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‎exercises/development/advanced/exercise-32.md‎

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## Development - Advanced, exercise 32
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### Text
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A **primality test** is an algorithm for determining whether an input integer greater than zero is prime. The simplest primality test is trial division: given an input number `n`, one must check whether it is divisible by any number between `2` and `√n` (square root of `n`). If so, then `n` is composite; otherwise, it is prime.
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Write an algorithm in Python – `def is_prime(n)` – which takes a positive integer `n` and returns `True` if `n` is prime, otherwise it returns `False`. In the implementation, you must follow strictly the approach introduced above (i.e. checking whether `n` is divisible by any number between `2` and `√n`). Hint: to compute the square root of a number in Python, the function `sqrt` of the library math can be used – please remember to import it in the code. Some examples of execution:
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* `is_prime(1)` will return `True`
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* `is_prime(2)` will return `True`
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* `is_prime(3)` will return `True`
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* `is_prime(4)` will return `False`
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* `is_prime(5)` will return `True`
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* `is_prime(6)` will return `False`
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### Solution
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```python
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from math import sqrt
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# Test case for the function
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def test_is_prime(n, expected):
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result = is_prime(n)
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if result is expected:
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return True
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else:
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return False
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# Code of the function
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def is_prime(n):
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d = 2
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while d <= sqrt(n):
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if n % d == 0:
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return False
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d += 1
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return True
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# Tests
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print(test_is_prime(1, True))
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print(test_is_prime(2, True))
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print(test_is_prime(3, True))
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print(test_is_prime(4, False))
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print(test_is_prime(5, True))
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print(test_is_prime(6, False))
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print(test_is_prime(17, True))
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print(test_is_prime(22, False))
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```
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### Additional material
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The runnable [Python file](exercise_32.py) is available online.

‎exercises/development/advanced/exercise-33.md‎

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## Development - Advanced, exercise 33
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### Text
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The algorithm **globbing** is an algorithm for matching wildcards, which is useful when comparing text strings that may contain wildcard syntax. The most used wildcard is "*" and represent zero or more characters. Examples of use of wildcard search are listed as follows:
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* `*foo*` matches any string containing `"foo"`, e.g. `"foo"`, `"fidafoo"`, `"farfoofi"`, `"footer"`;
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* `fee*` matches any string that begins with `"fee"`, e.g. `"fee"`, `"feedoo"`;
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* `*fae` matches any string that ends with `"fae"`, e.g. `"fae"`, `"fafae"`;
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* `doe` (i.e. no wildcards used) matches exactly with the string `"doe"`.
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Write an algorithm in Python – `def glob(p, s)` – which takes a string `p` representing the pattern (that may includes zero or more wildcards "*") and another string `s` on which searching for the pattern, and returns `True` if `p` is matched in `s`, otherwise it returns `False`.
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### Solution
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```python
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# Test case for the function
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def test_glob(p, s, expected):
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result = glob(p, s)
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if result is expected:
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return True
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else:
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return False
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# Code of the function
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def glob(p, s):
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matches = p.split("*")
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for idx, pattern in enumerate(matches):
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if pattern in s:
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pos = s.index(pattern)
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if idx == len(matches) - 1 and pattern == "":
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new_start = len(s)
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elif idx > 0:
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new_start = pos + len(pattern)
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elif pos == 0:
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new_start = len(pattern)
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else:
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return False
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s = s[new_start:]
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else:
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return False
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return s == ""
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# Tests
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print(test_glob("*foo*", "foo", True))
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print(test_glob("*foo*", "fidafoo", True))
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print(test_glob("*foo*", "farfoofi", True))
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print(test_glob("*foo*", "footer", True))
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print(test_glob("*foo*", "fee", False))
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print(test_glob("fee*", "fee", True))
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print(test_glob("fee*", "feedoo", True))
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print(test_glob("fee*", "fooee", False))
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print(test_glob("*fae", "fae", True))
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print(test_glob("*fae", "fafae", True))
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print(test_glob("*fae", "fafaefa", False))
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print(test_glob("*fae", "fee", False))
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print(test_glob("doe", "doe", True))
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print(test_glob("doe", "john doe", False))
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print(test_glob("*pa*pe*", "paperino", True))
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print(test_glob("*pa*foo*", "paparfoo", True))
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print(test_glob("*pa*po*foo*", "papopaporfoo", True))
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print(test_glob("*pa*foo*", "paparfoo", True))
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```
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### Additional material
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The runnable [Python file](exercise_33.py) is available online.

‎exercises/development/advanced/exercise_32.py‎

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# -*- coding: utf-8 -*-
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# Copyright (c) 2022, Silvio Peroni <essepuntato@gmail.com>
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#
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# Permission to use, copy, modify, and/or distribute this software for any purpose
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# with or without fee is hereby granted, provided that the above copyright notice
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# and this permission notice appear in all copies.
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#
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# THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES WITH
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# REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND
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# FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT,
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# OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE,
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# DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS
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# ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS
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# SOFTWARE.
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from math import sqrt
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# Test case for the function
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def test_is_prime(n, expected):
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result = is_prime(n)
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if result is expected:
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return True
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else:
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return False
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# Code of the function
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def is_prime(n):
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d = 2
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while d <= sqrt(n):
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if n % d == 0:
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return False
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d += 1
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return True
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# Tests
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print(test_is_prime(1, True))
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print(test_is_prime(2, True))
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print(test_is_prime(3, True))
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print(test_is_prime(4, False))
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print(test_is_prime(5, True))
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print(test_is_prime(6, False))
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print(test_is_prime(17, True))
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print(test_is_prime(22, False))

‎exercises/development/advanced/exercise_33.py‎

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# -*- coding: utf-8 -*-
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# Copyright (c) 2022, Silvio Peroni <essepuntato@gmail.com>
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#
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# Permission to use, copy, modify, and/or distribute this software for any purpose
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# with or without fee is hereby granted, provided that the above copyright notice
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# and this permission notice appear in all copies.
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#
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# THE SOFTWARE IS PROVIDED "AS IS" AND THE AUTHOR DISCLAIMS ALL WARRANTIES WITH
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# REGARD TO THIS SOFTWARE INCLUDING ALL IMPLIED WARRANTIES OF MERCHANTABILITY AND
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# FITNESS. IN NO EVENT SHALL THE AUTHOR BE LIABLE FOR ANY SPECIAL, DIRECT, INDIRECT,
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# OR CONSEQUENTIAL DAMAGES OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE,
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# DATA OR PROFITS, WHETHER IN AN ACTION OF CONTRACT, NEGLIGENCE OR OTHER TORTIOUS
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# ACTION, ARISING OUT OF OR IN CONNECTION WITH THE USE OR PERFORMANCE OF THIS
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# SOFTWARE.
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# Test case for the function
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def test_glob(p, s, expected):
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result = glob(p, s)
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if result is expected:
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return True
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else:
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return False
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# Code of the function
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def glob(p, s):
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matches = p.split("*")
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for idx, pattern in enumerate(matches):
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if pattern in s:
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pos = s.index(pattern)
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if idx == len(matches) - 1 and pattern == "":
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new_start = len(s)
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elif idx > 0:
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new_start = pos + len(pattern)
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elif pos == 0:
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new_start = len(pattern)
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else:
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return False
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s = s[new_start:]
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else:
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return False
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return s == ""
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# Tests
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print(test_glob("*foo*", "foo", True))
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print(test_glob("*foo*", "fidafoo", True))
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print(test_glob("*foo*", "farfoofi", True))
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print(test_glob("*foo*", "footer", True))
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print(test_glob("*foo*", "fee", False))
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print(test_glob("fee*", "fee", True))
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print(test_glob("fee*", "feedoo", True))
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print(test_glob("fee*", "fooee", False))
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print(test_glob("*fae", "fae", True))
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print(test_glob("*fae", "fafae", True))
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print(test_glob("*fae", "fafaefa", False))
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print(test_glob("*fae", "fee", False))
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print(test_glob("doe", "doe", True))
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print(test_glob("doe", "john doe", False))
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print(test_glob("*pa*pe*", "paperino", True))
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print(test_glob("*pa*foo*", "paparfoo", True))
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print(test_glob("*pa*po*foo*", "papopaporfoo", True))
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print(test_glob("*pa*foo*", "paparfoo", True))

‎exercises/development/beginner/exercise-28.md‎

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### Solution
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```python
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# Test case for the function
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def test_f(i, expected):
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result = f(i)
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def test_f(s, i, expected):
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result = f(s, i)
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if expected == result:
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return True
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else:
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return False
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# Code of the function
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def f(i):
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return i % 2 == 0
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def f(s, i):
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if i < len(s):
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return s[i] in "aeiou"
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else:
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return False
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# Tests
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print(test_f(2, True))
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print(test_f(3, False))
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print(test_f(0, True))
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print(test_f(7, False))
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print(test_f(108, True))
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print(test_f("ciao", 2, True))
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print(test_f("ciao", 0, False))
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print(test_f("ciao", 1, True))
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print(test_f("ciao", 7, False))
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```
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### Additional material

‎exercises/development/beginner/exercise-29.md‎

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## Development - Beginner, exercise 29
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### Text
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Write down a small function in Python that takes in input two strings and returns `True` if they are identical, `False` if they are not identical but contains the same number of characters, otherwise it returns the shorter one.
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### Solution
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```python
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# Test case for the function
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def test_f(s, t, expected):
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result = f(s, t)
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if expected == result:
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return True
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else:
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return False
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# Code of the function
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def f(s, t):
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if s == t:
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return True
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elif len(s) == len(t):
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return False
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elif len(s) < len(t):
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return s
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else:
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return t
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# Tests
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print(test_f("ciao", "ciao", True))
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print(test_f("ciao", "oaic", False))
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print(test_f("ciao", "me", "me"))
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print(test_f("me", "ciao", "me"))
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```
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### Additional material
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The runnable [Python file](exercise_29.py) is available online.

‎exercises/development/beginner/exercise-30.md‎

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## Development - Beginner, exercise 30
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### Text
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Write down a small function in Python that takes in input two integers and returns `0` if they are equal, `-1` if the first is divisible by the second (i.e. the rest of the division is `0`), `1` if the second is divisible by the first (i.e. the rest of the division is `0`), otherwise it returns `None`.
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### Solution
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```python
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def test_f(x, y, expected):
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result = f(x, y)
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if expected == result:
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return True
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else:
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return False
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# Code of the function
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def f(x, y):
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if x == y:
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return 0
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elif x % y == 0:
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return -1
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elif y % x == 0:
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return 1
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else:
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return None
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# Tests
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print(test_f(5, 5, 0))
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print(test_f(5, 10, 1))
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print(test_f(10, 5, -1))
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print(test_f(5, 7, None))
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```
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### Additional material
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The runnable [Python file](exercise_30.py) is available online.

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