Improve Project Euler problem 203 solution 1

project_euler/problem_203/sol1.py

@@ -29,8 +29,6 @@
 """
 from __future__ import annotations
 
-import math
-
 
 def get_pascal_triangle_unique_coefficients(depth: int) -> set[int]:
  """
@@ -61,76 +59,9 @@ def get_pascal_triangle_unique_coefficients(depth: int) -> set[int]:
  return coefficients
 
 
-def get_primes_squared(max_number: int) -> list[int]:
- """
- Calculates all primes between 2 and round(sqrt(max_number)) and returns
- them squared up.
-
- >>> get_primes_squared(2)
- []
- >>> get_primes_squared(4)
- [4]
- >>> get_primes_squared(10)
- [4, 9]
- >>> get_primes_squared(100)
- [4, 9, 25, 49]
- """
- max_prime = math.isqrt(max_number)
- non_primes = [False] * (max_prime + 1)
- primes = []
- for num in range(2, max_prime + 1):
- if non_primes[num]:
- continue
-
- for num_counter in range(num**2, max_prime + 1, num):
- non_primes[num_counter] = True
-
- primes.append(num**2)
- return primes
-
-
-def get_squared_primes_to_use(
- num_to_look: int, squared_primes: list[int], previous_index: int
-) -> int:
- """
- Returns an int indicating the last index on which squares of primes
- in primes are lower than num_to_look.
-
- This method supposes that squared_primes is sorted in ascending order and that
- each num_to_look is provided in ascending order as well. Under these
- assumptions, it needs a previous_index parameter that tells what was
- the index returned by the method for the previous num_to_look.
-
- If all the elements in squared_primes are greater than num_to_look, then the
- method returns -1.
-
- >>> get_squared_primes_to_use(1, [4, 9, 16, 25], 0)
- -1
- >>> get_squared_primes_to_use(4, [4, 9, 16, 25], 0)
- 1
- >>> get_squared_primes_to_use(16, [4, 9, 16, 25], 1)
- 3
+def get_squarefrees(unique_coefficients: set[int]) -> set[int]:
  """
- idx = max(previous_index, 0)
-
- while idx < len(squared_primes) and squared_primes[idx] <= num_to_look:
- idx += 1
-
- if idx == 0 and squared_primes[idx] > num_to_look:
- return -1
-
- if idx == len(squared_primes) and squared_primes[-1] > num_to_look:
- return -1
-
- return idx
-
-
-def get_squarefree(
- unique_coefficients: set[int], squared_primes: list[int]
-) -> set[int]:
- """
- Calculates the squarefree numbers inside unique_coefficients given a
- list of square of primes.
+ Calculates the squarefree numbers inside unique_coefficients.
 
  Based on the definition of a non-squarefree number, then any non-squarefree
  n can be decomposed as n = p*p*r, where p is positive prime number and r
@@ -140,27 +71,27 @@ def get_squarefree(
  squarefree as r cannot be negative. On the contrary, if any r exists such
  that n = p*p*r, then the number is non-squarefree.
 
- >>> get_squarefree({1}, [])
-set()
- >>> get_squarefree({1, 2}, [])
-set()
- >>> get_squarefree({1, 2, 3, 4, 5, 6, 7, 35, 10, 15, 20, 21}, [4, 9, 25])
+ >>> get_squarefrees({1})
+{1}
+ >>> get_squarefrees({1, 2})
+{1, 2}
+ >>> get_squarefrees({1, 2, 3, 4, 5, 6, 7, 35, 10, 15, 20, 21})
  {1, 2, 3, 5, 6, 7, 35, 10, 15, 21}
  """
 
- if len(squared_primes) == 0:
- return set()
-
  non_squarefrees = set()
- prime_squared_idx = 0
- for num in sorted(unique_coefficients):
- prime_squared_idx = get_squared_primes_to_use(
- num, squared_primes, prime_squared_idx
- )
- if prime_squared_idx == -1:
- continue
- if any(num % prime == 0 for prime in squared_primes[:prime_squared_idx]):
- non_squarefrees.add(num)
+ for number in unique_coefficients:
+ divisor = 2
+ copy_number = number
+ while divisor**2 <= copy_number:
+ multiplicity = 0
+ while copy_number % divisor == 0:
+ copy_number //= divisor
+ multiplicity += 1
+ if multiplicity >= 2:
+ non_squarefrees.add(number)
+ break
+ divisor += 1
 
  return unique_coefficients.difference(non_squarefrees)
 
@@ -170,15 +101,14 @@ def solution(n: int = 51) -> int:
  Returns the sum of squarefrees for a given Pascal's Triangle of depth n.
 
  >>> solution(1)
-0
+1
  >>> solution(8)
  105
  >>> solution(9)
  175
  """
  unique_coefficients = get_pascal_triangle_unique_coefficients(n)
- primes = get_primes_squared(max(unique_coefficients))
- squarefrees = get_squarefree(unique_coefficients, primes)
+ squarefrees = get_squarefrees(unique_coefficients)
  return sum(squarefrees)
 
 

project_euler/problem_203/sol1.py

@@ -29,8 +29,6 @@
 """
 from __future__ import annotations
 
-import math
-
 
 def get_pascal_triangle_unique_coefficients(depth: int) -> set[int]:
  """
@@ -61,76 +59,9 @@ def get_pascal_triangle_unique_coefficients(depth: int) -> set[int]:
  return coefficients
 
 
-def get_primes_squared(max_number: int) -> list[int]:
- """
- Calculates all primes between 2 and round(sqrt(max_number)) and returns
- them squared up.
-
- >>> get_primes_squared(2)
- []
- >>> get_primes_squared(4)
- [4]
- >>> get_primes_squared(10)
- [4, 9]
- >>> get_primes_squared(100)
- [4, 9, 25, 49]
- """
- max_prime = math.isqrt(max_number)
- non_primes = [False] * (max_prime + 1)
- primes = []
- for num in range(2, max_prime + 1):
- if non_primes[num]:
- continue
-
- for num_counter in range(num**2, max_prime + 1, num):
- non_primes[num_counter] = True
-
- primes.append(num**2)
- return primes
-
-
-def get_squared_primes_to_use(
- num_to_look: int, squared_primes: list[int], previous_index: int
-) -> int:
- """
- Returns an int indicating the last index on which squares of primes
- in primes are lower than num_to_look.
-
- This method supposes that squared_primes is sorted in ascending order and that
- each num_to_look is provided in ascending order as well. Under these
- assumptions, it needs a previous_index parameter that tells what was
- the index returned by the method for the previous num_to_look.
-
- If all the elements in squared_primes are greater than num_to_look, then the
- method returns -1.
-
- >>> get_squared_primes_to_use(1, [4, 9, 16, 25], 0)
- -1
- >>> get_squared_primes_to_use(4, [4, 9, 16, 25], 0)
- 1
- >>> get_squared_primes_to_use(16, [4, 9, 16, 25], 1)
- 3
+def get_squarefrees(unique_coefficients: set[int]) -> set[int]:
  """
- idx = max(previous_index, 0)
-
- while idx < len(squared_primes) and squared_primes[idx] <= num_to_look:
- idx += 1
-
- if idx == 0 and squared_primes[idx] > num_to_look:
- return -1
-
- if idx == len(squared_primes) and squared_primes[-1] > num_to_look:
- return -1
-
- return idx
-
-
-def get_squarefree(
- unique_coefficients: set[int], squared_primes: list[int]
-) -> set[int]:
- """
- Calculates the squarefree numbers inside unique_coefficients given a
- list of square of primes.
+ Calculates the squarefree numbers inside unique_coefficients.
 
  Based on the definition of a non-squarefree number, then any non-squarefree
  n can be decomposed as n = p*p*r, where p is positive prime number and r
@@ -140,27 +71,27 @@ def get_squarefree(
  squarefree as r cannot be negative. On the contrary, if any r exists such
  that n = p*p*r, then the number is non-squarefree.
 
- >>> get_squarefree({1}, [])
-set()
- >>> get_squarefree({1, 2}, [])
-set()
- >>> get_squarefree({1, 2, 3, 4, 5, 6, 7, 35, 10, 15, 20, 21}, [4, 9, 25])
+ >>> get_squarefrees({1})
+{1}
+ >>> get_squarefrees({1, 2})
+{1, 2}
+ >>> get_squarefrees({1, 2, 3, 4, 5, 6, 7, 35, 10, 15, 20, 21})
  {1, 2, 3, 5, 6, 7, 35, 10, 15, 21}
  """
 
- if len(squared_primes) == 0:
- return set()
-
  non_squarefrees = set()
- prime_squared_idx = 0
- for num in sorted(unique_coefficients):
- prime_squared_idx = get_squared_primes_to_use(
- num, squared_primes, prime_squared_idx
- )
- if prime_squared_idx == -1:
- continue
- if any(num % prime == 0 for prime in squared_primes[:prime_squared_idx]):
- non_squarefrees.add(num)
+ for number in unique_coefficients:
+ divisor = 2
+ copy_number = number
+ while divisor**2 <= copy_number:
+ multiplicity = 0
+ while copy_number % divisor == 0:
+ copy_number //= divisor
+ multiplicity += 1
+ if multiplicity >= 2:
+ non_squarefrees.add(number)
+ break
+ divisor += 1
 
  return unique_coefficients.difference(non_squarefrees)
 
@@ -170,15 +101,14 @@ def solution(n: int = 51) -> int:
  Returns the sum of squarefrees for a given Pascal's Triangle of depth n.
 
  >>> solution(1)
-0
+1
  >>> solution(8)
  105
  >>> solution(9)
  175
  """
  unique_coefficients = get_pascal_triangle_unique_coefficients(n)
- primes = get_primes_squared(max(unique_coefficients))
- squarefrees = get_squarefree(unique_coefficients, primes)
+ squarefrees = get_squarefrees(unique_coefficients)
  return sum(squarefrees)
 
 

project_euler/problem_203/sol1.py

@@ -29,8 +29,6 @@
 """
 from __future__ import annotations
 
-import math
-
 
 def get_pascal_triangle_unique_coefficients(depth: int) -> set[int]:
  """
@@ -61,76 +59,9 @@ def get_pascal_triangle_unique_coefficients(depth: int) -> set[int]:
  return coefficients
 
 
-def get_primes_squared(max_number: int) -> list[int]:
- """
- Calculates all primes between 2 and round(sqrt(max_number)) and returns
- them squared up.
-
- >>> get_primes_squared(2)
- []
- >>> get_primes_squared(4)
- [4]
- >>> get_primes_squared(10)
- [4, 9]
- >>> get_primes_squared(100)
- [4, 9, 25, 49]
- """
- max_prime = math.isqrt(max_number)
- non_primes = [False] * (max_prime + 1)
- primes = []
- for num in range(2, max_prime + 1):
- if non_primes[num]:
- continue
-
- for num_counter in range(num**2, max_prime + 1, num):
- non_primes[num_counter] = True
-
- primes.append(num**2)
- return primes
-
-
-def get_squared_primes_to_use(
- num_to_look: int, squared_primes: list[int], previous_index: int
-) -> int:
- """
- Returns an int indicating the last index on which squares of primes
- in primes are lower than num_to_look.
-
- This method supposes that squared_primes is sorted in ascending order and that
- each num_to_look is provided in ascending order as well. Under these
- assumptions, it needs a previous_index parameter that tells what was
- the index returned by the method for the previous num_to_look.
-
- If all the elements in squared_primes are greater than num_to_look, then the
- method returns -1.
-
- >>> get_squared_primes_to_use(1, [4, 9, 16, 25], 0)
- -1
- >>> get_squared_primes_to_use(4, [4, 9, 16, 25], 0)
- 1
- >>> get_squared_primes_to_use(16, [4, 9, 16, 25], 1)
- 3
+def get_squarefrees(unique_coefficients: set[int]) -> set[int]:
  """
- idx = max(previous_index, 0)
-
- while idx < len(squared_primes) and squared_primes[idx] <= num_to_look:
- idx += 1
-
- if idx == 0 and squared_primes[idx] > num_to_look:
- return -1
-
- if idx == len(squared_primes) and squared_primes[-1] > num_to_look:
- return -1
-
- return idx
-
-
-def get_squarefree(
- unique_coefficients: set[int], squared_primes: list[int]
-) -> set[int]:
- """
- Calculates the squarefree numbers inside unique_coefficients given a
- list of square of primes.
+ Calculates the squarefree numbers inside unique_coefficients.
 
  Based on the definition of a non-squarefree number, then any non-squarefree
  n can be decomposed as n = p*p*r, where p is positive prime number and r
@@ -140,27 +71,27 @@ def get_squarefree(
  squarefree as r cannot be negative. On the contrary, if any r exists such
  that n = p*p*r, then the number is non-squarefree.
 
- >>> get_squarefree({1}, [])
-set()
- >>> get_squarefree({1, 2}, [])
-set()
- >>> get_squarefree({1, 2, 3, 4, 5, 6, 7, 35, 10, 15, 20, 21}, [4, 9, 25])
+ >>> get_squarefrees({1})
+{1}
+ >>> get_squarefrees({1, 2})
+{1, 2}
+ >>> get_squarefrees({1, 2, 3, 4, 5, 6, 7, 35, 10, 15, 20, 21})
  {1, 2, 3, 5, 6, 7, 35, 10, 15, 21}
  """
 
- if len(squared_primes) == 0:
- return set()
-
  non_squarefrees = set()
- prime_squared_idx = 0
- for num in sorted(unique_coefficients):
- prime_squared_idx = get_squared_primes_to_use(
- num, squared_primes, prime_squared_idx
- )
- if prime_squared_idx == -1:
- continue
- if any(num % prime == 0 for prime in squared_primes[:prime_squared_idx]):
- non_squarefrees.add(num)
+ for number in unique_coefficients:
+ divisor = 2
+ copy_number = number
+ while divisor**2 <= copy_number:
+ multiplicity = 0
+ while copy_number % divisor == 0:
+ copy_number //= divisor
+ multiplicity += 1
+ if multiplicity >= 2:
+ non_squarefrees.add(number)
+ break
+ divisor += 1
 
  return unique_coefficients.difference(non_squarefrees)
 
@@ -170,15 +101,14 @@ def solution(n: int = 51) -> int:
  Returns the sum of squarefrees for a given Pascal's Triangle of depth n.
 
  >>> solution(1)
-0
+1
  >>> solution(8)
  105
  >>> solution(9)
  175
  """
  unique_coefficients = get_pascal_triangle_unique_coefficients(n)
- primes = get_primes_squared(max(unique_coefficients))
- squarefrees = get_squarefree(unique_coefficients, primes)
+ squarefrees = get_squarefrees(unique_coefficients)
  return sum(squarefrees)
 
 

project_euler/problem_203/sol1.py

@@ -29,8 +29,6 @@
 """
 from __future__ import annotations
 
-import math
-
 
 def get_pascal_triangle_unique_coefficients(depth: int) -> set[int]:
  """
@@ -61,76 +59,9 @@ def get_pascal_triangle_unique_coefficients(depth: int) -> set[int]:
  return coefficients
 
 
-def get_primes_squared(max_number: int) -> list[int]:
- """
- Calculates all primes between 2 and round(sqrt(max_number)) and returns
- them squared up.
-
- >>> get_primes_squared(2)
- []
- >>> get_primes_squared(4)
- [4]
- >>> get_primes_squared(10)
- [4, 9]
- >>> get_primes_squared(100)
- [4, 9, 25, 49]
- """
- max_prime = math.isqrt(max_number)
- non_primes = [False] * (max_prime + 1)
- primes = []
- for num in range(2, max_prime + 1):
- if non_primes[num]:
- continue
-
- for num_counter in range(num**2, max_prime + 1, num):
- non_primes[num_counter] = True
-
- primes.append(num**2)
- return primes
-
-
-def get_squared_primes_to_use(
- num_to_look: int, squared_primes: list[int], previous_index: int
-) -> int:
- """
- Returns an int indicating the last index on which squares of primes
- in primes are lower than num_to_look.
-
- This method supposes that squared_primes is sorted in ascending order and that
- each num_to_look is provided in ascending order as well. Under these
- assumptions, it needs a previous_index parameter that tells what was
- the index returned by the method for the previous num_to_look.
-
- If all the elements in squared_primes are greater than num_to_look, then the
- method returns -1.
-
- >>> get_squared_primes_to_use(1, [4, 9, 16, 25], 0)
- -1
- >>> get_squared_primes_to_use(4, [4, 9, 16, 25], 0)
- 1
- >>> get_squared_primes_to_use(16, [4, 9, 16, 25], 1)
- 3
+def get_squarefrees(unique_coefficients: set[int]) -> set[int]:
  """
- idx = max(previous_index, 0)
-
- while idx < len(squared_primes) and squared_primes[idx] <= num_to_look:
- idx += 1
-
- if idx == 0 and squared_primes[idx] > num_to_look:
- return -1
-
- if idx == len(squared_primes) and squared_primes[-1] > num_to_look:
- return -1
-
- return idx
-
-
-def get_squarefree(
- unique_coefficients: set[int], squared_primes: list[int]
-) -> set[int]:
- """
- Calculates the squarefree numbers inside unique_coefficients given a
- list of square of primes.
+ Calculates the squarefree numbers inside unique_coefficients.
 
  Based on the definition of a non-squarefree number, then any non-squarefree
  n can be decomposed as n = p*p*r, where p is positive prime number and r
@@ -140,27 +71,27 @@ def get_squarefree(
  squarefree as r cannot be negative. On the contrary, if any r exists such
  that n = p*p*r, then the number is non-squarefree.
 
- >>> get_squarefree({1}, [])
-set()
- >>> get_squarefree({1, 2}, [])
-set()
- >>> get_squarefree({1, 2, 3, 4, 5, 6, 7, 35, 10, 15, 20, 21}, [4, 9, 25])
+ >>> get_squarefrees({1})
+{1}
+ >>> get_squarefrees({1, 2})
+{1, 2}
+ >>> get_squarefrees({1, 2, 3, 4, 5, 6, 7, 35, 10, 15, 20, 21})
  {1, 2, 3, 5, 6, 7, 35, 10, 15, 21}
  """
 
- if len(squared_primes) == 0:
- return set()
-
  non_squarefrees = set()
- prime_squared_idx = 0
- for num in sorted(unique_coefficients):
- prime_squared_idx = get_squared_primes_to_use(
- num, squared_primes, prime_squared_idx
- )
- if prime_squared_idx == -1:
- continue
- if any(num % prime == 0 for prime in squared_primes[:prime_squared_idx]):
- non_squarefrees.add(num)
+ for number in unique_coefficients:
+ divisor = 2
+ copy_number = number
+ while divisor**2 <= copy_number:
+ multiplicity = 0
+ while copy_number % divisor == 0:
+ copy_number //= divisor
+ multiplicity += 1
+ if multiplicity >= 2:
+ non_squarefrees.add(number)
+ break
+ divisor += 1
 
  return unique_coefficients.difference(non_squarefrees)
 
@@ -170,15 +101,14 @@ def solution(n: int = 51) -> int:
  Returns the sum of squarefrees for a given Pascal's Triangle of depth n.
 
  >>> solution(1)
-0
+1
  >>> solution(8)
  105
  >>> solution(9)
  175
  """
  unique_coefficients = get_pascal_triangle_unique_coefficients(n)
- primes = get_primes_squared(max(unique_coefficients))
- squarefrees = get_squarefree(unique_coefficients, primes)
+ squarefrees = get_squarefrees(unique_coefficients)
  return sum(squarefrees)
 
 

project_euler/problem_203/sol1.py

@@ -29,8 +29,6 @@
 """
 from __future__ import annotations
 
-import math
-
 
 def get_pascal_triangle_unique_coefficients(depth: int) -> set[int]:
  """
@@ -61,76 +59,9 @@ def get_pascal_triangle_unique_coefficients(depth: int) -> set[int]:
  return coefficients
 
 
-def get_primes_squared(max_number: int) -> list[int]:
- """
- Calculates all primes between 2 and round(sqrt(max_number)) and returns
- them squared up.
-
- >>> get_primes_squared(2)
- []
- >>> get_primes_squared(4)
- [4]
- >>> get_primes_squared(10)
- [4, 9]
- >>> get_primes_squared(100)
- [4, 9, 25, 49]
- """
- max_prime = math.isqrt(max_number)
- non_primes = [False] * (max_prime + 1)
- primes = []
- for num in range(2, max_prime + 1):
- if non_primes[num]:
- continue
-
- for num_counter in range(num**2, max_prime + 1, num):
- non_primes[num_counter] = True
-
- primes.append(num**2)
- return primes
-
-
-def get_squared_primes_to_use(
- num_to_look: int, squared_primes: list[int], previous_index: int
-) -> int:
- """
- Returns an int indicating the last index on which squares of primes
- in primes are lower than num_to_look.
-
- This method supposes that squared_primes is sorted in ascending order and that
- each num_to_look is provided in ascending order as well. Under these
- assumptions, it needs a previous_index parameter that tells what was
- the index returned by the method for the previous num_to_look.
-
- If all the elements in squared_primes are greater than num_to_look, then the
- method returns -1.
-
- >>> get_squared_primes_to_use(1, [4, 9, 16, 25], 0)
- -1
- >>> get_squared_primes_to_use(4, [4, 9, 16, 25], 0)
- 1
- >>> get_squared_primes_to_use(16, [4, 9, 16, 25], 1)
- 3
+def get_squarefrees(unique_coefficients: set[int]) -> set[int]:
  """
- idx = max(previous_index, 0)
-
- while idx < len(squared_primes) and squared_primes[idx] <= num_to_look:
- idx += 1
-
- if idx == 0 and squared_primes[idx] > num_to_look:
- return -1
-
- if idx == len(squared_primes) and squared_primes[-1] > num_to_look:
- return -1
-
- return idx
-
-
-def get_squarefree(
- unique_coefficients: set[int], squared_primes: list[int]
-) -> set[int]:
- """
- Calculates the squarefree numbers inside unique_coefficients given a
- list of square of primes.
+ Calculates the squarefree numbers inside unique_coefficients.
 
  Based on the definition of a non-squarefree number, then any non-squarefree
  n can be decomposed as n = p*p*r, where p is positive prime number and r
@@ -140,27 +71,27 @@ def get_squarefree(
  squarefree as r cannot be negative. On the contrary, if any r exists such
  that n = p*p*r, then the number is non-squarefree.
 
- >>> get_squarefree({1}, [])
-set()
- >>> get_squarefree({1, 2}, [])
-set()
- >>> get_squarefree({1, 2, 3, 4, 5, 6, 7, 35, 10, 15, 20, 21}, [4, 9, 25])
+ >>> get_squarefrees({1})
+{1}
+ >>> get_squarefrees({1, 2})
+{1, 2}
+ >>> get_squarefrees({1, 2, 3, 4, 5, 6, 7, 35, 10, 15, 20, 21})
  {1, 2, 3, 5, 6, 7, 35, 10, 15, 21}
  """
 
- if len(squared_primes) == 0:
- return set()
-
  non_squarefrees = set()
- prime_squared_idx = 0
- for num in sorted(unique_coefficients):
- prime_squared_idx = get_squared_primes_to_use(
- num, squared_primes, prime_squared_idx
- )
- if prime_squared_idx == -1:
- continue
- if any(num % prime == 0 for prime in squared_primes[:prime_squared_idx]):
- non_squarefrees.add(num)
+ for number in unique_coefficients:
+ divisor = 2
+ copy_number = number
+ while divisor**2 <= copy_number:
+ multiplicity = 0
+ while copy_number % divisor == 0:
+ copy_number //= divisor
+ multiplicity += 1
+ if multiplicity >= 2:
+ non_squarefrees.add(number)
+ break
+ divisor += 1
 
  return unique_coefficients.difference(non_squarefrees)
 
@@ -170,15 +101,14 @@ def solution(n: int = 51) -> int:
  Returns the sum of squarefrees for a given Pascal's Triangle of depth n.
 
  >>> solution(1)
-0
+1
  >>> solution(8)
  105
  >>> solution(9)
  175
  """
  unique_coefficients = get_pascal_triangle_unique_coefficients(n)
- primes = get_primes_squared(max(unique_coefficients))
- squarefrees = get_squarefree(unique_coefficients, primes)
+ squarefrees = get_squarefrees(unique_coefficients)
  return sum(squarefrees)
 
 

project_euler/problem_203/sol1.py

@@ -29,8 +29,6 @@
 """
 from __future__ import annotations
 
-import math
-
 
 def get_pascal_triangle_unique_coefficients(depth: int) -> set[int]:
  """
@@ -61,76 +59,9 @@ def get_pascal_triangle_unique_coefficients(depth: int) -> set[int]:
  return coefficients
 
 
-def get_primes_squared(max_number: int) -> list[int]:
- """
- Calculates all primes between 2 and round(sqrt(max_number)) and returns
- them squared up.
-
- >>> get_primes_squared(2)
- []
- >>> get_primes_squared(4)
- [4]
- >>> get_primes_squared(10)
- [4, 9]
- >>> get_primes_squared(100)
- [4, 9, 25, 49]
- """
- max_prime = math.isqrt(max_number)
- non_primes = [False] * (max_prime + 1)
- primes = []
- for num in range(2, max_prime + 1):
- if non_primes[num]:
- continue
-
- for num_counter in range(num**2, max_prime + 1, num):
- non_primes[num_counter] = True
-
- primes.append(num**2)
- return primes
-
-
-def get_squared_primes_to_use(
- num_to_look: int, squared_primes: list[int], previous_index: int
-) -> int:
- """
- Returns an int indicating the last index on which squares of primes
- in primes are lower than num_to_look.
-
- This method supposes that squared_primes is sorted in ascending order and that
- each num_to_look is provided in ascending order as well. Under these
- assumptions, it needs a previous_index parameter that tells what was
- the index returned by the method for the previous num_to_look.
-
- If all the elements in squared_primes are greater than num_to_look, then the
- method returns -1.
-
- >>> get_squared_primes_to_use(1, [4, 9, 16, 25], 0)
- -1
- >>> get_squared_primes_to_use(4, [4, 9, 16, 25], 0)
- 1
- >>> get_squared_primes_to_use(16, [4, 9, 16, 25], 1)
- 3
+def get_squarefrees(unique_coefficients: set[int]) -> set[int]:
  """
- idx = max(previous_index, 0)
-
- while idx < len(squared_primes) and squared_primes[idx] <= num_to_look:
- idx += 1
-
- if idx == 0 and squared_primes[idx] > num_to_look:
- return -1
-
- if idx == len(squared_primes) and squared_primes[-1] > num_to_look:
- return -1
-
- return idx
-
-
-def get_squarefree(
- unique_coefficients: set[int], squared_primes: list[int]
-) -> set[int]:
- """
- Calculates the squarefree numbers inside unique_coefficients given a
- list of square of primes.
+ Calculates the squarefree numbers inside unique_coefficients.
 
  Based on the definition of a non-squarefree number, then any non-squarefree
  n can be decomposed as n = p*p*r, where p is positive prime number and r
@@ -140,27 +71,27 @@ def get_squarefree(
  squarefree as r cannot be negative. On the contrary, if any r exists such
  that n = p*p*r, then the number is non-squarefree.
 
- >>> get_squarefree({1}, [])
-set()
- >>> get_squarefree({1, 2}, [])
-set()
- >>> get_squarefree({1, 2, 3, 4, 5, 6, 7, 35, 10, 15, 20, 21}, [4, 9, 25])
+ >>> get_squarefrees({1})
+{1}
+ >>> get_squarefrees({1, 2})
+{1, 2}
+ >>> get_squarefrees({1, 2, 3, 4, 5, 6, 7, 35, 10, 15, 20, 21})
  {1, 2, 3, 5, 6, 7, 35, 10, 15, 21}
  """
 
- if len(squared_primes) == 0:
- return set()
-
  non_squarefrees = set()
- prime_squared_idx = 0
- for num in sorted(unique_coefficients):
- prime_squared_idx = get_squared_primes_to_use(
- num, squared_primes, prime_squared_idx
- )
- if prime_squared_idx == -1:
- continue
- if any(num % prime == 0 for prime in squared_primes[:prime_squared_idx]):
- non_squarefrees.add(num)
+ for number in unique_coefficients:
+ divisor = 2
+ copy_number = number
+ while divisor**2 <= copy_number:
+ multiplicity = 0
+ while copy_number % divisor == 0:
+ copy_number //= divisor
+ multiplicity += 1
+ if multiplicity >= 2:
+ non_squarefrees.add(number)
+ break
+ divisor += 1
 
  return unique_coefficients.difference(non_squarefrees)
 
@@ -170,15 +101,14 @@ def solution(n: int = 51) -> int:
  Returns the sum of squarefrees for a given Pascal's Triangle of depth n.
 
  >>> solution(1)
-0
+1
  >>> solution(8)
  105
  >>> solution(9)
  175
  """
  unique_coefficients = get_pascal_triangle_unique_coefficients(n)
- primes = get_primes_squared(max(unique_coefficients))
- squarefrees = get_squarefree(unique_coefficients, primes)
+ squarefrees = get_squarefrees(unique_coefficients)
  return sum(squarefrees)
 
 

project_euler/problem_203/sol1.py

@@ -29,8 +29,6 @@
 """
 from __future__ import annotations
 
-import math
-
 
 def get_pascal_triangle_unique_coefficients(depth: int) -> set[int]:
  """
@@ -61,76 +59,9 @@ def get_pascal_triangle_unique_coefficients(depth: int) -> set[int]:
  return coefficients
 
 
-def get_primes_squared(max_number: int) -> list[int]:
- """
- Calculates all primes between 2 and round(sqrt(max_number)) and returns
- them squared up.
-
- >>> get_primes_squared(2)
- []
- >>> get_primes_squared(4)
- [4]
- >>> get_primes_squared(10)
- [4, 9]
- >>> get_primes_squared(100)
- [4, 9, 25, 49]
- """
- max_prime = math.isqrt(max_number)
- non_primes = [False] * (max_prime + 1)
- primes = []
- for num in range(2, max_prime + 1):
- if non_primes[num]:
- continue
-
- for num_counter in range(num**2, max_prime + 1, num):
- non_primes[num_counter] = True
-
- primes.append(num**2)
- return primes
-
-
-def get_squared_primes_to_use(
- num_to_look: int, squared_primes: list[int], previous_index: int
-) -> int:
- """
- Returns an int indicating the last index on which squares of primes
- in primes are lower than num_to_look.
-
- This method supposes that squared_primes is sorted in ascending order and that
- each num_to_look is provided in ascending order as well. Under these
- assumptions, it needs a previous_index parameter that tells what was
- the index returned by the method for the previous num_to_look.
-
- If all the elements in squared_primes are greater than num_to_look, then the
- method returns -1.
-
- >>> get_squared_primes_to_use(1, [4, 9, 16, 25], 0)
- -1
- >>> get_squared_primes_to_use(4, [4, 9, 16, 25], 0)
- 1
- >>> get_squared_primes_to_use(16, [4, 9, 16, 25], 1)
- 3
+def get_squarefrees(unique_coefficients: set[int]) -> set[int]:
  """
- idx = max(previous_index, 0)
-
- while idx < len(squared_primes) and squared_primes[idx] <= num_to_look:
- idx += 1
-
- if idx == 0 and squared_primes[idx] > num_to_look:
- return -1
-
- if idx == len(squared_primes) and squared_primes[-1] > num_to_look:
- return -1
-
- return idx
-
-
-def get_squarefree(
- unique_coefficients: set[int], squared_primes: list[int]
-) -> set[int]:
- """
- Calculates the squarefree numbers inside unique_coefficients given a
- list of square of primes.
+ Calculates the squarefree numbers inside unique_coefficients.
 
  Based on the definition of a non-squarefree number, then any non-squarefree
  n can be decomposed as n = p*p*r, where p is positive prime number and r
@@ -140,27 +71,27 @@ def get_squarefree(
  squarefree as r cannot be negative. On the contrary, if any r exists such
  that n = p*p*r, then the number is non-squarefree.
 
- >>> get_squarefree({1}, [])
-set()
- >>> get_squarefree({1, 2}, [])
-set()
- >>> get_squarefree({1, 2, 3, 4, 5, 6, 7, 35, 10, 15, 20, 21}, [4, 9, 25])
+ >>> get_squarefrees({1})
+{1}
+ >>> get_squarefrees({1, 2})
+{1, 2}
+ >>> get_squarefrees({1, 2, 3, 4, 5, 6, 7, 35, 10, 15, 20, 21})
  {1, 2, 3, 5, 6, 7, 35, 10, 15, 21}
  """
 
- if len(squared_primes) == 0:
- return set()
-
  non_squarefrees = set()
- prime_squared_idx = 0
- for num in sorted(unique_coefficients):
- prime_squared_idx = get_squared_primes_to_use(
- num, squared_primes, prime_squared_idx
- )
- if prime_squared_idx == -1:
- continue
- if any(num % prime == 0 for prime in squared_primes[:prime_squared_idx]):
- non_squarefrees.add(num)
+ for number in unique_coefficients:
+ divisor = 2
+ copy_number = number
+ while divisor**2 <= copy_number:
+ multiplicity = 0
+ while copy_number % divisor == 0:
+ copy_number //= divisor
+ multiplicity += 1
+ if multiplicity >= 2:
+ non_squarefrees.add(number)
+ break
+ divisor += 1
 
  return unique_coefficients.difference(non_squarefrees)
 
@@ -170,15 +101,14 @@ def solution(n: int = 51) -> int:
  Returns the sum of squarefrees for a given Pascal's Triangle of depth n.
 
  >>> solution(1)
-0
+1
  >>> solution(8)
  105
  >>> solution(9)
  175
  """
  unique_coefficients = get_pascal_triangle_unique_coefficients(n)
- primes = get_primes_squared(max(unique_coefficients))
- squarefrees = get_squarefree(unique_coefficients, primes)
+ squarefrees = get_squarefrees(unique_coefficients)
  return sum(squarefrees)
 
 

project_euler/problem_203/sol1.py

@@ -29,8 +29,6 @@
 """
 from __future__ import annotations
 
-import math
-
 
 def get_pascal_triangle_unique_coefficients(depth: int) -> set[int]:
  """
@@ -61,76 +59,9 @@ def get_pascal_triangle_unique_coefficients(depth: int) -> set[int]:
  return coefficients
 
 
-def get_primes_squared(max_number: int) -> list[int]:
- """
- Calculates all primes between 2 and round(sqrt(max_number)) and returns
- them squared up.
-
- >>> get_primes_squared(2)
- []
- >>> get_primes_squared(4)
- [4]
- >>> get_primes_squared(10)
- [4, 9]
- >>> get_primes_squared(100)
- [4, 9, 25, 49]
- """
- max_prime = math.isqrt(max_number)
- non_primes = [False] * (max_prime + 1)
- primes = []
- for num in range(2, max_prime + 1):
- if non_primes[num]:
- continue
-
- for num_counter in range(num**2, max_prime + 1, num):
- non_primes[num_counter] = True
-
- primes.append(num**2)
- return primes
-
-
-def get_squared_primes_to_use(
- num_to_look: int, squared_primes: list[int], previous_index: int
-) -> int:
- """
- Returns an int indicating the last index on which squares of primes
- in primes are lower than num_to_look.
-
- This method supposes that squared_primes is sorted in ascending order and that
- each num_to_look is provided in ascending order as well. Under these
- assumptions, it needs a previous_index parameter that tells what was
- the index returned by the method for the previous num_to_look.
-
- If all the elements in squared_primes are greater than num_to_look, then the
- method returns -1.
-
- >>> get_squared_primes_to_use(1, [4, 9, 16, 25], 0)
- -1
- >>> get_squared_primes_to_use(4, [4, 9, 16, 25], 0)
- 1
- >>> get_squared_primes_to_use(16, [4, 9, 16, 25], 1)
- 3
+def get_squarefrees(unique_coefficients: set[int]) -> set[int]:
  """
- idx = max(previous_index, 0)
-
- while idx < len(squared_primes) and squared_primes[idx] <= num_to_look:
- idx += 1
-
- if idx == 0 and squared_primes[idx] > num_to_look:
- return -1
-
- if idx == len(squared_primes) and squared_primes[-1] > num_to_look:
- return -1
-
- return idx
-
-
-def get_squarefree(
- unique_coefficients: set[int], squared_primes: list[int]
-) -> set[int]:
- """
- Calculates the squarefree numbers inside unique_coefficients given a
- list of square of primes.
+ Calculates the squarefree numbers inside unique_coefficients.
 
  Based on the definition of a non-squarefree number, then any non-squarefree
  n can be decomposed as n = p*p*r, where p is positive prime number and r
@@ -140,27 +71,27 @@ def get_squarefree(
  squarefree as r cannot be negative. On the contrary, if any r exists such
  that n = p*p*r, then the number is non-squarefree.
 
- >>> get_squarefree({1}, [])
-set()
- >>> get_squarefree({1, 2}, [])
-set()
- >>> get_squarefree({1, 2, 3, 4, 5, 6, 7, 35, 10, 15, 20, 21}, [4, 9, 25])
+ >>> get_squarefrees({1})
+{1}
+ >>> get_squarefrees({1, 2})
+{1, 2}
+ >>> get_squarefrees({1, 2, 3, 4, 5, 6, 7, 35, 10, 15, 20, 21})
  {1, 2, 3, 5, 6, 7, 35, 10, 15, 21}
  """
 
- if len(squared_primes) == 0:
- return set()
-
  non_squarefrees = set()
- prime_squared_idx = 0
- for num in sorted(unique_coefficients):
- prime_squared_idx = get_squared_primes_to_use(
- num, squared_primes, prime_squared_idx
- )
- if prime_squared_idx == -1:
- continue
- if any(num % prime == 0 for prime in squared_primes[:prime_squared_idx]):
- non_squarefrees.add(num)
+ for number in unique_coefficients:
+ divisor = 2
+ copy_number = number
+ while divisor**2 <= copy_number:
+ multiplicity = 0
+ while copy_number % divisor == 0:
+ copy_number //= divisor
+ multiplicity += 1
+ if multiplicity >= 2:
+ non_squarefrees.add(number)
+ break
+ divisor += 1
 
  return unique_coefficients.difference(non_squarefrees)
 
@@ -170,15 +101,14 @@ def solution(n: int = 51) -> int:
  Returns the sum of squarefrees for a given Pascal's Triangle of depth n.
 
  >>> solution(1)
-0
+1
  >>> solution(8)
  105
  >>> solution(9)
  175
  """
  unique_coefficients = get_pascal_triangle_unique_coefficients(n)
- primes = get_primes_squared(max(unique_coefficients))
- squarefrees = get_squarefree(unique_coefficients, primes)
+ squarefrees = get_squarefrees(unique_coefficients)
  return sum(squarefrees)