Develop

.github/workflows/mergefile.yml

@@ -34,9 +34,11 @@ jobs:
       - name: Install dependencies
         run: |
           python -m pip install --upgrade pip
-          pip install ruff
+          pip install ruff isort
       - name: Run Ruff
         run: ruff format .
+      - name: import sort
+        run: isort --dedup code/main.py
       - name: Get last commit message
         id: last-commit
         run: |

README.md

@@ -1,5 +1,9 @@
 # hidehic0's library
 
+[![run unittest](https://github.com/hidehic0/library/actions/workflows/unittest.yml/badge.svg?branch=main)](https://github.com/hidehic0/library/actions/workflows/unittest.yml)
+[![CodeQL Advanced](https://github.com/hidehic0/library/actions/workflows/codeql.yml/badge.svg)](https://github.com/hidehic0/library/actions/workflows/codeql.yml)
+</br>
+
 [![total lines](https://tokei.rs/b1/github/hidehic0/library)](https://github.com/XAMPPRocky/tokei)
 ![GitHub code size in bytes](https://img.shields.io/github/languages/code-size/hidehic0/library)
 ![GitHub repo size](https://img.shields.io/github/repo-size/hidehic0/library)
@@ -13,5 +17,3 @@
 ファイルは、分割したのは、libsに、全文はcodeに、置いてあります</br>
 </br></br>
 
-[![run unittest](https://github.com/hidehic0/library/actions/workflows/unittest.yml/badge.svg?branch=main)](https://github.com/hidehic0/library/actions/workflows/unittest.yml)
-[![CodeQL Advanced](https://github.com/hidehic0/library/actions/workflows/codeql.yml/badge.svg)](https://github.com/hidehic0/library/actions/workflows/codeql.yml)

libs/math_func.py

@@ -1,3 +1,6 @@
+from typing import List
+
+
 # 数学型関数
 def is_prime(n):
     """
@@ -110,6 +113,42 @@ def factorization(n):
     return result
 
 
+def factorization_plural(L: List[int]) -> List[List[int]]:
+    """
+    複数の数の素因数分解を行ないます
+    計算量は、O(N * (√max(L) log log √max(L)))
+    みたいな感じです
+
+    最初に素数を列挙するため、普通の素因数分解より効率がいいです
+    """
+    res = []
+    primes = eratosthenes(int(max(L) ** 0.5) + 20)
+
+    def solve(n):
+        t = []
+        for p in primes:
+            if n % p == 0:
+                cnt = 0
+                while n % p == 0:
+                    cnt += 1
+                    n //= p
+
+                t.append([p, cnt])
+
+        if n != 1:
+            t.append([n, 1])
+
+        if t == []:
+            t.append([n, 1])
+
+        return t
+
+    for n in L:
+        res.append(solve(n))
+
+    return res
+
+
 def simple_sigma(n: int) -> int:
     """
     1からnまでの総和を求める関数

test.py

@@ -1,6 +1,6 @@
 import unittest
 from libs.grid import coordinate_check, grid_moves
-from libs.math_func import is_prime, simple_sigma
+from libs.math_func import is_prime, simple_sigma, factorization_plural
 from libs.utils import lowerlist, upperlist, INF
 from libs.modint import mod_add, mod_sub
 
@@ -51,6 +51,13 @@ def test_simple_sigma(self):
             with self.subTest(i=i):
                 self.assertEqual(simple_sigma(i), ans)
 
+    def test_factorization_plural(self):
+        test_cases = [([5, 10], [[[5, 1]], [[2, 1], [5, 1]]])]
+
+        for l, ans in test_cases:
+            with self.subTest(l=l):
+                self.assertEqual(factorization_plural(l), ans)
+
 
 class TestUtilsVariable(unittest.TestCase):
     def test_lowerlist(self):

tests/factorization_plural_new.py

@@ -0,0 +1,63 @@
+# python tests/factorization_plural_new.py  2.58s user 0.01s system 99% cpu 2.591 total
+
+
+def eratosthenes(n):
+    """
+    n以下の素数を列挙します
+    計算量は、O(n log log n)です
+    先程の素数判定法で列挙するよりも、少し速いです
+    列挙した素数は昇順に並んでいます
+    アルゴリズムはエラトステネスです
+    """
+    primes = [True] * (n + 1)
+    primes[0], primes[1] = False, False
+    i = 2
+    while i**2 <= n:
+        if primes[i]:
+            for k in range(i * 2, n + 1, i):
+                primes[k] = False
+
+        i += 1
+
+    return [i for i, p in enumerate(primes) if p]
+
+
+def factorization_plural(L):
+    """
+    複数の数の素因数分解を行ないます
+    計算量は、O(N * (√max(L) log log √max(L)))
+    みたいな感じです
+
+    最初に素数を列挙するため、普通の素因数分解より効率がいいです
+    """
+    res = []
+    primes = eratosthenes(int(max(L) ** 0.5) + 20)
+
+    def solve(n):
+        t = []
+        for p in primes:
+            if n % p == 0:
+                cnt = 0
+                while n % p == 0:
+                    cnt += 1
+                    n //= p
+
+                t.append([p, cnt])
+
+        if n != 1:
+            t.append([n, 1])
+
+        if t == []:
+            t.append([n, 1])
+
+        return t
+
+    for n in L:
+        res.append(solve(n))
+
+    return res
+
+
+t = [10**10] * (10**4)
+
+factorization_plural(t)

tests/factorization_plural_old.py

@@ -0,0 +1,32 @@
+# python tests/factorization_plural_old.py  42.42s user 0.00s system 99% cpu 42.515 total
+
+
+def factorization(n):
+    """
+    nを素因数分解します
+    計算量は、√Nです(要改善)
+    複数回素因数分解を行なう場合は、√N以下の素数を列挙したので試し割りした法が速いです
+    """
+    result = []
+    tmp = n
+    for i in range(2, int(-(-(n**0.5) // 1)) + 1):
+        if tmp % i == 0:
+            cnt = 0
+            while tmp % i == 0:
+                cnt += 1
+                tmp //= i
+            result.append([i, cnt])
+
+    if tmp != 1:
+        result.append([tmp, 1])
+
+    if result == []:
+        result.append([n, 1])
+
+    return result
+
+
+t = [10**10] * (10**4)
+
+for n in t:
+    factorization(n)