{"id":694,"date":"2020-04-23T17:46:19","date_gmt":"2020-04-23T09:46:19","guid":{"rendered":"http:\/\/www.mustenaka.cn\/?p=694"},"modified":"2020-04-23T19:58:31","modified_gmt":"2020-04-23T11:58:31","slug":"primenumbersinpython","status":"publish","type":"post","link":"https:\/\/www.mustenaka.cn\/index.php\/2020\/04\/23\/primenumbersinpython\/","title":{"rendered":"Python\u6c42\u7d20\u6570\u4ee5\u53ca\u76f8\u5173\u95ee\u9898[\u6734\u7d20\u6cd5][\u57c3\u6c0f\u7b5b\u6cd5][\u6b27\u62c9\u7b5b\uff08\u7ebf\u6027\u7b5b\uff09]"},"content":{"rendered":"<h2>\u6c42\u89e3\u7d20\u6570\u7684\u4e09\u79cd\u65b9\u6cd5<\/h2>\n<hr \/>\n<p>\u9996\u5148\u660e\u767d\u4e00\u4e0b\u4ec0\u4e48\u662f\u7d20\u6570\uff0c\u7d20\u6570\u53c8\u540d\u8d28\u6570\uff0c\u9664\u4e862\u4ee5\u5916\u5c31\u662f\u5b83\u672c\u8eab\u53ea\u80fd\u62c6\u5206\u62101\u548c\u81ea\u8eab\u76f8\u4e58\u800c\u7684\u6765\u7684\u6570\uff0c\u59827\u5c31\u662f\u4e00\u4e2a\u7d20\u6570\uff0c\u4ed6\u53ea\u80fd\u75311*7\u5f97\u5230\uff0c\u800c6\u4e0d\u662f\u4e00\u4e2a\u7d20\u6570\uff0c\u56e0\u4e3a\u5b83\u65e2\u53ef\u4ee5\u75311*6\u5f97\u5230\uff0c\u4e5f\u53ef\u4ee5\u75312*3\u5f97\u5230\u3002<\/p>\n<h3>1.\u3010\u6734\u7d20\u6cd5\u3011\u6c42\u89e3\uff1a<\/h3>\n<p>\u90a3\u4e48\u77e5\u9053\u4e00\u4e2a\u7d20\u6570\u7684\u6982\u5ff5\uff0c\u6211\u4eec\u4fbf\u6709\u4e86\u4e00\u4e2a\u6700\u6734\u7d20\u7684\u65b9\u6cd5\u6c42\u89e3\uff0c\u5373\u4ece2~n\uff0c\u6bcf\u4e00\u4e2a\u6570i\u8fdb\u884c\u4e00\u4e2a\u5224\u65ad\uff0c\u8fd9\u4e2a\u6570\u5b57i\u4ece2\u5230i-1\u4e4b\u95f4\uff0c\u662f\u5426\u5b58\u5728\u4e00\u4e2a\u6570\u5b57\u53ef\u4ee5\u4e0e\u4e4b\u6c42\u4f59=0\u7684\u60c5\u51b5\uff0c\u5982\u679c\u6ca1\u6709\uff0c\u5219\u8fd9\u662f\u4e00\u4e2a\u7d20\u6570\u3002<\/p>\n<pre class=\"pure-highlightjs\"><code class=\"\" python=\"\">primesNumber = []\r\n\r\n\r\ndef is_prime(n):\r\n    for i in range(2, n-1):\r\n        if n % i == 0:\r\n            return False\r\n    return True\r\n\r\n\r\ndef primes(number):\r\n    for i in range(2, number):\r\n        if is_prime(i):\r\n            primesNumber.append(i)\r\n\r\n\r\nprimes(10000)\r\nprint(primesNumber)\r\n<\/code><\/pre>\n<p>\u4e00\u4e2a\u7b80\u5355\u7684\u4f18\u5316\u5c31\u662f\uff0c\u5728\u7b5b\u9009\u7684\u65f6\u5019\u5c06\u5224\u65ad\u6570\u636e\u7684\u4e0a\u5c4a\u4f7f\u7528sqrt\u5f00\u5e73\u65b9\u7684\u65b9\u5f0f\u7b80\u5316\u5224\u65ad\u6570\u636e\uff0c\u4f7f\u75286\u8fd9\u4e2a\u6570\u5b57\u5c31\u53ef\u4ee5\u5f88\u597d\u7406\u89e3\uff0csqrt(6)\u7ea6\u7b49\u4e8e2.4\uff0c\u53d6\u6574\u540e\u5c31\u662f2\uff0c\u90a3\u4e48\u5b58\u5728\u4e00\u4e2a2*3=6\u53ef\u4ee5\u6ee1\u8db3\uff0c\u8fd9\u4e0e\u6c42\u5b8c\u6574\u7684\u6570\u636e\u662f\u4e00\u6837\u7684\uff0c\u53ea\u4e0d\u8fc7\u66f4\u52a0\u9ad8\u6548\u3002<\/p>\n<pre class=\"pure-highlightjs\"><code class=\"\" python=\"\">primesNumber = []\r\n\r\n\r\ndef is_prime(n):\r\n    for i in range(2, int(n ** 0.5)):\r\n        if n % i == 0:\r\n            return False\r\n    return True\r\n\r\n\r\ndef primes(number):\r\n    for i in range(2, number):\r\n        if is_prime(i):\r\n            primesNumber.append(i)\r\n\r\n#30000\u7684\u65f6\u5019\u4f1a\u9047\u5230Python\u7684List\u5b58\u50a8\u8d85\u9650\u7684\u95ee\u9898\uff0c\u5bfc\u81f4\u65e0\u6cd5\u5168\u90e8\u5b58\u5165\r\nprimes(20000)\r\nprint(primesNumber)\r\n<\/code><\/pre>\n<ul>\n<li>\u6734\u7d20\u6c42\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u662fO(n^2)\u3002<\/li>\n<\/ul>\n<p>\u6b64\u5916\uff0c\u6734\u7d20\u65b9\u6cd5\u4e00\u4e9b\u53d8\u79cd\u53ef\u4ee5\u95f4\u63a5\u6027\u7684\u589e\u52a0\u5904\u7406\u901f\u5ea6\uff0c\u4f46\u57fa\u672c\u4e0a\u90fd\u662f\u4fdd\u6301\u5728\u8fd9\u4e2a\u590d\u6742\u5ea6\u4e86\u3002<\/p>\n<p>\u8fd9\u91cc\u8981\u6ce8\u610f\u4e00\u4e2aPython\u7684\u95ee\u9898\uff0c\u6211\u4eec\u91c7\u53d6List\u8fdb\u884c\u5b58\u653e\u7d20\u6570\uff0c\u7136\u800cPython\u7684List\u7684\u7a7a\u95f4\u9650\u5236\u539f\u56e0\uff0c\u5bfc\u81f4\u6211\u4eec\u6c42\u5230\u5927\u69823*10^4\u5927\u5c0f\u7684\u6570\u5b57\u7684\u540c\u65f6\u4f1a\u53d1\u751f\u4e00\u4e9b\u6ea2\u51fa\u73b0\u8c61\uff0c\u8fd9\u4e2a\u65f6\u5019\u662f\u6ca1\u6709\u62a5\u9519\u7684\uff0c\u53ef\u4ee5\u6709\u4e24\u4e2a\u89e3\u51b3\u7684\u601d\u8def\uff0c\u8fd9\u91cc\u5c31\u4e0d\u5e2e\u52a9\u89e3\u51b3\u4e86\uff08<del>\u4e0d\u7136\u504f\u9898<\/del>\uff09<\/p>\n<ol>\n<li>List\u6269\u5bb9\uff0c\u6216\u8005\u4f7f\u7528\u591a\u6bb5List\uff08\u64cd\u4f5c\u4e0a\u6ca1\u6709\u90a3\u4e48\u65b9\u4fbf\uff09<\/li>\n<li>\u4e0d\u5b58\u50a8\u7d20\u6570\uff0c\u5c06\u6240\u9700\u8981\u7684\u6570\u636e\u76f4\u63a5\u8f93\u51fa<\/li>\n<\/ol>\n<h3>2.<span>\u57c3\u6c0f\u7b5b\u6cd5<\/span><\/h3>\n<p><span>\u57c3\u5f0f\u7b5b\u6cd5\u7684\u601d\u60f3\u662f\uff1a\u5bf9\u4e8e\u4e0d\u8d85\u8fc7 n \u7684\u6bcf\u4e2a\u975e\u8d1f\u6574\u6570 p\uff0c\u5220\u9664 2*p, 3*p, 4*p,&#8230;\uff0c\u5f53\u5904\u7406\u5b8c\u6240\u6709\u6570\u4e4b\u540e\uff0c\u8fd8\u6ca1\u6709\u88ab\u5220\u9664\u7684\u5c31\u662f\u7d20\u6570\u3002<\/span><\/p>\n<p>\u6211\u4eec\u53ef\u4ee5\u4ece2\u5f00\u59cb\uff0c\u4ece\u5c0f\u5230\u5927\u626b\u63cf\u6bcf\u4e2a\u6570x,\u628ax\u7684\u500d\u6570x*2,x*3,&#8230;x*(N\/x)\u6807\u8bb0\u4e3a\u975e\u8d28\u6570\u3010\u6b64\u5904\u5176\u5b9e\u53ef\u4ee5\u4f18\u5316\uff0c\u4e0d\u7528\u4ece2\u500d\u5f00\u59cb\uff0c\u56e0\u4e3a\u5bf9\u4e8e\u6bcf\u4e2a\u6570x,x\u76842\u500d\uff0c3\u500d\u90fd\u4f1a\u88ab2,3\uff0c..&lt;x\u7684\u6570\u7b5b\u8fc7\uff0c\u56e0\u6b64\u53ea\u9700\u4ecex\u500d\u5f00\u59cb\u3011\u3002<\/p>\n<p>\u5f53\u626b\u63cf\u5230\u4e00\u4e2a\u6570x\u65f6\uff0c\u82e5\u672a\u88ab\u6807\u8bb0\u4e3a\u975e\u8d28\u6570\uff0c\u90a3\u4e48\u8be5\u6570\u4fbf\u662f\u8d28\u6570\uff0c\u56e0\u4e3a\u5b83\u80fd\u5728\u6bd4\u5b83\u5c0f\u7684\u6570\u7684\u8fc7\u7b5b\u8fc7\u7a0b\u4e2d\u9003\u8fc7\uff0c\u5c31\u8bf4\u660e\u5b83\u524d\u9762\u6ca1\u6709\u4e00\u4e2a\u6570\u662f\u5b83\u7684\u500d\u6570\uff0c\u7136\u4e00\u4e2a\u6570\u7684\u56e0\u5b50\u53ea\u53ef\u80fd\u6bd4\u5b83\u5c0f\uff0c\u56e0\u6b64\u6211\u4eec\u53ef\u4ee5\u65ad\u5b9a\uff0c\u8be5\u6570x\u4fbf\u662f\u4e00\u4e2a\u7d20\u6570\u3002<\/p>\n<blockquote><p>\u4e00\u4e2a\u7b80\u5355\u7684\u7406\u89e3\u5c31\u662f\uff1a\u5229\u7528\u500d\u6570\u89c4\u5219\uff0c\u5c062\u7684\u500d\u6570\uff0c3\u7684\u500d\u6570\uff0c4\u7684\u500d\u6570\uff0c5\u7684\u500d\u6570\u7b49\u6570\u5b57\u4f9d\u6b21\u4ece\u7d20\u6570\u8868\u4e2d\u5220\u9664\uff0c\u672c\u8d28\u4e0a\u662f\u5bfb\u627e\u975e\u7d20\u6570\uff0c\u4f46\u662f\u603b\u6570-\u975e\u7d20\u6570=\u7d20\u6570\u3002<\/p><\/blockquote>\n<p>\u5177\u4f53\u7684\u4ee3\u7801\u5982\u4e0b\uff1a<\/p>\n<pre class=\"pure-highlightjs\"><code class=\"\" python=\"\"># \u751f\u6210\u4e00\u4e2a\u5947\u6570\u5e8f\u5217\r\ndef _odd_iter():\r\n    n = 1\r\n    while True:\r\n        n = n + 2\r\n        yield n\r\n\r\n\r\n# \u7b5b\u9009\u51fd\u6570\uff0c\u4fdd\u7559\u4e0d\u80fd\u6574\u9664\u7684\uff0c\u7b5b\u6389\u53ef\u4ee5\u6574\u9664\u7684\uff0c\u5373\u500d\u6570\u3002\r\ndef _not_divisible(n):\r\n    return lambda x: x % n &gt; 0\r\n\r\n\r\n# \u6c42\u7d20\u6570\u51fd\u6570\u3002\r\ndef primes():\r\n    yield 2\r\n    it = _odd_iter()  # \u521d\u59cb\u5e8f\u5217\r\n    while True:\r\n        n = next(it)\r\n        yield n\r\n        it = filter(_not_divisible(n), it)  # it\u5728\u4e0d\u65ad\u7684next\u8c03\u7528\u4e2d\uff0c\u8fdb\u884c\u7b5b\u9009\u3002\r\n\r\n\r\n# \u8f93\u51fa100000\u4ee5\u5185\u7684\u6240\u6709\u7d20\u6570,\u901f\u5ea6\u7a0d\u5fae\u5feb\u4e00\u4e22\u4e22\uff1a\r\nfor n in primes():\r\n    if n &lt; 100000:\r\n        print(n, end=' ')\r\n    else:\r\n        break\r\n<\/code><\/pre>\n<p>\u8fd9\u4efd\u4ee3\u7801\u91c7\u53d6\u5229\u7528\u751f\u6210\u5668\u2014\u2014filter()\u7b5b\u9009\u51fd\u6570\u8fdb\u884c\u8fc7\u6ee4\uff0c\u8fd9\u6837\u5199\u6bd4\u8f83\u76f4\u89c2\u800c\u4e14filter\u8fc7\u6ee4\u7684\u901f\u5ea6\u76f8\u5f53\u5feb\uff0c\u4f46\u5982\u679c\u57fa\u7840\u4e0d\u662f\u5f88\u597d\u53ef\u4ee5\u53c2\u8003\u4e00\u4e0b\u8fd9\u4e2aC\u8bed\u8a00\u7248\u672c\u7684\uff0c\u8f83\u4e3a\u5bb9\u6613\u7406\u89e3\u3002<\/p>\n<pre class=\"pure-highlightjs\"><code class=\"\" cpp=\"\">    bool isprime[10000005];\r\n\u00a0\u00a0\u00a0\u00a0void aishiPrime(int n){\r\n\tmemset(isprime,true,sizeof(isprime));\r\n\tisprime[1]=false;\r\n\tfor (int i=2; i*i&lt;=n; i++){\r\n\t\tif (isprime[i])\t{    \r\n\t\t  \tfor(int j=i*i;j&lt;=n; j+=i) \r\n            \t\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0isprime[j]=false; \r\n    \t\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0}\r\n\t}\t    \r\n\u00a0\u00a0\u00a0\u00a0}<\/code><\/pre>\n<ul>\n<li><span>\u57c3\u6c0f\u7b5b\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3a\uff1aO(n*logn)<\/span><\/li>\n<\/ul>\n<h3><span>3.\u6b27\u62c9\u7b5b\uff08\u7ebf\u6027\u7b5b\uff09<\/span><\/h3>\n<p>\u6b27\u62c9\u7b5b\u7684\u601d\u60f3\u662f\uff1a\u5728\u57c3\u6c0f\u7b5b\u6cd5\u7684\u57fa\u7840\u4e0a\uff0c\u8ba9\u6bcf\u4e2a\u5408\u6570\u53ea\u88ab\u5b83\u7684\u6700\u5c0f\u8d28\u56e0\u5b50\u7b5b\u9009\u4e00\u6b21\uff0c\u4ee5\u8fbe\u5230\u4e0d\u91cd\u590d\u7684\u76ee\u7684\u3002<\/p>\n<blockquote><p>\u5408\u6570\uff1a\u3010\u6458\u81ea\u767e\u5ea6\u767e\u79d1\u3011<span>\u5408\u6570\u662f\u6307<\/span><a target=\"_blank\" href=\"https:\/\/baike.baidu.com\/item\/\/385394\" data-lemmaid=\"385394\" rel=\"noopener noreferrer\"><\/a><span>\u5728\u5927\u4e8e1\u7684\u6574\u6570\u4e2d\u9664\u4e86\u80fd\u88ab1\u548c\u672c\u8eab\u6574\u9664\u5916\uff0c\u8fd8\u80fd\u88ab\u5176\u4ed6\u6570\uff080\u9664\u5916\uff09<\/span>\u6574\u9664<span>\u7684\u6570\u3002\u4e0e\u4e4b\u76f8\u5bf9\u7684\u662f<\/span>\u8d28\u6570<span>\uff0c\u800c1\u65e2\u4e0d\u5c5e\u4e8e\u8d28\u6570\u4e5f\u4e0d\u5c5e\u4e8e\u5408\u6570\u3002\u6700\u5c0f\u7684\u5408\u6570\u662f<\/span><a target=\"_blank\" href=\"https:\/\/baike.baidu.com\/item\/4\/32006\" data-lemmaid=\"32006\" rel=\"noopener noreferrer\">4<\/a><span>\u3002\u5176\u4e2d\uff0c<\/span>\u5b8c\u5168\u6570<span>\u4e0e<\/span>\u76f8\u4eb2\u6570<span>\u662f\u4ee5\u5b83\u4e3a\u57fa\u7840\u7684\u3002<\/span><\/p><\/blockquote>\n<p>\u5982\uff1a385\u8fd9\u4e2a\u6570\uff0c385= 5 * 7* 11\uff0c\u4f1a\u88ab5\u7684\u500d\u6570\u65f6\u6807\u8bb0\u4e00\u6b21\uff0c7\u7684\u500d\u6570\u65f6\u6807\u8bb0\u4e00\u6b21\uff0c11\u7684\u500d\u6570\u65f6\u6807\u8bb0\u4e00\u6b21\uff0c\u9020\u6210\u6548\u7387\u8fbe\u4e0d\u5230\u6700\u4f18\u3002\u800c\u7ebf\u6027\u7b5b\u6cd5\u57fa\u4e8e\u6539\u8fdb\u8fd9\u4e2a\u4e0d\u8db3\u7684\u57fa\u7840\u4e0a\uff0c\u5728\u7ebf\u6027\u65f6\u95f4\u5185\uff0c\u4e5f\u5c31\u662fO(n)\uff0c\u7528\u7b5b\u9009\u7684\u65b9\u6cd5\u628a\u7d20\u6570\u627e\u51fa\u6765\u3002<\/p>\n<p><del>(\u4ece\u7f51\u4e0a\u76d7\u6765\u7684\u56fe2333333)<\/del><\/p>\n<p><img fetchpriority=\"high\" decoding=\"async\" src=\"https:\/\/www.mustenaka.cn\/wp-content\/uploads\/2020\/04\/aishisai.png\" alt=\"\" width=\"907\" height=\"598\" class=\"alignnone wp-image-697\" srcset=\"https:\/\/www.mustenaka.cn\/wp-content\/uploads\/2020\/04\/aishisai.png 824w, https:\/\/www.mustenaka.cn\/wp-content\/uploads\/2020\/04\/aishisai-300x198.png 300w, https:\/\/www.mustenaka.cn\/wp-content\/uploads\/2020\/04\/aishisai-768x506.png 768w\" sizes=\"(max-width: 907px) 100vw, 907px\" \/><\/p>\n<p>\u4ee3\u7801\u5982\u4e0b\u4e3a\uff1a<\/p>\n<pre class=\"pure-highlightjs\"><code class=\"\" python=\"\">#\u6b27\u62c9\u7b5b\u9009--\u7ebf\u6027\u7b5b\r\n# \u8fd4\u56de\u5c0f\u4e8er\u7684\u7d20\u6570\u5217\u8868\r\ndef oula(r):\r\n    # \u5168\u90e8\u521d\u59cb\u5316\u4e3a0\r\n    prime = [0 for i in range(r+1)]\r\n    # \u5b58\u653e\u7d20\u6570\r\n    common = []\r\n    for i in range(2, r+1):\r\n        if prime[i] == 0:\r\n            common.append(i)\r\n        for j in common:\r\n            if i*j &gt; r:\r\n                break\r\n            prime[i*j] = 1\r\n            #\u5c06\u91cd\u590d\u7b5b\u9009\u5254\u9664\r\n            if i % j == 0:\r\n                break\r\n    return common\r\n\r\n\r\nprime = oula(20000)\r\nprint(prime)\r\n<\/code><\/pre>\n<ul>\n<li>\u6b27\u62c9\u7b5b\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO(n)<\/li>\n<\/ul>\n<p>\u4ece\u65f6\u95f4\u7684\u8fd0\u884c\u4e0a\u76f8\u5bf9\u800c\u8a00\uff0c\u7d20\u6570\u7684\u7b5b\u9009\uff0c\u6700\u7406\u60f3\u7684\u8fd8\u662f\u6b27\u62c9\u7b5b\uff0c\u4f46\u662f\u9700\u8981\u5728\u524d\u6587\u7406\u89e3\u7684\u57fa\u7840\u4e0a\u624d\u80fd\u591f\u5f88\u597d\u7684\u5199\u51fa\u6765\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u6c42\u89e3\u7d20\u6570\u7684\u4e09\u79cd\u65b9\u6cd5 \u9996\u5148\u660e\u767d\u4e00\u4e0b\u4ec0\u4e48\u662f\u7d20\u6570\uff0c\u7d20\u6570\u53c8\u540d\u8d28\u6570\uff0c\u9664\u4e862\u4ee5\u5916\u5c31\u662f\u5b83\u672c\u8eab\u53ea\u80fd\u62c6\u5206\u62101\u548c\u81ea\u8eab\u76f8\u4e58 [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[30],"tags":[31],"class_list":["post-694","post","type-post","status-publish","format-standard","hentry","category-python","tag-python"],"views":3286,"_links":{"self":[{"href":"https:\/\/www.mustenaka.cn\/index.php\/wp-json\/wp\/v2\/posts\/694","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.mustenaka.cn\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.mustenaka.cn\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.mustenaka.cn\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.mustenaka.cn\/index.php\/wp-json\/wp\/v2\/comments?post=694"}],"version-history":[{"count":4,"href":"https:\/\/www.mustenaka.cn\/index.php\/wp-json\/wp\/v2\/posts\/694\/revisions"}],"predecessor-version":[{"id":699,"href":"https:\/\/www.mustenaka.cn\/index.php\/wp-json\/wp\/v2\/posts\/694\/revisions\/699"}],"wp:attachment":[{"href":"https:\/\/www.mustenaka.cn\/index.php\/wp-json\/wp\/v2\/media?parent=694"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.mustenaka.cn\/index.php\/wp-json\/wp\/v2\/categories?post=694"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.mustenaka.cn\/index.php\/wp-json\/wp\/v2\/tags?post=694"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}