From 33d8869e6db8265ee56f97ee323cb54a203ddc30 Mon Sep 17 00:00:00 2001
From: mindaugl <mindelek@gmail.com>
Date: Sun, 6 Apr 2025 16:01:11 +0800
Subject: [PATCH 1/3] Add initial files for the euler project problem 127
solution.
---
project_euler/problem_127/__init__.py | 0
project_euler/problem_127/sol1.py | 65 +++++++++++++++++++++++++++
2 files changed, 65 insertions(+)
create mode 100644 project_euler/problem_127/__init__.py
create mode 100644 project_euler/problem_127/sol1.py
diff --git a/project_euler/problem_127/__init__.py b/project_euler/problem_127/__init__.py
new file mode 100644
index 000000000000..e69de29bb2d1
diff --git a/project_euler/problem_127/sol1.py b/project_euler/problem_127/sol1.py
new file mode 100644
index 000000000000..b89b83ded644
--- /dev/null
+++ b/project_euler/problem_127/sol1.py
@@ -0,0 +1,65 @@
+from numpy import sqrt
+
+N = 120000
+
+
+def generate_primes(n: int):
+ primes = [True] * (n + 1)
+ primes[0] = primes[1] = False
+ for i in range(2, int(sqrt(n + 1)) + 1):
+ if primes[i]:
+ j = i * i
+ while j <= n:
+ primes[j] = False
+ j += i
+ return primes
+
+
+def rad(n: int, primes_list: list[int]):
+ f = 1
+ for p in primes_list:
+ if p > n:
+ break
+ if n % p == 0:
+ f *= p
+ return f
+
+
+def gcd(a: int, b: int):
+ while b:
+ a, b = b, a % b
+ return a
+
+
+def solution(c_less: int = 120000) -> int:
+ primes_bool = generate_primes(c_less)
+ primes_list = []
+ print("primes generated")
+ for i in range(2, len(primes_bool)):
+ if primes_bool[i]:
+ primes_list += [i]
+
+ rads = [1] * (c_less + 1)
+ for i in range(c_less + 1):
+ if i % 100 == 0:
+ print("rads", i)
+ rads[i] = rad(i, primes_list)
+
+ sum_c = 0
+ print("start main")
+ for a in range(1, c_less):
+ rad_a = rads[a]
+ if a % 2 == 1:
+ r = range(1, min(a, c_less - a))
+ else:
+ r = range(1, min(a, c_less - a), 2)
+ for b in r:
+ c = a + b
+ if rad_a * rads[b] * rads[c] < c and gcd(rad_a, rads[b]) == 1:
+ sum_c += c
+
+ return sum_c
+
+
+if __name__ == "__main__":
+ print(f"{solution() = }")
From 249109569bafc79547d2404ffeecb0905fbf34b3 Mon Sep 17 00:00:00 2001
From: mindaugl <mindelek@gmail.com>
Date: Sun, 6 Apr 2025 16:18:42 +0800
Subject: [PATCH 2/3] Add documentation for the euler project problem 127
solution.
---
project_euler/problem_127/sol1.py | 35 ++++++++++++++++++++++++++-----
1 file changed, 30 insertions(+), 5 deletions(-)
diff --git a/project_euler/problem_127/sol1.py b/project_euler/problem_127/sol1.py
index b89b83ded644..1e8f91419da5 100644
--- a/project_euler/problem_127/sol1.py
+++ b/project_euler/problem_127/sol1.py
@@ -1,9 +1,24 @@
+"""
+Project Euler Problem 127: https://projecteuler.net/problem=127
+
+abc-hits
+
+It takes about 10 minutes to run.
+'Brute-force' solution that uses the following simplifications:
+- if gcd(a, b) = 1 then gcd(a, c) = 1 and gcd(b, c) = 1
+- rad(a*b*c) = rad(a) * rad(b) * rad(c), for gcd(a, b) = 1
+- if a is even, b cannot b even for gcd(a, b) = 1 to be true.
+"""
+
from numpy import sqrt
N = 120000
-def generate_primes(n: int):
+def generate_primes(n: int) -> list[bool]:
+ """
+ Generates primes boolean array up to n.
+ """
primes = [True] * (n + 1)
primes[0] = primes[1] = False
for i in range(2, int(sqrt(n + 1)) + 1):
@@ -15,7 +30,11 @@ def generate_primes(n: int):
return primes
-def rad(n: int, primes_list: list[int]):
+def rad(n: int, primes_list: list[int]) -> int:
+ """
+ Calculated rad - product of unique prime factors for n, using prime numbers
+ list primes_list.
+ """
f = 1
for p in primes_list:
if p > n:
@@ -25,16 +44,23 @@ def rad(n: int, primes_list: list[int]):
return f
-def gcd(a: int, b: int):
+def gcd(a: int, b: int) -> int:
+ """
+ Calculates greatest common divisor of a and b.
+
+ """
while b:
a, b = b, a % b
return a
def solution(c_less: int = 120000) -> int:
+ """
+ Calculates all primes, rads, and then loops over a, b checking the conditions.
+
+ """
primes_bool = generate_primes(c_less)
primes_list = []
- print("primes generated")
for i in range(2, len(primes_bool)):
if primes_bool[i]:
primes_list += [i]
@@ -46,7 +72,6 @@ def solution(c_less: int = 120000) -> int:
rads[i] = rad(i, primes_list)
sum_c = 0
- print("start main")
for a in range(1, c_less):
rad_a = rads[a]
if a % 2 == 1:
From cee612502378b36f579fec936e25e0dcdbcafeab Mon Sep 17 00:00:00 2001
From: mindaugl <mindelek@gmail.com>
Date: Sun, 6 Apr 2025 16:29:15 +0800
Subject: [PATCH 3/3] Add test case and remove print() for the euler project
problem 127 solution.
---
project_euler/problem_127/sol1.py | 23 +++++++++++++++++++++--
1 file changed, 21 insertions(+), 2 deletions(-)
diff --git a/project_euler/problem_127/sol1.py b/project_euler/problem_127/sol1.py
index 1e8f91419da5..17e888438355 100644
--- a/project_euler/problem_127/sol1.py
+++ b/project_euler/problem_127/sol1.py
@@ -8,6 +8,9 @@
- if gcd(a, b) = 1 then gcd(a, c) = 1 and gcd(b, c) = 1
- rad(a*b*c) = rad(a) * rad(b) * rad(c), for gcd(a, b) = 1
- if a is even, b cannot b even for gcd(a, b) = 1 to be true.
+
+>>> solution(1000)
+12523
"""
from numpy import sqrt
@@ -18,6 +21,11 @@
def generate_primes(n: int) -> list[bool]:
"""
Generates primes boolean array up to n.
+
+ >>> generate_primes(2)
+ [False, False, True]
+ >>> generate_primes(5)
+ [False, False, True, True, False, True]
"""
primes = [True] * (n + 1)
primes[0] = primes[1] = False
@@ -34,6 +42,11 @@ def rad(n: int, primes_list: list[int]) -> int:
"""
Calculated rad - product of unique prime factors for n, using prime numbers
list primes_list.
+
+ >>> rad(1, [1])
+ 1
+ >>> rad(12, [2, 3])
+ 6
"""
f = 1
for p in primes_list:
@@ -48,6 +61,10 @@ def gcd(a: int, b: int) -> int:
"""
Calculates greatest common divisor of a and b.
+ >>> gcd(1, 10)
+ 1
+ >>> gcd(14, 48)
+ 2
"""
while b:
a, b = b, a % b
@@ -58,6 +75,10 @@ def solution(c_less: int = 120000) -> int:
"""
Calculates all primes, rads, and then loops over a, b checking the conditions.
+ >>> solution(10)
+ 9
+ >>> solution(100)
+ 316
"""
primes_bool = generate_primes(c_less)
primes_list = []
@@ -67,8 +88,6 @@ def solution(c_less: int = 120000) -> int:
rads = [1] * (c_less + 1)
for i in range(c_less + 1):
- if i % 100 == 0:
- print("rads", i)
rads[i] = rad(i, primes_list)
sum_c = 0