tutorials 5-7

00-Introduction.ipynb

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 # Introduction to Python (for Algorithms 2)
 
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 by *James Booth* and *Ghislain Antony Vaillant*
 
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 ### Disclaimer
 
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 This notebook is by no means a comprehensive introduction to the Python programming language. It covers the essential language features required to implement, test and validate the Algorithms 202 courseworks. It is strongly advised to complement this tutorial with additional reading such as the [official Python documentation](https://docs.python.org/3/), [Python 101](https://leanpub.com/python_101) or the excellent [Hitchhiker's guide to Python](http://docs.python-guide.org/en/latest/).
 
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 ## Language basics
 
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 ### Syntax and features
 
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 #### Hello world
 
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 ``` python
 print("Hello, world!")
 ```
 
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 #### Built-in [functions](https://docs.python.org/3/library/functions.html)
 
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 ``` python
 print("Hello, world!")
 print("Hello,", "world!")
 print("{}, {}!".format("Hello", "world"))
 ```
 
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 ``` python
 help(print)
 ```
 
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 ``` python
 type(1.0)
 ```
 
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 ``` python
 assert(2 % 2 == 0)
 #assert(2 / 2 == 0)
 ```
 
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 #### Built-in [types](https://docs.python.org/3/library/stdtypes.html)
 
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 ``` python
 # Booleans
 B = True
 print(type(B))
 
 # Numeric types
 N = 1
 print(type(N))
 
 N = 1.0
 print(type(N))
 
 N = 1j
 print(type(N))
 
 # Strings
 N = "Hello, word"
 print(type(N))
 
 # Lists
 L = [False, 1.0, "Hello"]
 print(type(L))
 
 # Ranges
 R = range(10)
 print(type(R))
 
 # None
 print(type(None))
 ```
 
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 #### Dynamic typing
 
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 ``` python
 x = 3  # Defines a binding a variable named "x",
        # to an object of type integer with value 3.
 print('x is of type {} with value {}'.format(type(x), x))
 
 x = 2.0  # Redefine the binding between "x" and an
          # object of type float with value 2.0.
 print('x is of type {} with value {}'.format(type(x), x))
 ```
 
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 #### Strong typing
 
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 ``` python
 print(1 + '2')  # What is the intent here?
                 # "Explicit is better than implicit."
 ```
 
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 ``` python
 print(str(1) + '2')  # String concatenation.
 print(1 + int('2'))  # Integer summation.
 ```
 
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 #### Variables and scopes
 
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 ``` python
 a = 0
 
 if False:
     b = 1
 
 def my_function(c):
     d = 3
     print(a)  # a is global
     print(b)  # b is global
     print(c)  # c is local
     print(d)  # d is local
 
 my_function(2)
 ```
 
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 ### Control flow
 
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 #### `if` statements
 
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 ``` python
 # simple branching
 if condition:
     do_something()
 
 # 2-way branching
 if condition:
     do_something()
 else:
     do_other_thing()
 
 # switch-case style
 if condition:
     do_something()
 elif other_condition:
     do_other_thing()
 else:
     do_default_thing()
 ```
 
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 #### `while` statements
 
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 ``` python
 # loop until
 while condition:
     do_something()
 
 # loop until with break clause
 while condition:
     do_something()
     if specific_condition:
         break  # exit while loop regardless
     do_other_thing()
 
 # loop until with break clause
 while condition:
     do_something()
     if specific_condition:
         continue  # loop-back regardless
     do_other_thing()
 ```
 
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 #### `for` statements
 
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 ``` python
 for n in range(10):
     print(n)
 ```
 
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 ``` python
 numbers = [1, 2, 3]
 for number in numbers:
     print(number)
 ```
 
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 ``` python
 ingredients = ['carrots', 'leeks', 'potatoes']
 for index, ingredient in enumerate(ingredients):
     print(index, ingredient)
 ```
 
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 ### Data structures
 
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 #### Common concepts
 
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 ``` python
 # literals
 vowels = ['a', 'e', 'i', 'o', 'u', 'y']
 print('vowels: {}'.format(vowels))
 
 ```
 
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 ``` python
 # indexing
 print('the first vowel is: ' + vowels[0])
 print('the last vowel is: ' + vowels[-1])
 print('the second-to-last vowel is: ' + vowels[-2])
 ```
 
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 ``` python
 # slicing
 print('first three: {}'.format(vowels[:3]))
 print('last two: {}'.format(vowels[-2:]))
 print('middle ones: {}'.format(vowels[1:-1]))
 print('one each two: {}'.format(vowels[::2]))
 ```
 
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 ``` python
 # iteration
 for vowel in vowels:
     print(vowel.upper())
 ```
 
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 ``` python
 # enumeration
 for index, vowel in enumerate(vowels):
     print("vowel {} is {}".format(1+index, vowel))
 ```
 
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 #### Immutable sequences
 
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 ``` python
 vowels = ('a', 'e', 'i', 'o', 'u', 'y')
 print(type(vowels))
 ```
 
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 ``` python
 vowels[1] = 'b'
 ```
 
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 #### Mutable sequences
 
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 ``` python
 vowels = ['a', 'e', 'i', 'o', 'u', 'y']
 print(type(vowels))
 ```
 
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 ``` python
 vowels[1] = 'b'
 print(vowels)
 ```
 
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 #### Dictionaries
 
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 ``` python
 # build using literal construct: {k1: v1, k2:v2}
 D = {"one": 1,
      "two": 2,
      "three": 3}
 
 print('D: {}'.format(D))
 ```
 
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 ``` python
 # indexing
 print(D["one"])
 print(D["two"])
 print(D["three"])
 ```
 
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 ``` python
 # iterating
 for item in D.items():
     print(item)
 
 for key in D.keys():
     print(key)
 
 for value in D.values():
     print(value)
 ```
 
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 ### Functions
 
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 ``` python
 # Standard definiton
 def my_function(arg1, arg2):
     # Do something with arg1, arg2
     # ...
     return result
 ```
 
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 ``` python
 # Lambda definition
 x_power_x = lambda x: x**x
 print(x_power_x(2))
 ```
 
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 ## Application: Complexity analysis of bubble sort
 
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 ### Implementation
 
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 ``` python
 def bubble_sort(L):
     """
     Sorts the input list inplace using a deterministic version of the bubble sort algorithm [1].
 
     [1] https://en.wikipedia.org/wiki/Bubble_sort
     """
     max_pass = len(L) - 1
     for pass_num in range(max_pass):
         for i in range(max_pass-pass_num):
             if L[i+1] < L[i]:
                 L[i], L[i+1] = L[i+1], L[i]
     return L
 
 
 def my_sorted(iterable):
     """
     Returns the sorted elements of the iterable as a list.
     """
     return bubble_sort(list(iterable))
 ```
 
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 ### Unit testing
 
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 ``` python
 test_cases = [
     [3, 2, 1, 6, 5, 4],
     [6, 5, 4, 3, 2, 1],  # Worst case
     [1, 3, 2, 4, 6, 5],  # One pass required
 ]
 
 for case in test_cases:
     # Validate against built-in sorted
     #print(my_sorted(case), sorted(case))
     assert(my_sorted(case) == sorted(case))
 ```
 
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 ### Complexity analysis
 
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 #### Data generation
 
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 ``` python
 from random import randint
 help(randint)
 ```
 
 %%%% Output: stream
 
     Help on method randint in module random:
     
     randint(a, b) method of random.Random instance
         Return random integer in range [a, b], including both end points.
     
 
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 ``` python
 randlist = lambda n: [randint(1e1, 1e6) for i in range(n)]
 print(randlist(20))
 ```
 
 %%%% Output: stream
 
-    [973886, 409460, 337342, 398719, 273231, 700388, 243130, 347759, 604817, 319332, 721668, 8793, 485780, 541846, 42575, 77128, 47963, 528511, 342950, 552766]
+    [658042, 242361, 863569, 787057, 225873, 237945, 236740, 938816, 355375, 141558, 892528, 211345, 581149, 33164, 158996, 838642, 498178, 151876, 1675, 23323]
 
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 #### Timing method
 
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 ``` python
 def timed(f, *args, **kwargs):
     from time import clock
     before = clock()
     result = f(*args, **kwargs)
     after = clock()
     return after-before
 
 # Collect enough time samples
 timings = [timed(my_sorted, case) for case in [randlist(6) for n in range(1000)]]
 
 from statistics import mean
 print("min = {}, max = {}, mean = {}".format(
     min(timings), max(timings), mean(timings)))
 ```
 
 %%%% Output: stream
 
     min = 3.8399983616006945e-06, max = 0.0001740799257258993, mean = 9.804795816620452e-06
 
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 #### Experiment
 
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 ``` python
 sizes = list(range(1, 1000, 100)) + list(range(1000, 10000, 1000))
 timings = [timed(my_sorted, case) for case in [randlist(size) for size in sizes]]
 ```
 
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 #### Plotting
 
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 ``` python
 %matplotlib inline
 import matplotlib.pyplot as plt
 # Uncomment for details about the plot function
 #help(plt.plot)
 ```
 
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 ``` python
 plt.plot(sizes, timings, linewidth=4)
 plt.xlabel('size')
 plt.ylabel('time (s)')
 plt.xlim(0)
 plt.ylim(0)
 ```
 
 %%%% Output: execute_result
 
     (0, 16.67753193491971)
 
 %%%% Output: display_data
 
     ![](data:image/png;base64,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)
 
 %% Cell type:markdown id: tags:
 
 #### Fitting
 
 %% Cell type:code id: tags:
 
 ``` python
 from numpy import polyfit
 # Uncomment for details about polyfit
 #help(polyfit)
 
 poly = polyfit(sizes, timings, deg=2)
 ```
 
 %% Cell type:code id: tags:
 
 ``` python
 from numpy import polyval
 # Uncomment for details about polyval
 #help(polyval)
 
 fitted = polyval(poly, sizes)
 ```
 
 %% Cell type:code id: tags:
 
 ``` python
 plt.plot(sizes, timings, '-', linewidth=4)
 plt.plot(sizes, fitted, '--', linewidth=4)
 plt.xlabel('size')
 plt.ylabel('time (s)')
 plt.xlim(0)
 plt.ylim(0)
 ```
 
 %%%% Output: execute_result
 
     (0, 17.591113768918017)
 
 %%%% Output: display_data
 
     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)
 
 %% Cell type:markdown id: tags:
 
 ### Going further
 
 %% Cell type:markdown id: tags:
 
 - Provide an alternative implementation of bubble sort with the optimization tricks explained in the Wikipedia article.
 - Modify the `my_sorted` function to allow users to choose between the deterministic and the optimized implementations. By default, `my_sorted` should still be using the determinisitic version.
 - Run the experiment above with the optimized bubble sort implementation.
 - Compare the deterministic and optimized implementations with a plot.
 - Draw some conclusions from this analysis.

02-Dynamic-Programming.ipynb

 %% Cell type:markdown id: tags:
 
-# CO202 - Software Engineering - Algorithms
+# CO202 - Algorithms 2
 
 %% Cell type:markdown id: tags:
 
 ## Tutorial on Dynamic Programming: Fibonacci
 
 %% Cell type:markdown id: tags:
 
 ### Naive Divide-and-Conquer Approach
 
 %% Cell type:code id: tags:
 
 ``` python
 def naive_fib(n):
     if n == 0:
         return 0
     elif n == 1:
         return 1
     else:
         return naive_fib(n-1) + naive_fib(n-2)
 
 print(naive_fib(10))
 %timeit naive_fib(10)
 ```
 
+%%%% Output: stream
+
+    55
+    54.9 µs ± 10.4 µs per loop (mean ± std. dev. of 7 runs, 10000 loops each)
+
 %% Cell type:markdown id: tags: