{"id":940419,"date":"2024-12-26T20:59:34","date_gmt":"2024-12-26T12:59:34","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/940419.html"},"modified":"2024-12-26T20:59:37","modified_gmt":"2024-12-26T12:59:37","slug":"python%e5%a6%82%e4%bd%95%e6%b1%82%e7%b4%a0%e6%95%b0","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/940419.html","title":{"rendered":"python\u5982\u4f55\u6c42\u7d20\u6570"},"content":{"rendered":"<p style=\"text-align:center;\" ><img decoding=\"async\" src=\"https:\/\/cdn-kb.worktile.com\/kb\/wp-content\/uploads\/2024\/04\/25075047\/cc97f9c2-0963-46ae-86f9-870fc1a7f3ae.webp\" alt=\"python\u5982\u4f55\u6c42\u7d20\u6570\" \/><\/p>\n<p><p> <strong>\u5728Python\u4e2d\u6c42\u7d20\u6570\u7684\u65b9\u6cd5\u6709\u591a\u79cd\uff0c\u5e38\u7528\u7684\u5305\u62ec\uff1a\u904d\u5386\u9664\u6cd5\u3001\u57c3\u62c9\u6258\u65af\u7279\u5c3c\u7b5b\u6cd5\u3001\u4f18\u5316\u7684\u8bd5\u9664\u6cd5\u3002<\/strong><br \/>\u5176\u4e2d\uff0c\u57c3\u62c9\u6258\u65af\u7279\u5c3c\u7b5b\u6cd5\u662f\u4e00\u79cd\u9ad8\u6548\u7684\u7b97\u6cd5\uff0c\u9002\u7528\u4e8e\u6c42\u53d6\u67d0\u4e2a\u8303\u56f4\u5185\u7684\u6240\u6709\u7d20\u6570\u3002  <\/p>\n<\/p>\n<p><p>\u904d\u5386\u9664\u6cd5\u662f\u6700\u76f4\u63a5\u7684\u65b9\u6cd5\uff0c\u901a\u8fc7\u904d\u5386\u4ece2\u5230n-1\u7684\u6240\u6709\u6574\u6570\uff0c\u68c0\u67e5n\u80fd\u5426\u88ab\u6574\u9664\u6765\u5224\u65adn\u662f\u5426\u4e3a\u7d20\u6570\u3002\u8fd9\u79cd\u65b9\u6cd5\u867d\u7136\u7b80\u5355\uff0c\u4f46\u5f53n\u8f83\u5927\u65f6\u6548\u7387\u8f83\u4f4e\u3002\u57c3\u62c9\u6258\u65af\u7279\u5c3c\u7b5b\u6cd5\u5219\u901a\u8fc7\u6784\u5efa\u4e00\u4e2a\u5e03\u5c14\u6570\u7ec4\u6765\u6807\u8bb0\u975e\u7d20\u6570\uff0c\u4ece\u800c\u8fc5\u901f\u627e\u51fa\u8303\u56f4\u5185\u7684\u6240\u6709\u7d20\u6570\u3002\u8fd9\u79cd\u65b9\u6cd5\u9002\u7528\u4e8e\u6c42\u53d6\u8f83\u5927\u8303\u56f4\u5185\u7684\u7d20\u6570\u3002  <\/p>\n<\/p>\n<p><p><strong>\u57c3\u62c9\u6258\u65af\u7279\u5c3c\u7b5b\u6cd5\u8be6\u7ec6\u63cf\u8ff0\uff1a<\/strong><br \/>\u57c3\u62c9\u6258\u65af\u7279\u5c3c\u7b5b\u6cd5\u662f\u53e4\u5e0c\u814a\u6570\u5b66\u5bb6\u53d1\u660e\u7684\u4e00\u79cd\u7b97\u6cd5\uff0c\u7528\u4e8e\u627e\u51fa\u67d0\u4e2a\u8303\u56f4\u5185\u7684\u6240\u6709\u7d20\u6570\u3002\u5176\u57fa\u672c\u601d\u60f3\u662f\u4ece2\u5f00\u59cb\uff0c\u5c06\u6bcf\u4e2a\u7d20\u6570\u7684\u500d\u6570\u6807\u8bb0\u4e3a\u975e\u7d20\u6570\uff0c\u6700\u540e\u6ca1\u6709\u88ab\u6807\u8bb0\u7684\u5373\u4e3a\u7d20\u6570\u3002\u5177\u4f53\u6b65\u9aa4\u5982\u4e0b\uff1a<\/p>\n<\/p>\n<ol>\n<li>\u521b\u5efa\u4e00\u4e2a\u5e03\u5c14\u6570\u7ec4\uff0c\u5927\u5c0f\u4e3an+1\uff0c\u521d\u59cb\u503c\u4e3aTrue\uff0c\u8868\u793a\u6240\u6709\u6570\u90fd\u662f\u7d20\u6570\u3002<\/li>\n<li>\u4ece2\u5f00\u59cb\uff0c\u9010\u4e2a\u68c0\u67e5\u6570\u7ec4\u7684\u6bcf\u4e2a\u5143\u7d20\u3002<\/li>\n<li>\u5982\u679c\u5143\u7d20\u4e3aTrue\uff0c\u5219\u5176\u4e3a\u7d20\u6570\uff0c\u5c06\u5176\u6240\u6709\u500d\u6570\u6807\u8bb0\u4e3aFalse\u3002<\/li>\n<li>\u7ee7\u7eed\u4e0b\u4e00\u4e2a\u672a\u88ab\u6807\u8bb0\u7684\u5143\u7d20\uff0c\u91cd\u590d\u6b65\u9aa43\uff0c\u76f4\u5230\u904d\u5386\u5b8c\u6574\u4e2a\u6570\u7ec4\u3002<\/li>\n<li>\u6700\u540e\uff0c\u6570\u7ec4\u4e2d\u4ecd\u4e3aTrue\u7684\u4f4d\u7f6e\u5bf9\u5e94\u7684\u6570\u5373\u4e3a\u7d20\u6570\u3002<\/li>\n<\/ol>\n<p><p>\u8fd9\u79cd\u65b9\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO(n log log n)\uff0c\u5bf9\u4e8e\u8f83\u5927\u7684n\u4ecd\u7136\u975e\u5e38\u9ad8\u6548\u3002  <\/p>\n<\/p>\n<p><p>\u63a5\u4e0b\u6765\uff0c\u6211\u4eec\u5c06\u8be6\u7ec6\u63a2\u8ba8\u5404\u79cd\u65b9\u6cd5\u7684\u5b9e\u73b0\u548c\u6bd4\u8f83\u3002<\/p>\n<\/p>\n<p><p>\u4e00\u3001\u904d\u5386\u9664\u6cd5<\/p>\n<\/p>\n<p><p>\u904d\u5386\u9664\u6cd5\u662f\u5224\u65ad\u4e00\u4e2a\u6570\u662f\u5426\u4e3a\u7d20\u6570\u7684\u6700\u7b80\u5355\u65b9\u6cd5\u3002\u57fa\u672c\u601d\u60f3\u662f\u68c0\u67e5\u4e00\u4e2a\u6570\u80fd\u5426\u88ab\u4ece2\u5230\u5176\u5e73\u65b9\u6839\u4e4b\u95f4\u7684\u4efb\u4e00\u6574\u6570\u6574\u9664\u3002\u5982\u679c\u4e0d\u80fd\uff0c\u5219\u8be5\u6570\u4e3a\u7d20\u6570\u3002\u4ee5\u4e0b\u662f\u904d\u5386\u9664\u6cd5\u7684\u5b9e\u73b0\u7ec6\u8282\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">def is_prime(n):<\/p>\n<p>    if n &lt;= 1:<\/p>\n<p>        return False<\/p>\n<p>    for i in range(2, int(n0.5) + 1):<\/p>\n<p>        if n % i == 0:<\/p>\n<p>            return False<\/p>\n<p>    return True<\/p>\n<p>def find_primes(limit):<\/p>\n<p>    primes = []<\/p>\n<p>    for num in range(2, limit + 1):<\/p>\n<p>        if is_prime(num):<\/p>\n<p>            primes.append(num)<\/p>\n<p>    return primes<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p><strong>\u89e3\u91ca\uff1a<\/strong><\/p>\n<\/p>\n<ul>\n<li><code>is_prime<\/code>\u51fd\u6570\u7528\u4e8e\u5224\u65ad\u4e00\u4e2a\u6570\u662f\u5426\u4e3a\u7d20\u6570\u3002\u82e5n\u5c0f\u4e8e\u7b49\u4e8e1\uff0c\u5219\u8fd4\u56deFalse\uff0c\u56e0\u4e3a\u7d20\u6570\u5b9a\u4e49\u4e3a\u5927\u4e8e1\u7684\u81ea\u7136\u6570\u3002<\/li>\n<li>\u5bf9\u4e8e\u5927\u4e8e1\u7684\u6570\uff0c\u904d\u5386\u4ece2\u5230n\u7684\u5e73\u65b9\u6839\u7684\u6574\u6570\uff0c\u82e5n\u80fd\u88ab\u6574\u9664\uff0c\u5219\u8fd4\u56deFalse\u3002<\/li>\n<li><code>find_primes<\/code>\u51fd\u6570\u7528\u4e8e\u627e\u51fa\u6307\u5b9a\u8303\u56f4\u5185\u7684\u6240\u6709\u7d20\u6570\u3002<\/li>\n<\/ul>\n<p><p>\u8fd9\u79cd\u65b9\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO(n\u221an)\uff0c\u5bf9\u4e8e\u8f83\u5927\u7684n\uff0c\u6548\u7387\u76f8\u5bf9\u8f83\u4f4e\u3002<\/p>\n<\/p>\n<p><p>\u4e8c\u3001\u57c3\u62c9\u6258\u65af\u7279\u5c3c\u7b5b\u6cd5<\/p>\n<\/p>\n<p><p>\u57c3\u62c9\u6258\u65af\u7279\u5c3c\u7b5b\u6cd5\u662f\u4e00\u79cd\u9ad8\u6548\u6c42\u7d20\u6570\u7684\u7b97\u6cd5\uff0c\u7279\u522b\u9002\u5408\u6c42\u53d6\u8f83\u5927\u8303\u56f4\u5185\u7684\u6240\u6709\u7d20\u6570\u3002\u5176\u57fa\u672c\u601d\u60f3\u662f\u4f9d\u6b21\u6807\u8bb0\u6bcf\u4e2a\u7d20\u6570\u7684\u500d\u6570\u4e3a\u975e\u7d20\u6570\u3002\u4ee5\u4e0b\u662f\u57c3\u62c9\u6258\u65af\u7279\u5c3c\u7b5b\u6cd5\u7684\u5b9e\u73b0\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">def sieve_of_eratosthenes(limit):<\/p>\n<p>    is_prime = [True] * (limit + 1)<\/p>\n<p>    p = 2<\/p>\n<p>    while (p * p &lt;= limit):<\/p>\n<p>        if is_prime[p]:<\/p>\n<p>            for i in range(p * p, limit + 1, p):<\/p>\n<p>                is_prime[i] = False<\/p>\n<p>        p += 1<\/p>\n<p>    return [p for p in range(2, limit) if is_prime[p]]<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p><strong>\u89e3\u91ca\uff1a<\/strong><\/p>\n<\/p>\n<ul>\n<li>\u521d\u59cb\u5316\u4e00\u4e2a\u5e03\u5c14\u6570\u7ec4<code>is_prime<\/code>\uff0c\u957f\u5ea6\u4e3alimit+1\uff0c\u521d\u59cb\u503c\u4e3aTrue\u3002<\/li>\n<li>\u4ece2\u5f00\u59cb\uff0c\u904d\u5386\u5230limit\u7684\u5e73\u65b9\u6839\u3002<\/li>\n<li>\u5982\u679c<code>is_prime[p]<\/code>\u4e3aTrue\uff0c\u5219p\u662f\u7d20\u6570\uff0c\u5c06\u5176\u500d\u6570\u6807\u8bb0\u4e3aFalse\u3002<\/li>\n<li>\u6700\u540e\uff0c\u8fd4\u56de\u6570\u7ec4\u4e2d\u503c\u4e3aTrue\u7684\u7d22\u5f15\u503c\uff0c\u5373\u4e3a\u7d20\u6570\u3002<\/li>\n<\/ul>\n<p><p>\u8fd9\u79cd\u65b9\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO(n log log n)\uff0c\u5bf9\u4e8e\u5927\u8303\u56f4\u6c42\u7d20\u6570\u975e\u5e38\u9ad8\u6548\u3002<\/p>\n<\/p>\n<p><p>\u4e09\u3001\u4f18\u5316\u7684\u8bd5\u9664\u6cd5<\/p>\n<\/p>\n<p><p>\u4f18\u5316\u7684\u8bd5\u9664\u6cd5\u662f\u5728\u904d\u5386\u9664\u6cd5\u7684\u57fa\u7840\u4e0a\u8fdb\u884c\u6539\u8fdb\u3002\u901a\u8fc7\u51cf\u5c11\u4e0d\u5fc5\u8981\u7684\u68c0\u67e5\u6765\u63d0\u9ad8\u6548\u7387\u3002\u4ee5\u4e0b\u662f\u4f18\u5316\u7684\u8bd5\u9664\u6cd5\u7684\u5b9e\u73b0\uff1a<\/p>\n<\/p>\n<p><pre><code class=\"language-python\">def is_prime_optimized(n):<\/p>\n<p>    if n &lt;= 1:<\/p>\n<p>        return False<\/p>\n<p>    if n &lt;= 3:<\/p>\n<p>        return True<\/p>\n<p>    if n % 2 == 0 or n % 3 == 0:<\/p>\n<p>        return False<\/p>\n<p>    i = 5<\/p>\n<p>    while (i * i &lt;= n):<\/p>\n<p>        if n % i == 0 or n % (i + 2) == 0:<\/p>\n<p>            return False<\/p>\n<p>        i += 6<\/p>\n<p>    return True<\/p>\n<p>def find_primes_optimized(limit):<\/p>\n<p>    primes = []<\/p>\n<p>    for num in range(2, limit + 1):<\/p>\n<p>        if is_prime_optimized(num):<\/p>\n<p>            primes.append(num)<\/p>\n<p>    return primes<\/p>\n<p><\/code><\/pre>\n<\/p>\n<p><p><strong>\u89e3\u91ca\uff1a<\/strong><\/p>\n<\/p>\n<ul>\n<li><code>is_prime_optimized<\/code>\u51fd\u6570\u901a\u8fc7\u51cf\u5c11\u4e0d\u5fc5\u8981\u7684\u9664\u6cd5\u64cd\u4f5c\u6765\u63d0\u9ad8\u6548\u7387\u3002<\/li>\n<li>\u5bf9\u4e8e\u5927\u4e8e3\u7684\u6570\uff0c\u5148\u6392\u9664\u5076\u6570\u548c3\u7684\u500d\u6570\uff0c\u7136\u540e\u4ece5\u5f00\u59cb\u68c0\u67e5\uff0c\u6b65\u957f\u4e3a6\u3002<\/li>\n<\/ul>\n<p><p>\u8fd9\u79cd\u4f18\u5316\u65b9\u6cd5\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\u53ef\u4ee5\u663e\u8457\u63d0\u9ad8\u6548\u7387\uff0c\u5c24\u5176\u662f\u5bf9\u4e8e\u8f83\u5927\u7684n\u3002<\/p>\n<\/p>\n<p><p>\u56db\u3001\u6bd4\u8f83\u4e0e\u9009\u62e9<\/p>\n<\/p>\n<p><p>\u5728\u5b9e\u9645\u5e94\u7528\u4e2d\uff0c\u9009\u62e9\u5408\u9002\u7684\u6c42\u7d20\u6570\u65b9\u6cd5\u53d6\u51b3\u4e8e\u5177\u4f53\u7684\u9700\u6c42\u548c\u9650\u5236\uff1a<\/p>\n<\/p>\n<ul>\n<li>\u82e5\u4ec5\u5224\u65ad\u5355\u4e2a\u6570\u662f\u5426\u4e3a\u7d20\u6570\uff0c\u904d\u5386\u9664\u6cd5\u548c\u4f18\u5316\u7684\u8bd5\u9664\u6cd5\u90fd\u53ef\u4ee5\u4f7f\u7528\u3002<\/li>\n<li>\u82e5\u9700\u8981\u6c42\u53d6\u8f83\u5927\u8303\u56f4\u5185\u7684\u6240\u6709\u7d20\u6570\uff0c\u57c3\u62c9\u6258\u65af\u7279\u5c3c\u7b5b\u6cd5\u662f\u6700\u4f73\u9009\u62e9\u3002<\/li>\n<li>\u5728\u6027\u80fd\u8981\u6c42\u8f83\u9ad8\u7684\u60c5\u51b5\u4e0b\uff0c\u4f18\u5316\u7684\u8bd5\u9664\u6cd5\u53ef\u4ee5\u7528\u4e8e\u8f83\u5c0f\u8303\u56f4\u7684\u5feb\u901f\u5224\u65ad\u3002<\/li>\n<\/ul>\n<p><p>\u901a\u8fc7\u7ed3\u5408\u8fd9\u4e9b\u65b9\u6cd5\uff0c\u53ef\u4ee5\u6839\u636e\u5177\u4f53\u9700\u6c42\u7075\u6d3b\u9009\u62e9\uff0c\u4ee5\u8fbe\u5230\u9ad8\u6548\u7684\u7d20\u6570\u6c42\u89e3\u3002<\/p>\n<\/p>\n<h2><strong>\u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n<p> <strong>\u4ec0\u4e48\u662f\u7d20\u6570\uff0c\u5982\u4f55\u5728Python\u4e2d\u5b9a\u4e49\u5b83\u4eec\uff1f<\/strong><br \/>\u7d20\u6570\u662f\u5927\u4e8e1\u7684\u81ea\u7136\u6570\uff0c\u4e14\u53ea\u80fd\u88ab1\u548c\u81ea\u8eab\u6574\u9664\u3002\u5728Python\u4e2d\uff0c\u53ef\u4ee5\u901a\u8fc7\u5b9a\u4e49\u4e00\u4e2a\u51fd\u6570\u6765\u68c0\u67e5\u4e00\u4e2a\u6570\u662f\u5426\u4e3a\u7d20\u6570\u3002\u901a\u5e38\uff0c\u8fd9\u4e2a\u51fd\u6570\u4f1a\u8fed\u4ee3\u4ece2\u5230\u8be5\u6570\u7684\u5e73\u65b9\u6839\uff0c\u68c0\u67e5\u662f\u5426\u5b58\u5728\u56e0\u6570\u3002<\/p>\n<p><strong>\u5728Python\u4e2d\u68c0\u67e5\u7d20\u6570\u7684\u6700\u4f73\u65b9\u6cd5\u662f\u4ec0\u4e48\uff1f<\/strong><br \/>\u4e00\u79cd\u5e38\u89c1\u7684\u65b9\u5f0f\u662f\u4f7f\u7528\u201c\u57c3\u62c9\u6258\u65af\u7279\u5c3c\u7b5b\u6cd5\u201d\uff08Sieve of Eratosthenes\uff09\uff0c\u8fd9\u662f\u4e00\u79cd\u9ad8\u6548\u7684\u7b97\u6cd5\uff0c\u53ef\u4ee5\u627e\u51fa\u4e00\u5b9a\u8303\u56f4\u5185\u7684\u6240\u6709\u7d20\u6570\u3002\u8be5\u65b9\u6cd5\u901a\u8fc7\u6807\u8bb0\u5408\u6570\uff0c\u4ece\u800c\u7b5b\u9009\u51fa\u7d20\u6570\uff0c\u6548\u7387\u8f83\u9ad8\uff0c\u9002\u5408\u5904\u7406\u8f83\u5927\u7684\u6570\u5b57\u8303\u56f4\u3002<\/p>\n<p><strong>\u5982\u4f55\u5728Python\u4e2d\u751f\u6210\u6307\u5b9a\u8303\u56f4\u5185\u7684\u6240\u6709\u7d20\u6570\uff1f<\/strong><br \/>\u53ef\u4ee5\u4f7f\u7528\u5faa\u73af\u7ed3\u5408\u4e0a\u8ff0\u7684\u7d20\u6570\u68c0\u67e5\u51fd\u6570\uff0c\u904d\u5386\u4e00\u4e2a\u8303\u56f4\uff08\u4f8b\u59821\u5230100\uff09\uff0c\u5e76\u5c06\u6240\u6709\u7d20\u6570\u5b58\u5165\u5217\u8868\u4e2d\u3002\u901a\u8fc7\u5217\u8868\u63a8\u5bfc\u5f0f\uff0c\u53ef\u4ee5\u7b80\u5316\u4ee3\u7801\u5e76\u63d0\u9ad8\u53ef\u8bfb\u6027\uff0c\u4ece\u800c\u5feb\u901f\u751f\u6210\u6307\u5b9a\u8303\u56f4\u5185\u7684\u7d20\u6570\u5217\u8868\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"\u5728Python\u4e2d\u6c42\u7d20\u6570\u7684\u65b9\u6cd5\u6709\u591a\u79cd\uff0c\u5e38\u7528\u7684\u5305\u62ec\uff1a\u904d\u5386\u9664\u6cd5\u3001\u57c3\u62c9\u6258\u65af\u7279\u5c3c\u7b5b\u6cd5\u3001\u4f18\u5316\u7684\u8bd5\u9664\u6cd5\u3002\u5176\u4e2d\uff0c\u57c3\u62c9\u6258\u65af\u7279\u5c3c\u7b5b [&hellip;]","protected":false},"author":3,"featured_media":940425,"comment_status":"closed","ping_status":"","sticky":false,"template":"","format":"standard","meta":{"_acf_changed":false,"footnotes":""},"categories":[37],"tags":[],"acf":[],"_links":{"self":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/940419"}],"collection":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/users\/3"}],"replies":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/comments?post=940419"}],"version-history":[{"count":"1","href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/940419\/revisions"}],"predecessor-version":[{"id":940426,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/940419\/revisions\/940426"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media\/940425"}],"wp:attachment":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media?parent=940419"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/categories?post=940419"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/tags?post=940419"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}