feat: 添加欧拉计划第49题“素数排列”的Python解法

solutions/0049.PrimePermutations/euler_49.py

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+"""
+The arithmetic sequence, 1487,4817,8147, in which each of the terms increases by 3330,
+is unusual in two ways: (i) each of the three terms are prime, and, (ii) each of the
+4-digit numbers are permutations of one another.
+
+There are no arithmetic sequences made up of three 1-, 2-, or 3-digit primes, exhibiting this property,
+but there is one other 4-digit increasing sequence.
+
+What 12-digit number do you form by concatenating the three terms in this sequence?
+"""
+
+import time
+
+
+def timer(func):
+    def wrapper(*args, **kwargs):
+        start_time = time.time()
+        result = func(*args, **kwargs)
+        end_time = time.time()
+        elapsed_time = end_time - start_time
+        print(f"{func.__name__} time: {elapsed_time:.6f} seconds")
+        return result
+
+    return wrapper
+
+
+def list_primes(start: int, end: int) -> list[int]:
+    # 只需要筛到 sqrt(9999) ≈ 100 即可标记合数
+    limit = int(end**0.5) + 1
+    base_primes = [True] * limit
+    base_primes[0] = base_primes[1] = False
+
+    # 生成基础质数（2到100）
+    for i in range(2, int(limit**0.5) + 1):
+        if base_primes[i]:
+            for j in range(i * i, limit, i):
+                base_primes[j] = False
+
+    # 分段筛：只标记1000-9999范围
+    size = end - start + 1
+    is_prime = [True] * size
+
+    for p in range(2, limit):
+        if base_primes[p]:
+            # 找到第一个大于等于start的p的倍数
+            first = max(p * p, ((start + p - 1) // p) * p)
+            for j in range(first, end + 1, p):
+                is_prime[j - start] = False
+
+    return [i + start for i, val in enumerate(is_prime) if val]
+
+
+def list_com(a: list, b: list) -> bool:
+    if len(set(a)) != len(set(b)):
+        return False
+    xb = b.copy()
+    for x in a:
+        if x not in xb:
+            return False
+        else:
+            xb.remove(x)
+    return True
+
+
+@timer
+def main():
+    primes = list_primes(1000, 9999)
+    max_sp = max(primes)
+    res = []
+    for i, v in enumerate(primes):
+        if v == max_sp:
+            break
+        gap = int((max_sp - v) / 3)
+        for g in range(gap, (primes[i + 1] - v - 1), -1):
+            if v + g in primes and v + 2 * g in primes:
+                if list_com(list(str(v)), list(str(v + g))):
+                    if list_com(list(str(v)), list(str(v + 2 * g))):
+                        res.append(str(v) + str(v + g) + str(v + 2 * g))
+                else:
+                    continue
+    print(res)
+
+
+if __name__ == "__main__":
+    main()