for i in range(1,10)]print(Remainder5)

P-Remainders = [i**2%p for i in range(0,p)

Quadratic Reciprocity [(p+1)/2]

Carl Friedrich Gauss

3. Movie that starts with ‘G’

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gmovies = [title for title in movies if title.startswith(“G”)]print(gmovies)

movies = [a,b,c,....,n]gmovies = []for title in movies:

if title.startswith(“G”):gmovies.append(title)

print(gmovies)

4. List of tuples containing movie name & R year

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gmovies = [title for(title,year) in movies if year<2000]print(gmovies)

movies = [(a,1941),(b,2000),....,(n,2017)]gmovies = []for (title,year) in movies:

if year<2000:gmovies.append(title)

print(gmovies)

5. Scalar Multiplication

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v = [10, -2, 3]vem = [4*x for x in v]print(vem)

6. Cartesian Product

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A = {1,3} & B = {x,y}A x B = {(1,x),(1,y),(3,x),(3,y)}

cp = [(a,b) for a in A for b in B]print(cp)

Rene Descartes

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def double(x):return x*2

Xy = [double(x) for x in range(10]print(Xy)

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print([x+y for x in [10,20,30] for y in [1,2,3]])

Num_list = [y for y in range(100) if y%2==0 if y%5==0]print(Num_list)

Ob = [“Even” if i%2==0 else “Odd” for i in range(10)]print(Ob)

List Comprehension

➔ An elegant way to define and create lists based on existing lists➔ More compact & faster than normal functions & loops for creating lists➔ Every LC can be converted into for loop but viceversa may not be true

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Benchmark Analysis

➔ If comparisons done correctly: its called benchmarking➔ Lets analyze some sorting algorithms

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# Integers 100 10,000 1,000,000

Insertion 0.57 6064

Selection 0.63 6293

Bubble 1.43 15628

Merge 0.25 48.3 7023

Quick 0.25 44.4 7153

Tim 0.02 3.7 690

Randomly Ordered Input (Time in Milliseconds)

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# Integers 10,000 1,000,000

Insertion 8.8

Selection 6278

Bubble 1.6

Merge 45.5 6561

Quick 35.9 5044

Tim 0.2 20.8

Already Sorted Input (Time in Milliseconds)

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# Integers 10,000 1,000,000

Insertion 12028

Selection 6882

Bubble 22338

Merge 48.2 6851

Quick 37.1 5285

Tim 0.2 20

Reverse Sorted Input (Time in Milliseconds)

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# Integers 10,000 1,000,000

Insertion 6037

Selection 6270

Bubble 15496

Merge 48.4 6871

Quick 43.6 Failed

Tim 3.3 386

Random Ordered Input with many duplicates

Observations

➔ Python’s built-in Timsort is crazy fast in all tests➔ Bubble sort: extremely slow except already sorted➔ Insertion sort faster than selection sort except for reverse sorted input➔ Quicksort is generally faster than Mergesort

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Timsort

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def TimSort():for x in range(0, len(arr), RUN):

arr[x:x+RUN] = Insertion(arr[x:x+RUN])RUNinc = RUNWhile RUNinc < len(arr):

for x in range(0, len(arr), 2*RUNinc):arr[x:x+2*RUNinc]=merge(arr[x:x+RUNinc], arr[x+RUNinc:x+2*RUNinc])

RUNinc=RUNinc*2

Timsort

➔ Designed in 2002 by Tim Peters➔ Adaptive, Inplace & Stable➔ Default Sorting: JAVA, Android, Python➔ Time Complexity(Asymptotic Analysis)

◆ Best: O(n)◆ Worst: O(nlogn)

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Tuples

Seemingly Similar to Lists

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Tuples are immutable

Unlike lists we cannot change elements

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Dictionaries

➔ List◆ A linear collection of values that stay in order

➔ Dictionary◆ A bag of values, each with its own label

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Dictionaries

➔ It organizes linked information➔ Examples:

◆ Word & Definition◆ Name & Phone Number◆ Username & Password

➔ If you know the 1st entry, you can immediately get the 2nd one➔ The first item is key and second is value➔ Keys: Immutable➔ Lists can’t be keys, why?

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Dictionaries

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>>d={“id”:100, “code”: “A500ND10”, “language”: “English”, “location”: “(27.450745, 87.349823)}

Key Value

id 100

code A500ND10

language English

location 27.450745, 87.349823

Dictionaries

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>>type(d)<class ‘dict’>

#Define dictionary using dict constructor>>d2 = dict(code = “A500ND10”, language: “English”)

#Adding new data in d2 (quotes are necessary)>>d2[“id”]=100>>print(d2)>>print(d2[‘language’])

Dictionaries

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#Define dictionary using dict constructor>>d2 = dict(code = “A500ND10”, language: “English”)

#Adding new data in d2 (quotes are necessary)>>d2[“id”]=100>>print(d2) #It works>>print(d2[‘language’]) #It works>>print(d2[‘location’]) #Will it work?

Dictionaries

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#Define dictionary using dict constructor>>d2 = dict(code = “A500ND10”, language: “English”)

>>print(d2[‘location’]) #Will it work?>>#Solution 1>>if ‘location’ in d2:

print(d2[‘location’]) else:

print(“The collection doesn’t have location details”)

Dictionaries

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#Define dictionary using dict constructor>>d2 = dict(code = “A500ND10”, language: “English”)

>>print(d2[‘location’]) #Will it work?>>#Solution 2>>try:

print(d2[‘location’]) except keyError:

print(“The collection does not have location details”)

Dictionaries

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#How many methods dict have?>>dir(d2)

#To see what the specific method does>>help(d2.get)

>>loc = d2.get(‘location’, None)>>print(loc)

#To Print all key-value pairs>>for key in d2.keys():

value = d2[key] print(key, “=” , value)

Dictionaries

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#To Print all key-value pairs>>for key, value in d2.items(): print(key, “=” , value)

Defining Dictionaries

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No duplicate keys

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Old values gets overwritten instead…!

Access

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We can access values by keys, but not the other way around

All keys, values or both

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Use d.keys( ), d.items( ) and d.values( )

Loop over Dictionaries

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Print all key-value pairs of Dictionary

Dictionaries are collection of key-value pairs

Example: the keys are all words in the English language, and their corresponding values are the meanings.

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Dictionaries: Complexity Analysis

➔ O(1): Constant Time◆ Anytime program takes constant # instructions regardless of the input◆ Accessing any element in Dict or List◆ Appending an element in Dict or List◆ Pushing an element onto the front

➔ O(n): Linear Time◆ When the program takes time i.e directly proportional to the input size◆ Creating a List with n elements◆ Traversing

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Dictionaries: Complexity Analysis

➔ O(n2): Quadratic Time◆ When n hits a value of 10,000: n2 gets pretty big (100,000,000). ◆ Doubly nested loop that I've gone over in class so many time is O(n2)

● for i in xrange(n): for j in xrange(i): pass➔ O(logn): Logarithmic Time

◆ Binary Search➔ O(nlogn): Poly-Logarithmic Time

◆ Timsort

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THANK YOU

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