.ipynb .pdf

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Contents

Queues

Some programs need to retrieve data in the same order as it was stored. We call this to enqueue items of data. We could imagine doing this by using a list to add elements at the end and retrieve them from the front, as in the following example:

q = []

for i in range(10):
    # enqueue by placing at the end:
    q.append(i)
print(q)
print()

for i in range(10):
    # dequeue by removing from the front:
    print('Service first in queue:', q.pop(0))
    print(q)
    print()

[0, 1, 2, 3, 4, 5, 6, 7, 8, 9]

Service first in queue: 0
[1, 2, 3, 4, 5, 6, 7, 8, 9]

Service first in queue: 1
[2, 3, 4, 5, 6, 7, 8, 9]

Service first in queue: 2
[3, 4, 5, 6, 7, 8, 9]

Service first in queue: 3
[4, 5, 6, 7, 8, 9]

Service first in queue: 4
[5, 6, 7, 8, 9]

Service first in queue: 5
[6, 7, 8, 9]

Service first in queue: 6
[7, 8, 9]

Service first in queue: 7
[8, 9]

Service first in queue: 8
[9]

Service first in queue: 9
[]

The problem is that we know that pop(0) is linear time! We would like to have constant time instead (not more expensive than updating / reading an array).

This can be achieved by keeping track of the first and the last element and keeping the elements together via links. We call the pair of an element and a link a Node. We use a class with the name _Node for these nodes (remember that we use the convention of using an underscore at the begining of a name to indicate that it is an auxiliary function or name). As you can see in the definintion in next cell, a node has two instance variables: an element (item) and a link (next).

The class for queues is called Queue (no underscore!) and has two instance variables: the first node and the last node! It has methods to add items (enqueue)and to remove items (dequeue). Also for testing emptiness, for the number of elements and to make a string of the content.

You to inspect the code! Confirm that all operations are constant time (except __str__!)

# From the book Introduction to Programming in Python, chapter 4.3 on Stacks and Queues:
# https://introcs.cs.princeton.edu/python/43stack/

#----------------------------------------------------------------------

# A _Node object references an item and a next _Node object.
# A Queue object is composed of _Node objects.

class _Node:
    def __init__(self, item, next):
        self.item = item  # Reference to an item
        self.next = next  # Reference to the next _Node object



class Queue:

    #-------------------------------------------------------------------

    # Construct the Queue object self as an empty Queue object.

    def __init__(self):
        self._first  = None  # Reference to first _Node
        self._last   = None   # Reference to last _Node
        self._length = 0    # Number of items

    #-------------------------------------------------------------------

    # Return True if self is empty, and False otherwise.

    def is_empty(self):
        return self._first is None

    #-------------------------------------------------------------------

    # Add item to the end of self.

    def enqueue(self, item):
        oldLast = self._last
        self._last = _Node(item, None)
        if self.is_empty():
            self._first = self._last
        else:
            oldLast.next = self._last
        self._length += 1

    #-------------------------------------------------------------------

    # Remove the first item of self and return it.

    def dequeue(self):
        item = self._first.item
        self._first = self._first.next
        if self.is_empty():
            self._last = None
        self._length -= 1
        return item

    #-------------------------------------------------------------------

    # Return the number of items in self.

    def __len__(self):
        return self._length

    #-------------------------------------------------------------------

    # Return a string representation of self.

    def __str__(self):
        s = ''
        cur = self._first
        while cur is not None:
            s += str(cur.item) + ' '
            cur = cur.next
        return s

Here is the same example as before but using this implementation for queues:

q = Queue()

for i in range(10):
    q.enqueue(i)
    
print(q)
print()

for i in range(10):
    # dequeue by removing from the front:
    print('Service first in queue:', q.dequeue())
    print(q)
    print()

0 1 2 3 4 5 6 7 8 9 

Service first in queue: 0
1 2 3 4 5 6 7 8 9 

Service first in queue: 1
2 3 4 5 6 7 8 9 

Service first in queue: 2
3 4 5 6 7 8 9 

Service first in queue: 3
4 5 6 7 8 9 

Service first in queue: 4
5 6 7 8 9 

Service first in queue: 5
6 7 8 9 

Service first in queue: 6
7 8 9 

Service first in queue: 7
8 9 

Service first in queue: 8
9 

Service first in queue: 9

# In case we do not know how many times we can dequeue we can test for emptyness:

q = Queue()

for i in range(10):
    q.enqueue(i)
    
print(q)
print()

while not q.is_empty():
    # dequeue by removing from the front:
    print('Service first in queue:', q.dequeue())
    print(q)
    print()

0 1 2 3 4 5 6 7 8 9 

Service first in queue: 0
1 2 3 4 5 6 7 8 9 

Service first in queue: 1
2 3 4 5 6 7 8 9 

Service first in queue: 2
3 4 5 6 7 8 9 

Service first in queue: 3
4 5 6 7 8 9 

Service first in queue: 4
5 6 7 8 9 

Service first in queue: 5
6 7 8 9 

Service first in queue: 6
7 8 9 

Service first in queue: 7
8 9 

Service first in queue: 8
9 

Service first in queue: 9

Listing the contents of a folder

And now an example. Say you want to list the contents of a folder and of all folders under this one. In Python you can get a list of names of files and folders (directories) using the method listdir in the module os.

Here is how my directory for this lecture notes looks like:

import os

for name in os.listdir('..'):
    print(name)

design
ds
intro.md
panda.png
algs
_toc.yml
_build
_config.yml
.git
overview
panda.gif

Not all of these are directories, so if we want to list the contents of the directories we need to test whether a name corresponds to a directory. This can be done in Python using the method is_dir in the module os.path.

So, here we list all sub-directories also:

import os
for name in os.listdir('..'):
    print(name)
    if os.path.isdir('../' + name):
        print(os.listdir('../' + name))
        

design
['dc-mergesort.ipynb', 'dc-inversions.ipynb', 'dp-knapsack.ipynb', 'dp-wis.ipynb', 'dp-fib.ipynb', 'intro.md', 'dc-intro.md', '.ipynb_checkpoints', 'dp-intro.md']
ds
['heaps.ipynb', 'intro.md', 'lists.ipynb', 'lecture5.md', 'queues.ipynb', 'classes.ipynb', '.ipynb_checkpoints', 'heaps-intro.md']
intro.md
panda.png
algs
['programming-exercises-1.ipynb', 'execution-time.md', 'theory-exercises-1.md', 'math-and-experiments.ipynb', 'et.ipynb', 'programming-solutions-1.ipynb', 'intro.md', 'mul.ipynb', 'loops.ipynb', 'recursion.ipynb', '.ipynb_checkpoints', 'algs-lecture.md', 'primes.ipynb']
_toc.yml
_build
['.DS_Store', 'html', 'jupyter_execute', '.doctrees']
_config.yml
.git
['config', 'objects', 'HEAD', 'info', 'logs', 'description', 'hooks', 'refs', 'index', 'COMMIT_EDITMSG']
overview
['overview.md', 'sw-dev-cycle-ch7-sedgewick-cs.png', '.ipynb_checkpoints']
panda.gif

We would like to list as long as there are files, as deep as needed. We do it level by level, using a queue! This algorithm is called Breadth First Search.

def list_dir_tree(path):
    q = Queue()
    q.enqueue(path)
    
    while not q.is_empty():
        path = q.dequeue()
        print(path)
        if os.path.isdir(path):
            for name in os.listdir(path):
                q.enqueue(path + '/' + name)
     
    

list_dir_tree('..')

..
../design
../ds
../intro.md
../panda.png
../algs
../_toc.yml
../_build
../_config.yml
../.git
../overview
../panda.gif
../design/dc-mergesort.ipynb
../design/dc-inversions.ipynb
../design/dp-knapsack.ipynb
../design/dp-wis.ipynb
../design/dp-fib.ipynb
../design/intro.md
../design/dc-intro.md
../design/.ipynb_checkpoints
../design/dp-intro.md
../ds/heaps.ipynb
../ds/intro.md
../ds/lists.ipynb
../ds/lecture5.md
../ds/queues.ipynb
../ds/classes.ipynb
../ds/.ipynb_checkpoints
../ds/heaps-intro.md
../algs/programming-exercises-1.ipynb
../algs/execution-time.md
../algs/theory-exercises-1.md
../algs/math-and-experiments.ipynb
../algs/et.ipynb
../algs/programming-solutions-1.ipynb
../algs/intro.md
../algs/mul.ipynb
../algs/loops.ipynb
../algs/recursion.ipynb
../algs/.ipynb_checkpoints
../algs/algs-lecture.md
../algs/primes.ipynb
../_build/.DS_Store
../_build/html
../_build/jupyter_execute
../_build/.doctrees
../.git/config
../.git/objects
../.git/HEAD
../.git/info
../.git/logs
../.git/description
../.git/hooks
../.git/refs
../.git/index
../.git/COMMIT_EDITMSG
../overview/overview.md
../overview/sw-dev-cycle-ch7-sedgewick-cs.png
../overview/.ipynb_checkpoints
../design/.ipynb_checkpoints/dc-mergesort-checkpoint.ipynb
../design/.ipynb_checkpoints/dp-knapsack-checkpoint.ipynb
../design/.ipynb_checkpoints/dp-wis-checkpoint.ipynb
../design/.ipynb_checkpoints/dp-fib-checkpoint.ipynb
../design/.ipynb_checkpoints/dc-inversions-checkpoint.ipynb
../ds/.ipynb_checkpoints/lists-checkpoint.ipynb
../ds/.ipynb_checkpoints/heaps-checkpoint.ipynb
../ds/.ipynb_checkpoints/queues-checkpoint.ipynb
../ds/.ipynb_checkpoints/classes-checkpoint.ipynb
../algs/.ipynb_checkpoints/recursion-checkpoint.ipynb
../algs/.ipynb_checkpoints/programming-solutions-1-checkpoint.ipynb
../algs/.ipynb_checkpoints/math-and-experiments-checkpoint.ipynb
../algs/.ipynb_checkpoints/loops-checkpoint.ipynb
../algs/.ipynb_checkpoints/et-checkpoint.ipynb
../algs/.ipynb_checkpoints/mul-checkpoint.ipynb
../algs/.ipynb_checkpoints/programming-exercises-1-checkpoint.ipynb
../algs/.ipynb_checkpoints/primes-checkpoint.ipynb
../_build/html/design
../_build/html/week2-divide-and-conquer-and-analysis.html
../_build/html/index.html
../_build/html/.DS_Store
../_build/html/ds
../_build/html/searchindex.js
../_build/html/_panels_static
../_build/html/_sources
../_build/html/algs
../_build/html/_static
../_build/html/intro.html
../_build/html/.buildinfo
../_build/html/_images
../_build/html/genindex.html
../_build/html/search.html
../_build/html/overview
../_build/html/objects.inv
../_build/html/reports
../_build/jupyter_execute/design
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../.git/refs/remotes
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../_build/html/design/dc-inversions.html
../_build/html/design/dp-intro.html
../_build/html/design/dc-intro.html
../_build/html/design/intro.html
../_build/html/design/dp-wis.html
../_build/html/design/dp-fib.html
../_build/html/design/dc-mergesort.html
../_build/html/ds/heaps.html
../_build/html/ds/queues.html
../_build/html/ds/lists.html
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../_build/html/ds/lecture5.html
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Make sure you understand the algorithm and the output! Can you find the source of this notebook? It is

../ds/queues.ipynb.

The first thing is the starting path, then file and directory names directly under it, then next level for those names that were directories, etc.

I would recommend you to try to follow the algorithm by hand with a directory structure such as

A
    B
        e
        f
        
    c
    
    D
        g
        H
            i 
            j

where capital letters are dictionaries and small letters are files. Make sure you keep track of the queue! You should produce the output:

A

A/B
A/c
A/D

A/B/e
A/B/f
A/D/g
A/D/H

A/D/H/i
A/D/H/j

where I have added new lines to mark the depth levels.

By the way, what would the algorithm do if we used a stack instead?

def list_dir_tree_stack(path):
    s = []
    s.append(path)
    
    while not s == []:
        path = s.pop()
        print(path)
        if os.path.isdir(path):
            for name in os.listdir(path):
                s.append(path + '/' + name)

list_dir_tree_stack('..')

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As you can see it goes as deep as possible (instead of level by level) this algorithm is called DFS: Depth First Search.

Make sure you can follow the stack in the example with letters we suggested before. Here is the output you should expect:

A
A/B
A/B/e
A/B/f
A/c
A/D
A/D/g
A/D/H
A/D/H/i
A/D/H/j

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