\u7ed9\u5b9a\u6b63\u6574\u6570 $a,b$\uff0c\u6c42\u540c\u4f59\u65b9\u7a0b $ax\\equiv1\\pmod b$ \u7684\u6700\u5c0f\u6b63\u6574\u6570\u89e3 $x$\u3002<\/p>\n\n\n\n
\u7531\u4e8e\u9898\u76ee\u6ca1\u6709\u4fdd\u8bc1 $b$ \u4e3a\u8d28\u6570\uff0c\u6240\u4ee5\u4e0d\u80fd\u7528\u8d39\u9a6c\u5c0f\u5b9a\u7406\uff0c\u9700\u8981\u4f7f\u7528\u62d3\u5c55\u6b27\u51e0\u91cc\u5f97\u7b97\u6cd5\u6c42\u4e58\u6cd5\u9006\u5143\u3002<\/p>\n\n\n\n
$a$ \u5728\u6a21 $b$ \u4e0b\u5b58\u5728\u4e58\u6cd5\u9006\u5143\uff0c\u5f53\u4e14\u4ec5\u5f53 $\\gcd(a,b)=1$\u3002\u6b64\u65f6\u5b58\u5728\u6574\u6570 $x,y$ \u4f7f $a x + b y = 1$\uff08\u5373\u88f4\u8700\u5b9a\u7406\uff09\u3002\u7b49\u5f0f\u4e24\u8fb9\u540c\u65f6\u5bf9 $b$ \u53d6\u6a21\u53ef\u5f97 $a x \\equiv 1 \\pmod b$\uff0c\u6240\u4ee5\u8be5 $x$ \u5373\u4e3a\u6240\u6c42\u9006\u5143\u3002<\/p>\n\n\n\n
\u4f7f\u7528\u6269\u5c55\u6b27\u51e0\u91cc\u5f97\u7b97\u6cd5\u6c42\u51fa\u4e00\u5bf9 $x,y$ \u4f7f\u5f97 $ax+by=\\gcd(a,b)$\u3002\u7531\u4e8e\u9898\u76ee\u4fdd\u8bc1\u6709\u89e3\uff0c\u5373 $\\gcd(a,b)=1$\uff0c\u5219\u6b64\u65f6\u7b54\u6848\u4e3a $(x\\bmod b+b)\\bmod b$\uff0c\u4ece\u800c\u5f97\u5230\u6700\u5c0f\u975e\u8d1f\u89e3\u3002<\/p>\n\n\n\n
#include<bits\/stdc++.h>\n#define int long long\nusing namespace std;\ninline int extended_gcd(int a,int b,int &x,int &y)\/\/\u7528\u62d3\u5c55\u6b27\u51e0\u91cc\u5f97\u7b97\u6cd5\u6c42\u9006\u5143\n{\n if(!b) \n {\n x=1;\n y=0;\n return a;\n }\n int gcd;\n gcd=extended_gcd(b,a%b,y,x);\n y-=(a\/b)*x;\n return gcd;\n}\ninline int inv(int b,int m)\/\/a mod m \u610f\u4e49\u4e0b\u7684\u4e58\u6cd5\u9006\u5143\n{\n int x,y;\n int gcd=extended_gcd(b,m,x,y);\n return gcd!=1?-1:(x%m+m)%m;\n}\nsigned main() \n{\n int a,b;\n cin>>a>>b;\n int ans=inv(a,b);\n cout<<ans;\n return 0;\n}<\/code><\/pre>\n\n\n\n\u65f6\u95f4\u590d\u6742\u5ea6<\/h3>\n\n\n\n
$\\mathcal{O}(\\log\\min(a,b))$\u3002<\/p>\n","protected":false},"excerpt":{"rendered":"
\u9898\u610f \u7ed9\u5b9a\u6b63\u6574\u6570 $a,b$\uff0c\u6c42\u540c\u4f59\u65b9\u7a0b $ax\\equiv1\\pmod b$ \u7684\u6700\u5c0f\u6b63\u6574\u6570\u89e3 $x$\u3002 \u89e3\u6790 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[2],"tags":[3],"class_list":["post-46","post","type-post","status-publish","format-standard","hentry","category-oi","tag-oi"],"featured_image_src":null,"author_info":{"display_name":"CaelumRadish_c","author_link":"https:\/\/tblog.zeabur.app\/?author=1"},"_links":{"self":[{"href":"https:\/\/tblog.zeabur.app\/index.php?rest_route=\/wp\/v2\/posts\/46","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/tblog.zeabur.app\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/tblog.zeabur.app\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/tblog.zeabur.app\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/tblog.zeabur.app\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=46"}],"version-history":[{"count":1,"href":"https:\/\/tblog.zeabur.app\/index.php?rest_route=\/wp\/v2\/posts\/46\/revisions"}],"predecessor-version":[{"id":47,"href":"https:\/\/tblog.zeabur.app\/index.php?rest_route=\/wp\/v2\/posts\/46\/revisions\/47"}],"wp:attachment":[{"href":"https:\/\/tblog.zeabur.app\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=46"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/tblog.zeabur.app\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=46"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/tblog.zeabur.app\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=46"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}