Homework 01¶

Write code to solve all 10 problems. Each problem is worth 10 points. The grading rubric includes the following criteria:

Correctness
Readability
Efficiency

Please do not copy answwrs found on the web or elsewhere as it will not benefit your learning. Searching the web for general references etc is OK. Some discussion with friends is fine too - but again, do not just copy thier answer.

Honor Code: By submitting this assignment, you certify that this is your origianl work.

In [2]:

%%file ../data/animals.txt
name|species|age|weight
arun|cat|5|7.3
bob|bird|2|1.5
coco|cat|2|5.5
dumbo|elephant|23|454
elmo|dog|5|11
fido|dog|3|24.5
gumba|bird|2|2.7

Overwriting data/animals.txt

Q1. (10 pts) Using only the Unix shell commands, find only rows showing the 3rd, 4th and 5th heaviest animals in the file animals.txt.

In [20]:

%%bash

sort -n -t '|' -k4 ../data/animals.txt | head -n6 | tail -n3

coco|cat|2|5.5
arun|cat|5|7.3
elmo|dog|5|11

Q2. (10 pts) Using only the Unix shell commands, find all files in the current directory and all its subdirecotries that contain the word elephant regardless of case.

In [34]:

%%bash

grep -ril elephant .

./.ipynb_checkpoints/Homework01 Solutions-checkpoint.ipynb
./.ipynb_checkpoints/Homework01-checkpoint.ipynb
./Homework01 Solutions.ipynb
./Homework01.ipynb

Q3. (10 pts) Using only the Python standard library, find only rows showing the 3rd, 4th and 5th heaviest animals in the file animals.txt

In [22]:

with open('../data/animals.txt') as f:
    f.readline() # skip header row
    rows = []
    for line in f:
        row = line.strip().split('|')
        rows.append(row)
    sorted_rows = sorted(rows, key=lambda x: float(x[-1]))
sorted_rows[2:5]

Out[22]:

[['coco', 'cat', '2', '5.5'],
 ['arun', 'cat', '5', '7.3'],
 ['elmo', 'dog', '5', '11']]

Q4. (Removed) Using only the Python standard library, find all files in the current directory and all its sub-directories that contain the word elephant regardless of case.

In [35]:

import os

for root, dirs, files in os.walk('.'):
    for f in files:
        try:
            if 'elephant' in open(f).read():
                print(f)
        except FileNotFoundError:
            pass

Homework01 Solutions.ipynb
Homework01.ipynb

Q5. (10 pts) Starting with range(1, 20), make a list of the squares of each odd number in the following ways

With a for loop
Using a list comprehension
Using map and filter

The answer should be [1, 9, 25, 49, 81, 121, 169, 225, 289, 361]

In [36]:

xs = []
for i in range(1, 20):
    if i % 2 == 1:
        xs.append(i**2)
xs

Out[36]:

[1, 9, 25, 49, 81, 121, 169, 225, 289, 361]

In [37]:

[i**2 for i in range(1, 20) if i%2 == 1]

Out[37]:

[1, 9, 25, 49, 81, 121, 169, 225, 289, 361]

In [41]:

list(map(lambda i: i**2, filter(lambda i: i%2 == 1, range(1, 20))))

Out[41]:

[1, 9, 25, 49, 81, 121, 169, 225, 289, 361]

Q6. (10 pts) If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23. (Euler problem #1)

Write a program to find the sum of all the multiples of 3 or 5 below 1000.

The answer should be 233168.

In [46]:

m3 = {i for i in range(1000) if i%3 == 0}
m5 = {i for i in range(1000) if i%5 == 0}
sum(m3.union(m5))

Out[46]:

Q7 (10 pts). A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 × 99.

Write a program to find the largest palindrome made from the product of two 3-digit numbers. (Euler problem #4)

The answer should be 906609 = 993 × 913.

In [1]:

max([(i*j, i, j)
     for i in range(100, 1000)
     for j in range(100, 1000)
     if i*j == int(str(i*j)[::-1])])

Out[1]:

(906609, 993, 913)

Q8. (10 pts) The sum of the squares of the first ten natural numbers is,

\[ \begin{align}\begin{aligned}:nowrap:\\ 1^2 + 2^2 + ... + 10^2 = 385\\The square of the sum of the first ten natural numbers is,\end{aligned}\end{align} \]

\[ \begin{align}\begin{aligned}:nowrap:\\ (1 + 2 + ... + 10)^2 = 55^2 = 3025\\Hence the difference between the sum of the squares of the first ten\end{aligned}\end{align} \]

natural numbers and the square of the sum is 3025 − 385 = 2640.

Write a program to find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum. (Euler problem #6)

The answer should be 25164150.

In [2]:

s1 = sum(i**2 for i in range(1, 101))
s2 = sum(range(1, 101))**2
s2 - s1

Out[2]:

25164150

Q9. Problem 8: The four adjacent digits in the 1000-digit number that have the greatest product are 9 × 9 × 8 × 9 = 5832.

73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450

Write a program to find the thirteen adjacent digits in the 1000-digit number that have the greatest product. What is the value of this product? (Euler problem #8)

The answer shoud be 23514624000.

In [76]:

s = '''73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450'''

s = ''.join(s.split())
max(np.prod(list(map(int, list(s[start:start+13]))))
    for start in range(0, len(s)-13))

Out[76]:

23514624000

Q10.(10 pts) A Pythagorean triplet is a set of three natural numbers, a < b < c, for which,

\[ \begin{align}\begin{aligned}:nowrap:\\ a^2 + b^2 = c^2\\For example, :math:`3^2 + 4^2 = 9 + 16 = 25 = 5^2`\end{aligned}\end{align} \]

There exists exactly one Pythagorean triplet for which a + b + c = 1000. Write a program to find the product abc. (Euler problem #9)

The answer should be (200, 375, 425, 31875000).

In [87]:

triples = [(a, b, 1000-a-b) for a in range(1, 1000) for b in range(a, 1000)]
[(a, b, c, a*b*c) for a, b, c in triples if a**2 + b**2 == c**2]

Out[87]:

[(200, 375, 425, 31875000)]