Merge pull request #3 from 07734willy/main

Performance Optimizations

Author: mdbrnowski

.gitignore

@@ -1,2 +1,144 @@
+## Intellij
+
 .idea
-__pycache__
+
+## Python
+
+# Byte-compiled / optimized / DLL files
+__pycache__/
+*.py[cod]
+*$py.class
+
+# C extensions
+*.so
+
+# Distribution / packaging
+.Python
+build/
+develop-eggs/
+dist/
+downloads/
+eggs/
+.eggs/
+lib/
+lib64/
+parts/
+sdist/
+var/
+wheels/
+share/python-wheels/
+*.egg-info/
+.installed.cfg
+*.egg
+MANIFEST
+
+# PyInstaller
+#  Usually these files are written by a python script from a template
+#  before PyInstaller builds the exe, so as to inject date/other infos into it.
+*.manifest
+*.spec
+
+# Installer logs
+pip-log.txt
+pip-delete-this-directory.txt
+
+# Unit test / coverage reports
+htmlcov/
+.tox/
+.nox/
+.coverage
+.coverage.*
+.cache
+nosetests.xml
+coverage.xml
+*.cover
+*.py,cover
+.hypothesis/
+.pytest_cache/
+cover/
+
+# Translations
+*.mo
+*.pot
+
+# Django stuff:
+*.log
+local_settings.py
+db.sqlite3
+db.sqlite3-journal
+
+# Flask stuff:
+instance/
+.webassets-cache
+
+# Scrapy stuff:
+.scrapy
+
+# Sphinx documentation
+docs/_build/
+
+# PyBuilder
+.pybuilder/
+target/
+
+# Jupyter Notebook
+.ipynb_checkpoints
+
+# IPython
+profile_default/
+ipython_config.py
+
+# pyenv
+#   For a library or package, you might want to ignore these files since the code is
+#   intended to run in multiple environments; otherwise, check them in:
+# .python-version
+
+# pipenv
+#   According to pypa/pipenv#598, it is recommended to include Pipfile.lock in version control.
+#   However, in case of collaboration, if having platform-specific dependencies or dependencies
+#   having no cross-platform support, pipenv may install dependencies that don't work, or not
+#   install all needed dependencies.
+#Pipfile.lock
+
+# PEP 582; used by e.g. github.com/David-OConnor/pyflow
+__pypackages__/
+
+# Celery stuff
+celerybeat-schedule
+celerybeat.pid
+
+# SageMath parsed files
+*.sage.py
+
+# Environments
+.env
+.venv
+env/
+venv/
+ENV/
+env.bak/
+venv.bak/
+
+# Spyder project settings
+.spyderproject
+.spyproject
+
+# Rope project settings
+.ropeproject
+
+# mkdocs documentation
+/site
+
+# mypy
+.mypy_cache/
+.dmypy.json
+dmypy.json
+
+# Pyre type checker
+.pyre/
+
+# pytype static type analyzer
+.pytype/
+
+# Cython debug symbols
+cython_debug/

pythagorean_tuples.py

@@ -1,4 +1,4 @@
-from itertools import product
+from itertools import product, count
 from math import log, isqrt, ceil, prod
 from collections import Counter
 
@@ -49,7 +49,10 @@ def _prime_factors(n: int) -> list:
     while n % 2 == 0:
         factors.append(2)
         n //= 2
-    for i in range(3, isqrt(n) + 1, 2):
+    for i in count(3, 2):
+        if i ** 2 > n:
+            break
+
         while n % i == 0:
             factors.append(i)
             n //= i
@@ -81,14 +84,27 @@ def _pythagorean_triples_BP(a: int, factors: Counter):
     return triples
 
 
+def _product_powers(powers_table: list, limit: int, product=1):
+    if not powers_table:
+        yield product
+        return
+
+    powers, *rest = powers_table
+    for power in powers:
+        if product * power >= limit:
+            break
+        yield from _product_powers(rest, limit, product * power)
+
+
 def _pythagorean_triples_B(a: int, factors: Counter):
-    # TODO: minimise the number of possible deltas (without `itertools.product()`)
     triples = set()
     factors_list = list(factors)
     ranges = [range(0, min(ceil(log(a, factor)), 2 * factors[factor] + 1)) for factor in factors_list]
-    for powers in product(*ranges):
-        if (d := prod(factors_list[i] ** power for i, power in enumerate(powers))) < a:
-            triples.add(_TRIPLE(a, d))
+    
+    powers_table = [[factor ** exponent for exponent in exponents] 
+            for factor, exponents in zip(factors_list, ranges)]
+    for d in _product_powers(powers_table, a):
+        triples.add(_TRIPLE(a, d))
     return triples
 
 
@@ -106,12 +122,13 @@ def _pythagorean_triples_CP(a: int, factors: Counter):
 
 
 def _pythagorean_triples_C(a: int, factors: Counter):
-    # TODO: minimise the number of possibilities (without `itertools.product()`)
     triples = set()
     factors_list = list(factors)
     ranges = [range(0, min(ceil(log(a, factor)), 2 * factors[factor] + 1)) for factor in factors_list]
     ranges[0] = range(1, min(ceil(log(a, 2)), 2 * factors[2]))    # concerns the factor 2
-    for powers in product(*ranges):
-        if (d := prod(factors_list[i] ** power for i, power in enumerate(powers))) < a:
-            triples.add(_TRIPLE(a, d))
+    
+    powers_table = [[factor ** exponent for exponent in exponents] 
+            for factor, exponents in zip(factors_list, ranges)]
+    for d in _product_powers(powers_table, a):
+        triples.add(_TRIPLE(a, d))
     return triples