{"id":200958,"date":"2024-05-10T02:12:50","date_gmt":"2024-05-09T18:12:50","guid":{"rendered":"https:\/\/docs.pingcode.com\/ask\/ask-ask\/200958.html"},"modified":"2024-05-10T02:12:55","modified_gmt":"2024-05-09T18:12:55","slug":"java%e7%9a%84biginteger%e7%9a%84%e4%b9%98%e6%b3%95%e8%bf%90%e7%ae%97%e6%98%af%e7%94%a8%e4%bb%80%e4%b9%88%e7%ae%97%e6%b3%95%e5%ae%9e%e7%8e%b0%e7%9a%84","status":"publish","type":"post","link":"https:\/\/docs.pingcode.com\/ask\/200958.html","title":{"rendered":"java\u7684BigInteger\u7684\u4e58\u6cd5\u8fd0\u7b97\u662f\u7528\u4ec0\u4e48\u7b97\u6cd5\u5b9e\u73b0\u7684"},"content":{"rendered":"

\"java\u7684BigInteger\u7684\u4e58\u6cd5\u8fd0\u7b97\u662f\u7528\u4ec0\u4e48\u7b97\u6cd5\u5b9e\u73b0\u7684\"<\/p>\n

Java\u7684BigInteger<\/code>\u7c7b\u7684\u4e58\u6cd5\u8fd0\u7b97\u4e3b\u8981\u91c7\u7528"\u957f\u4e58\u6cd5"\uff08Long Multiplication\uff09\u3001"\u5361\u62c9\u695a\u5df4\u7b97\u6cd5"\uff08Karatsuba Algorithm\uff09\u548c"\u6258\u6885\u5e93\u514b\u4e58\u6cd5"\uff08Toom-Cook Multiplication\uff09\u4e09\u79cd\u7b97\u6cd5\u5b9e\u73b0\uff0c\u5177\u4f53\u4f7f\u7528\u54ea\u79cd\u7b97\u6cd5\u53d6\u51b3\u4e8e\u64cd\u4f5c\u6570\u7684\u5927\u5c0f\u3002\u5176\u4e2d\uff0c\u5361\u62c9\u695a\u5df4\u7b97\u6cd5\u662f\u6700\u4e3a\u7a81\u51fa\u548c\u5e7f\u6cdb\u4f7f\u7528\u7684\u4e00\u79cd\uff0c\u5b83\u4e8e1960\u5e74\u7531\u5b89\u7eb3\u6258\u5229\u00b7\u5361\u62c9\u695a\u5df4\u63d0\u51fa\uff0c\u662f\u4e00\u79cd\u5206\u6cbb\u7b97\u6cd5\uff0c\u901a\u8fc7\u51cf\u5c11\u4e58\u6cd5\u7684\u6b21\u6570\u6765\u63d0\u9ad8\u5927\u6570\u4e58\u6cd5\u7684\u6548\u7387\u3002<\/p>\n<\/p>\n

\u5361\u62c9\u695a\u5df4\u7b97\u6cd5\u7684\u6838\u5fc3\u5728\u4e8e\u5c06\u5927\u6570\u4e58\u6cd5\u95ee\u9898\u5206\u89e3\u4e3a\u5c0f\u6570\u4e58\u6cd5\u95ee\u9898\uff0c\u4ece\u800c\u51cf\u5c11\u8ba1\u7b97\u91cf\u3002\u5177\u4f53\u800c\u8a00\uff0c\u8bbe\u6709\u4e24\u4e2a\u5927\u6570X\u548cY\uff0c\u5b83\u4eec\u5747\u53ef\u8868\u793a\u4e3a(A\u00b7B^n + B)\uff08\u5176\u4e2dA\u548cB\u662fX\u548cY\u7684\u9ad8\u534a\u90e8\u548c\u4f4e\u534a\u90e8\uff0cn\u662f\u57fa\u6570\u4f4d\uff09\u3002\u6309\u7167\u666e\u901a\u4e58\u6cd5\uff0c\u8ba1\u7b97X\u548cY\u7684\u4e58\u79ef\u9700\u8981\u56db\u4e2a\u5c0f\u6570\u7684\u4e58\u6cd5\u3002\u5361\u62c9\u695a\u5df4\u7b97\u6cd5\u901a\u8fc7\u7279\u522b\u7684\u7ec4\u5408\uff0c\u5c06\u8fd9\u56db\u6b21\u4e58\u6cd5\u4f18\u5316\u4e3a\u4e09\u6b21\uff0c\u8fd9\u6837\u901a\u8fc7\u51cf\u5c11\u8fd0\u7b97\u6b21\u6570\u6765\u63d0\u9ad8\u6548\u7387\u3002<\/p>\n<\/p>\n

\u4e00\u3001\u57fa\u672c\u4e58\u6cd5\u7b97\u6cd5\uff08\u957f\u4e58\u6cd5\uff09<\/h3>\n<\/p>\n

\u957f\u4e58\u6cd5\u662f\u6700\u7b80\u5355\u76f4\u89c2\u7684\u4e58\u6cd5\u7b97\u6cd5\uff0c\u9002\u7528\u4e8e\u8f83\u5c0f\u7684\u6570\u3002\u5b83\u6a21\u4eff\u4e86\u624b\u5de5\u4e58\u6cd5\u7684\u8fc7\u7a0b\uff0c\u5373\u5c06\u4e00\u4e2a\u6570\u7684\u6bcf\u4e00\u4f4d\u4e0e\u53e6\u4e00\u4e2a\u6570\u7684\u6bcf\u4e00\u4f4d\u76f8\u4e58\uff0c\u5e76\u5904\u7406\u8fdb\u4f4d\uff0c\u7136\u540e\u5c06\u5f97\u5230\u7684\u6240\u6709\u4e58\u79ef\u6c42\u548c\u5f97\u5230\u6700\u7ec8\u7ed3\u679c\u3002\u5bf9\u4e8eBigInteger<\/code>\u7c7b\u5904\u7406\u5c0f\u6570\u4e58\u79ef\u65f6\uff0c\u901a\u5e38\u91c7\u7528\u8fd9\u79cd\u65b9\u5f0f\u3002\u8fd9\u79cd\u65b9\u6cd5\u867d\u7136\u7b80\u5355\uff0c\u4f46\u662f\u6548\u7387\u8f83\u4f4e\uff0c\u5c24\u5176\u662f\u5728\u5904\u7406\u5927\u6570\u4e58\u6cd5\u65f6\u3002<\/p>\n<\/p>\n

\u4e8c\u3001\u5361\u62c9\u695a\u5df4\u4e58\u6cd5<\/h3>\n<\/p>\n

\u5361\u62c9\u695a\u5df4\u4e58\u6cd5\u9002\u7528\u4e8e\u4e2d\u7b49\u5927\u5c0f\u7684\u6570\u3002\u5f53\u6570\u5b57\u8fbe\u5230\u4e00\u5b9a\u957f\u5ea6\u65f6\uff08\u5982\u5bf9Java BigInteger\u7c7b\u800c\u8a00\uff0c\u4e00\u822c\u662f\u6570\u7684\u4f4d\u6570\u8d85\u8fc780\u4f4d\u65f6\uff09\uff0c\u5c31\u4f1a\u91c7\u7528\u5361\u62c9\u695a\u5df4\u7b97\u6cd5\u3002\u8be5\u7b97\u6cd5\u7684\u5173\u952e\u5728\u4e8e\u5c06\u6bcf\u4e2a\u5927\u6570\u62c6\u5206\u4e3a\u4e24\u90e8\u5206\uff0c\u5e76\u5229\u7528\u4e09\u6b21\u4e58\u6cd5\u800c\u4e0d\u662f\u56db\u6b21\u6765\u8ba1\u7b97\u8fd9\u4e9b\u90e8\u5206\u7684\u4e58\u79ef\uff0c\u663e\u8457\u51cf\u5c11\u4e86\u8ba1\u7b97\u91cf\u3002<\/p>\n<\/p>\n

\u7b97\u6cd5\u6838\u5fc3\u6b65\u9aa4\uff1a<\/strong><\/p>\n<\/p>\n

    \n
  1. \u5c06\u5927\u6570X\u3001Y\u5747\u5206\u4e3a\u4e24\u90e8\u5206\uff0c\u5373(X=A\u00b7B^n + B)\u548c(Y=C\u00b7B^n + D)\u3002<\/li>\n
  2. \u8ba1\u7b97(A\u00b7C)\u3001(B\u00b7D)\u548c((A+B)\u00b7(C+D))\u3002<\/li>\n
  3. \u4f7f\u7528\u8fd9\u4e09\u4e2a\u7ed3\u679c\u8ba1\u7b97\u539f\u95ee\u9898\u7684\u7ed3\u679c\uff1a(X\u00b7Y = A\u00b7C\u00b7B^{2n} + ((A+B)\u00b7(C+D)-A\u00b7C-B\u00b7D)\u00b7B^n + B\u00b7D)\u3002<\/li>\n<\/ol>\n

    \u901a\u8fc7\u8fd9\u79cd\u65b9\u5f0f\uff0c\u5361\u62c9\u695a\u5df4\u7b97\u6cd5\u5927\u5e45\u964d\u4f4e\u4e86\u5927\u6570\u4e58\u6cd5\u7684\u590d\u6742\u5ea6\u3002<\/p>\n<\/p>\n

    \u4e09\u3001\u6258\u6885\u5e93\u514b\u4e58\u6cd5<\/h3>\n<\/p>\n

    \u5bf9\u4e8e\u975e\u5e38\u5927\u7684\u6570\uff0cBigInteger<\/code>\u4f1a\u91c7\u7528\u66f4\u4e3a\u590d\u6742\u7684\u6258\u6885\u5e93\u514b\u4e58\u6cd5\u3002\u8fd9\u79cd\u7b97\u6cd5\u662f\u5bf9\u5361\u62c9\u695a\u5df4\u7b97\u6cd5\u7684\u4e00\u79cd\u6269\u5c55\uff0c\u9002\u7528\u4e8e\u5927\u578b\u8fd0\u7b97\u3002\u5b83\u5c06\u6bcf\u4e2a\u6570\u5206\u4e3a\u66f4\u591a\u7684\u90e8\u5206\uff0c\u5229\u7528\u66f4\u590d\u6742\u7684\u65b9\u6cd5\u51cf\u5c11\u4e58\u6cd5\u7684\u603b\u6b21\u6570\u3002<\/p>\n<\/p>\n

    \u7b97\u6cd5\u6b65\u9aa4\u6982\u8ff0\uff1a<\/strong><\/p>\n<\/p>\n

      \n
    1. \u5c06\u5927\u6570\u5206\u4e3a\u591a\u4e2a\u5c0f\u90e8\u5206\u3002<\/li>\n
    2. \u901a\u8fc7\u4e00\u7cfb\u5217\u590d\u6742\u7684\u8ba1\u7b97\u6b65\u9aa4\uff0c\u7ec4\u5408\u8fd9\u4e9b\u5c0f\u90e8\u5206\u7684\u4e58\u79ef\u3002<\/li>\n
    3. \u7ed3\u5408\u8fd9\u4e9b\u4e58\u79ef\uff0c\u5f97\u5230\u6700\u7ec8\u7684\u5927\u6570\u4e58\u79ef\u3002<\/li>\n<\/ol>\n

      \u6258\u6885\u5e93\u514b\u4e58\u6cd5\u7279\u522b\u9002\u5408\u89e3\u51b3\u90a3\u4e9b\u8d85\u5927\u6570\u5b57\u7684\u4e58\u6cd5\u95ee\u9898\uff0c\u901a\u8fc7\u964d\u4f4e\u4e58\u6cd5\u6b21\u6570\u6765\u63d0\u9ad8\u6548\u7387\uff0c\u4f46\u7b97\u6cd5\u672c\u8eab\u6bd4\u5361\u62c9\u695a\u5df4\u7b97\u6cd5\u66f4\u4e3a\u590d\u6742\u3002<\/p>\n<\/p>\n

      \u56db\u3001\u5e94\u7528\u4e0e\u4f18\u5316<\/h3>\n<\/p>\n

      BigInteger<\/code>\u7684\u4e58\u6cd5\u8fd0\u7b97\u662fJava\u4e2d\u5904\u7406\u5927\u6570\u7b97\u6cd5\u7684\u6838\u5fc3\u3002\u901a\u8fc7\u667a\u80fd\u9009\u62e9\u6700\u5408\u9002\u7684\u7b97\u6cd5\uff0cBigInteger<\/code>\u80fd\u591f\u9ad8\u6548\u5730\u5904\u7406\u4e0d\u540c\u957f\u5ea6\u6570\u5b57\u7684\u4e58\u6cd5\u8fd0\u7b97\u3002\u5f00\u53d1\u8005\u53ef\u4ee5\u6839\u636e\u5177\u4f53\u7684\u5e94\u7528\u573a\u666f\uff0c\u9009\u62e9\u5408\u9002\u7684\u7b97\u6cd5\u6216\u6570\u636e\u8868\u793a\u65b9\u6cd5\u6765\u4f18\u5316\u5927\u6570\u8fd0\u7b97\u6027\u80fd\u3002<\/strong><\/p>\n<\/p>\n

      \u4f8b\u5982\uff0c\u5728\u8fdb\u884c\u5bc6\u94a5\u751f\u6210\u6216\u52a0\u5bc6\u7b97\u6cd5\u5b9e\u73b0\u65f6\uff0c\u7ecf\u5e38\u4f1a\u6d89\u53ca\u5230\u5927\u6570\u4e58\u6cd5\u8fd0\u7b97\u3002\u8fd9\u65f6\uff0c\u5408\u7406\u5e94\u7528BigInteger<\/code>\u7c7b\u7684\u4e58\u6cd5\u8fd0\u7b97\uff0c\u5bf9\u4e8e\u63d0\u5347\u7b97\u6cd5\u7684\u6267\u884c\u6548\u7387\u548c\u7cfb\u7edf\u7684\u6574\u4f53\u6027\u80fd\u5177\u6709\u91cd\u8981\u610f\u4e49\u3002\u901a\u8fc7\u5bf9\u4e0d\u540c\u4e58\u6cd5\u7b97\u6cd5\u7684\u6df1\u5165\u7406\u89e3\u548c\u5e94\u7528\uff0c\u5f00\u53d1\u8005\u53ef\u4ee5\u66f4\u597d\u5730\u5229\u7528Java\u8bed\u8a00\u5904\u7406\u590d\u6742\u7684\u6570\u5b66\u95ee\u9898\uff0c\u5b9e\u73b0\u9ad8\u6027\u80fd\u7684\u6570\u5b66\u8ba1\u7b97\u5e94\u7528\u3002<\/p>\n<\/p>\n

      \u76f8\u5173\u95ee\u7b54FAQs\uff1a<\/strong><\/h2>\n

      1. BigInteger\u7684\u4e58\u6cd5\u8fd0\u7b97\u5229\u7528\u4e86\u54ea\u79cd\u7b97\u6cd5\uff1f<\/strong><\/p>\n

      BigInteger\u7684\u4e58\u6cd5\u8fd0\u7b97\u662f\u901a\u8fc7\u91c7\u7528"\u57fa\u4e8e\u5206\u6cbb\u6cd5\u7684\u5feb\u901f\u6570\u8bba\u53d8\u6362"\u7b97\u6cd5\u5b9e\u73b0\u7684\u3002<\/p>\n

      \u5feb\u901f\u6570\u8bba\u53d8\u6362\uff08FFT\uff09\u662f\u4e00\u79cd\u9ad8\u6548\u7684\u4e58\u6cd5\u7b97\u6cd5\uff0c\u901a\u8fc7\u5c06\u6574\u6570\u8868\u793a\u4e3a\u591a\u9879\u5f0f\u7684\u5f62\u5f0f\uff0c\u5e76\u5229\u7528\u591a\u9879\u5f0f\u7684\u4e58\u6cd5\u6027\u8d28\u6765\u5b9e\u73b0\u4e58\u6cd5\u8fd0\u7b97\u3002FFT\u7b97\u6cd5\u7684\u57fa\u672c\u601d\u60f3\u662f\u5c06\u591a\u9879\u5f0f\u7684\u4e58\u6cd5\u8f6c\u5316\u4e3a\u591a\u4e2a\u8f83\u5c0f\u89c4\u6a21\u7684\u591a\u9879\u5f0f\u4e58\u6cd5\uff0c\u8fdb\u800c\u901a\u8fc7\u9012\u5f52\u5730\u8ba1\u7b97\u8fd9\u4e9b\u8f83\u5c0f\u89c4\u6a21\u7684\u4e58\u79ef\u6765\u5f97\u5230\u6700\u7ec8\u7ed3\u679c\u3002<\/p>\n

      2. BigInteger\u4e58\u6cd5\u8fd0\u7b97\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u662f\u591a\u5c11\uff1f<\/strong><\/p>\n

      BigInteger\u4e58\u6cd5\u8fd0\u7b97\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO(n log n)\uff0c\u5176\u4e2dn\u662f\u64cd\u4f5c\u6570\u7684\u4f4d\u6570\u3002\u8be5\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u8f83\u4f4e\uff0c\u4f7f\u5f97BigInteger\u80fd\u591f\u9ad8\u6548\u5730\u5904\u7406\u5927\u6574\u6570\u7684\u4e58\u6cd5\u8fd0\u7b97\u3002<\/p>\n

      3. \u9664\u4e86\u5feb\u901f\u6570\u8bba\u53d8\u6362\uff0c\u8fd8\u6709\u5176\u4ed6\u7684\u4e58\u6cd5\u7b97\u6cd5\u53ef\u7528\u4e8eBigInteger\u5417\uff1f<\/strong><\/p>\n

      \u662f\u7684\uff0c\u9664\u4e86\u5feb\u901f\u6570\u8bba\u53d8\u6362\uff0cBigInteger\u8fd8\u53ef\u4ee5\u4f7f\u7528\u4f20\u7edf\u7684\u7ad6\u5f0f\u4e58\u6cd5\u7b97\u6cd5\u6765\u8fdb\u884c\u4e58\u6cd5\u8fd0\u7b97\u3002\u7ad6\u5f0f\u4e58\u6cd5\u7b97\u6cd5\u662f\u4e00\u79cd\u9010\u4f4d\u76f8\u4e58\u5e76\u7d2f\u52a0\u7684\u65b9\u6cd5\uff0c\u5373\u5c06\u4e24\u4e2a\u5927\u6574\u6570\u7684\u6bcf\u4e00\u4f4d\u76f8\u4e58\u5f97\u5230\u4e00\u4e2a\u4e2d\u95f4\u7ed3\u679c\uff0c\u7136\u540e\u5c06\u8fd9\u4e9b\u4e2d\u95f4\u7ed3\u679c\u76f8\u52a0\u5f97\u5230\u6700\u7ec8\u7ed3\u679c\u3002<\/p>\n

      \u7ad6\u5f0f\u4e58\u6cd5\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u4e3aO(n^2)\uff0c\u5176\u4e2dn\u662f\u64cd\u4f5c\u6570\u7684\u4f4d\u6570\u3002\u76f8\u8f83\u4e8e\u5feb\u901f\u6570\u8bba\u53d8\u6362\uff0c\u7ad6\u5f0f\u4e58\u6cd5\u7b97\u6cd5\u7684\u65f6\u95f4\u590d\u6742\u5ea6\u8f83\u9ad8\uff0c\u4f46\u5b83\u7684\u5b9e\u73b0\u76f8\u5bf9\u7b80\u5355\uff0c\u9002\u7528\u4e8e\u5904\u7406\u5c0f\u89c4\u6a21\u7684\u4e58\u6cd5\u8fd0\u7b97\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"Java\u7684BigInteger\u7c7b\u7684\u4e58\u6cd5\u8fd0\u7b97\u4e3b\u8981\u91c7\u7528"\u957f\u4e58\u6cd5"\uff08Long Multiplic […]","protected":false},"author":3,"featured_media":200961,"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\/200958"}],"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=200958"}],"version-history":[{"count":0,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/posts\/200958\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media\/200961"}],"wp:attachment":[{"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/media?parent=200958"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/categories?post=200958"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/docs.pingcode.com\/wp-json\/wp\/v2\/tags?post=200958"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}