Operations on Sequences

City University of Hong Kong

CS1302 Introduction to Computer Programming

import random
%reload_ext divewidgets

Mutating a list¶

%%optlite -h 350
b = [*range(10)]  # aliasing
b[::2] = b[:5]
b[0:1] = b[:5]
b[::2] = b[:5]  # fails

Last assignment fails because [::2] with step size not equal to 1 is an extended slice, which can only be assigned to a list of equal size.

What is the difference between mutation and aliasing?

In the previous code:

The first assignment b = [*range(10)] is aliasing, which gives the list the target name/identifier b.
Other assignments such as b[::2] = b[:5] are mutations that calls __setitem__ because the target b[::2] is not an identifier.

list.__setitem__?

# %%optlite -l -h 400
a = b = [0]
b[0] = a[0] + 1
print(a[0] < b[0])

Solution to Exercise 1

The first line a = b makes a an alias of the same object b points to, and so
the second line mutates the same object a and b point to.
Hence, a[0] == b[0].

a = [0, 1]
i = 0
a.__setitem__(i := i + 1, i)
print(a)

a = [0, 1]
i = 0
a[i := i + 1] = a[i]
print(a)

Solution to Exercise 2

a[i := i + 1] = a[i] is not the same as calling a.__setitem__(i := i + 1, i). According to the python documentation,

the expression to be assigned, i.e., a[i], is first evaluated to a[0] and therefore 0;
since the target a[i := i + 1] is a user defined object, it continue to evaluate the target reference, i.e., the address of a, which corresponds to the list [0, 1],
followed by the subscription i:=i+1, which evaluates to 1;
Finally, a.__setitem__ is called with the subscription, 1, and expression to be assigned, 0, and so the list a points to is mutuated to [0, 1].

In comparison, directly calling a.__setitem__(i := i + 1, i)

first evaluates the first argument i := i + 1, which gives 1 that is assigned to i, and
then evaluates the second argument i to 1, and so
a.__setitem__(1, 1) is called instead, which does not change the list a points to.

Why mutate a list?

The following is another implementation of composite_sequence that takes advantage of the mutability of list.

%%optlite -r
def sieve_composite_sequence(stop):
    is_composite = [False] * stop  # initialization
    for factor in range(2, stop):
        if is_composite[factor]:
            continue
        for multiple in range(factor * 2, stop, factor):
            is_composite[multiple] = True
    return (x for x in range(4, stop) if is_composite[x])


for x in sieve_composite_sequence(100):
    print(x, end=" ")

The algorithm

changes is_composite[x] from False to True if x is a multiple of a smaller number factor, and
returns a generator that generates composite numbers according to is_composite.

composite_sequence = lambda stop: (
    x for x in range(2, stop) if any(x % divisor == 0 for divisor in range(2, x))
)

%%timeit
for x in composite_sequence(10000): pass

%%timeit
for x in sieve_composite_sequence(10000): pass

for x in sieve_composite_sequence(10000000): pass

Solution to Exercise 3

The line if is_composite[factor]: continue avoids the redundant computations of checking composite factors.

%%optlite -h 300
a = [[0] * 2] * 2
a[0][0] = a[1][1] = 1
print(a)

### BEGIN SOLUTION
a = [[0] * 2 for i in range(2)]
### END SOLUTION
a[0][0] = a[1][1] = 1
print(a)

Different methods to operate on a sequence¶

Recall the quicksort algorithm:

def quicksort(seq):
    '''Return a sorted list of items from seq.'''
    if len(seq) <= 1:
        return list(seq)
    i = random.randint(0, len(seq) - 1)
    pivot, others = seq[i], [*seq[:i], *seq[i + 1:]]
    left = quicksort([x for x in others if x < pivot])
    right = quicksort([x for x in others if x >= pivot])
    return [*left, pivot, *right]


seq = [random.randint(0, 99) for i in range(10)]
print(seq, quicksort(seq), sep='\n')

There is also a built-in function sorted for sorting a sequence:

sorted?
sorted(seq)

Is quicksort quicker?

%%timeit
quicksort(seq)

%%timeit
sorted(seq)

Python implements the Timsort algorithm, which is very efficient.

What are other operations on sequences?

The following compares the lists of public attributes for tuple and list.

We determine membership using the operator in or not in.
Different from the keyword in in a for loop, operator in calls the method __contains__.

list_attributes = dir(list)
tuple_attributes = dir(tuple)

print(
    'Common attributes:', ', '.join([
        attr for attr in list_attributes
        if attr in tuple_attributes and attr[0] != '_'
    ]))

print(
    'Tuple-specific attributes:', ', '.join([
        attr for attr in tuple_attributes
        if attr not in list_attributes and attr[0] != '_'
    ]))

print(
    'List-specific attributes:', ', '.join([
        attr for attr in list_attributes
        if attr not in tuple_attributes and attr[0] != '_'
    ]))

There are no public tuple-specific attributes, and
all the list-specific attributes are methods that mutate the list, except copy.

The common attributes

count method returns the number of occurrences of a value in a tuple/list, and
index method returns the index of the first occurrence of a value in a tuple/list.

%%optlite -l -h 450
a = (1,2,2,4,5)
count_of_2 = a.count(2)
index_of_1st_2 = a.index(2)

reverse method reverses the list instead of returning a reversed list.

%%optlite -h 300
a = [*range(10)]
print(reversed(a))
print(*reversed(a))
print(a.reverse())

copy method returns a copy of a list.
tuple does not have the copy method but it is easy to create a copy by slicing.

%%optlite -h 400
a = [*range(10)]
b = tuple(a)
a_reversed = a.copy()
a_reversed.reverse()
b_reversed = b[::-1]

sort method sorts the list in place instead of returning a sorted list.

%%optlite -h 300
import random
a = [random.randint(0,10) for i in range(10)]
print(sorted(a))
print(a.sort())

extend method that extends a list instead of creating a new concatenated list.
append method adds an object to the end of a list.
insert method insert an object to a specified location.

%%optlite -h 300
a = b = [*range(5)]
print(a + b)
print(a.extend(b))
print(a.append('stop'))
print(a.insert(0,'start'))

pop method deletes and return the last item of the list.
remove method removes the first occurrence of a value in the list.
clear method clears the entire list.

We can also use the function del to delete a selection of a list.

%%optlite -h 300
a = [*range(10)]
del a[::2]
print(a.pop())
print(a.remove(5))
print(a.clear())