{"id":332,"date":"2025-04-10T19:12:34","date_gmt":"2025-04-10T11:12:34","guid":{"rendered":"https:\/\/m.qzcy2.top\/?p=332"},"modified":"2025-04-11T14:46:22","modified_gmt":"2025-04-11T06:46:22","slug":"%e5%ae%9e%e7%94%a8%e7%9a%84%e5%9f%ba%e7%a1%80%e7%ae%97%e6%b3%95","status":"publish","type":"post","link":"https:\/\/m.qzcy2.top\/index.php\/2025\/04\/10\/%e5%ae%9e%e7%94%a8%e7%9a%84%e5%9f%ba%e7%a1%80%e7%ae%97%e6%b3%95\/","title":{"rendered":"\u5b9e\u7528\u7684\u57fa\u7840\u7b97\u6cd5"},"content":{"rendered":"<h1>\u8bf4\u660e<\/h1>\n<p>\u6b64\u6587\u7ae0\u4e3a\u4f5c\u8005\u6574\u7406\u7684\u4e00\u4e9b\u5e38\u89c1\u7684\u57fa\u7840\u7b97\u6cd5\u6a21\u677f\u3002\u5e38\u7528\u4e8e\u5404\u79cd\u9898\u76ee\u7684\u65f6\u95f4\u590d\u6742\u7684\u4f18\u5316\u4e0a\u3002<\/p>\n<h1>1.\u5feb\u901f\u5e42<\/h1>\n<p><span style=\"color: #008000; font-size: 18pt;\">\u76f8\u5173\u9898\u76ee\uff1a<\/span><\/p>\n<h2>\u3010\u6a21\u677f\u3011\u5feb\u901f\u5e42 <span style=\"color: #ff6600;\">\u666e\u53ca-<\/span><\/h2>\n<p>\u539f\u9898\u94fe\u63a5\uff1a<a href=\"https:\/\/www.luogu.com.cn\/problem\/P1226\" target=\"_blank\"  rel=\"nofollow\" >https:\/\/www.luogu.com.cn\/problem\/P1226<\/a><\/p>\n<h3>\u9898\u76ee\u63cf\u8ff0\uff1a<\/h3>\n<ul>\n<li>\u7ed9\u4f60\u4e09\u4e2a\u6574\u6570\u00a0<span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><span class=\"mpunct\">,<\/span><span class=\"mord mathnormal\">b<\/span><span class=\"mpunct\">,<\/span><span class=\"mord mathnormal\">p<\/span><\/span><\/span><\/span>\uff0c\u6c42\u00a0<span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord\"><span class=\"mord mathnormal\">a*<\/span><span class=\"msupsub\"><span class=\"vlist-t\"><span class=\"vlist-r\"><span class=\"vlist\"><span class=\"sizing reset-size6 size3 mtight\"><span class=\"mord mathnormal mtight\">b <\/span><\/span><\/span><\/span><\/span><\/span><\/span><span class=\"mbin\"><span class=\"mord\"><span class=\"mord mathrm\">mod <\/span><\/span><\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">p<\/span><\/span><\/span><\/span>\u3002<\/li>\n<li>\u8f93\u5165\u683c\u5f0f\uff1a\u8f93\u5165\u53ea\u6709\u4e00\u884c\u4e09\u4e2a\u6574\u6570\uff0c\u5206\u522b\u4ee3\u8868 a,b,p\u3002<\/li>\n<li>\u8f93\u51fa\u683c\u5f0f\uff1a\u8f93\u51fa\u4e00\u884c\u4e00\u4e2a\u5b57\u7b26\u4e32 a^b mod p=s\uff0c\u5176\u4e2d a,b,p \u5206\u522b\u4e3a\u9898\u76ee\u7ed9\u5b9a\u7684\u503c\uff0c s \u4e3a\u8fd0\u7b97\u7ed3\u679c\u3002<\/li>\n<\/ul>\n<h3>\u793a\u4f8b<\/h3>\n<ul>\n<li>\u8f93\u5165\uff1a2 10 9<\/li>\n<li>\u8f93\u51fa\uff1a2^10 mod 9=7<\/li>\n<li>\u8bf4\u660e\uff1a210=1024\uff0c1024 mod 9 = 7\u3002<\/li>\n<\/ul>\n<h3>\u4ee3\u7801<\/h3>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"cpp\">int qmi(int a , int b , int p)\r\n{\r\n    int res = 1;\r\n    while (b)\r\n    {\r\n        if (b &amp; 1) res = res * a % p;\r\n        a = a * a % p;\r\n        b &gt;&gt;= 1;\r\n    }\r\n    return res;\r\n}\r\n\r\nvoid solve()\r\n{\r\n    int a , b , p;\r\n    cin &gt;&gt; a &gt;&gt; b &gt;&gt; p;\r\n    cout &lt;&lt; a &lt;&lt; \"^\" &lt;&lt; b &lt;&lt; \" mod \" &lt;&lt; p &lt;&lt; \"=\" &lt;&lt; qmi(a , b , p) &lt;&lt; endl; \r\n}<\/pre>\n<p>&nbsp;<\/p>\n<h1>2.\u9ad8\u7cbe\u5ea6\u8fd0\u7b97<\/h1>\n<p><span style=\"color: #008000; font-size: 18pt;\">\u76f8\u5173\u9898\u76ee\uff1a<\/span><\/p>\n<h2>A + B Problem (\u9ad8\u7cbe) <span style=\"color: #ff6600;\">\u666e\u53ca-<\/span><\/h2>\n<p>\u539f\u9898\u94fe\u63a5\uff1a<a href=\"https:\/\/www.luogu.com.cn\/problem\/P1601\" target=\"_blank\"  rel=\"nofollow\" >https:\/\/www.luogu.com.cn\/problem\/P1601<\/a><\/p>\n<h3>\u9898\u76ee\u63cf\u8ff0<\/h3>\n<ul>\n<li>\u9ad8\u7cbe\u5ea6\u52a0\u6cd5\uff0c\u76f8\u5f53\u4e8e a+b problem\uff0c\u4e0d\u7528\u8003\u8651\u8d1f\u6570\u3002<\/li>\n<li>\u8f93\u5165\u683c\u5f0f\uff1a\u5206\u4e24\u884c\u8f93\u5165\u3002a,b\u226410^500\u3002<\/li>\n<li>\u8f93\u51fa\u683c\u5f0f\uff1a\u8f93\u51fa\u53ea\u6709\u4e00\u884c\uff0c\u4ee3\u8868\u00a0<span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><span class=\"mbin\">+<\/span><\/span><span class=\"base\"><span class=\"mord mathnormal\">b<\/span><\/span><\/span><\/span>\u00a0\u7684\u503c\u3002<\/li>\n<\/ul>\n<h3>\u793a\u4f8b<\/h3>\n<ul>\n<li>\u8f93\u5165\uff1a 1 1<\/li>\n<li>\u8f93\u51fa\uff1a2<\/li>\n<\/ul>\n<h3>\u4ee3\u7801<\/h3>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"cpp\">inline vector&lt;int&gt; add(vector&lt;int&gt; &amp;a , vector&lt;int&gt; &amp;b)\r\n{\r\n    if (a.size() &lt; b.size()) return add(b , a);\r\n    \r\n    vector&lt;int&gt; res;\t\r\n    int t = 0;\r\n    for (int i = 0 ; i &lt; a.size() ; i ++ )\r\n    {\r\n        t += a[i];\r\n        if (i &lt; b.size()) t += b[i];\r\n        res.push_back(t % 10);\r\n        t \/= 10;\t\r\n    }\t\r\n    \r\n    if (t) res.push_back(t);\r\n    \r\n    reverse(ALL(res));\r\n    return res;\r\n}\r\n\r\nvoid solve()\r\n{\r\n    string s1 , s2;\r\n    cin &gt;&gt; s1 &gt;&gt; s2;\r\n    vector&lt;int&gt; a , b;\r\n    for (auto i : s1) a.push_back(i - '0');\r\n    for (auto i : s2) b.push_back(i - '0');\r\n    \r\n    reverse(ALL(a)) , reverse(ALL(b));\r\n    auto ans = add(a , b);\r\n        \r\n    for (auto i : ans) cout &lt;&lt; i;\r\n    cout &lt;&lt; endl; \r\n}<\/pre>\n<p>&nbsp;<\/p>\n<h2>\u9ad8\u7cbe\u5ea6\u51cf\u6cd5 <span style=\"color: #ff6600;\">\u666e\u53ca-<\/span><\/h2>\n<p>\u539f\u9898\u94fe\u63a5\uff1a<a href=\"https:\/\/www.luogu.com.cn\/problem\/P2142\" target=\"_blank\"  rel=\"nofollow\" >https:\/\/www.luogu.com.cn\/problem\/P2142<\/a><\/p>\n<h3>\u9898\u76ee\u63cf\u8ff0<\/h3>\n<ul>\n<li>\u9ad8\u7cbe\u5ea6\u51cf\u6cd5\u3002<\/li>\n<li>\u8f93\u5165\u683c\u5f0f\uff1a\u4e24\u4e2a\u6574\u6570\u00a0<span class=\"katex\"><span class=\"katex-html\" aria-hidden=\"true\"><span class=\"base\"><span class=\"mord mathnormal\">a<\/span><span class=\"mpunct\">,<\/span><span class=\"mord mathnormal\">b<\/span><\/span><\/span><\/span>\uff08\u7b2c\u4e8c\u4e2a\u53ef\u80fd\u6bd4\u7b2c\u4e00\u4e2a\u5927\uff09\u3002<\/li>\n<li>\u8f93\u51fa\u683c\u5f0f\uff1a\u7ed3\u679c\uff08\u662f\u8d1f\u6570\u8981\u8f93\u51fa\u8d1f\u53f7\uff09\u3002<\/li>\n<\/ul>\n<h3>\u793a\u4f8b<\/h3>\n<ul>\n<li>\u8f93\u5165\uff1a2 1<\/li>\n<li>\u8f93\u51fa\uff1a1<\/li>\n<\/ul>\n<h3>\u4ee3\u7801<\/h3>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"cpp\">bool cmp(vector&lt;int&gt; a , vector&lt;int&gt; b)\r\n{\r\n    if (a.size() != b.size()) return a.size() &gt; b.size();\r\n    \r\n    for (int i = 0 ; i &lt; a.size() ; i ++ )\r\n    {\r\n        if (a[i] != b[i]) return a[i] &gt; b[i];\r\n    }\r\n    \r\n    return true;\r\n}\r\n\r\ninline vector&lt;int&gt; sub(vector&lt;int&gt; &amp;a , vector&lt;int&gt; &amp;b)\r\n{\r\n    vector&lt;int&gt; res;\r\n    int value = 0;\r\n    for (int i = 0 ; i &lt; a.size() ; i ++ )\r\n    {\r\n        value = a[i] - value;\r\n        \r\n        if (i &lt; b.size()) value -= b[i];\r\n        \r\n        res.push_back((value + 10) % 10);\r\n        \r\n        if (value &lt; 0) value = 1;\r\n        else value = 0;\r\n    }\r\n    \r\n    while (res.size() &gt; 1 &amp;&amp; !res.back()) res.pop_back();\r\n    \r\n    reverse(ALL(res));\r\n    return res;\r\n    \r\n}\r\n\r\nvoid solve()\r\n{\r\n    string s1 , s2;\r\n    cin &gt;&gt; s1 &gt;&gt; s2;\r\n    vector&lt;int&gt; a , b;\r\n    for (auto i : s1) a.push_back(i - '0');\r\n    for (auto i : s2) b.push_back(i - '0');\r\n    \r\n    reverse(ALL(a)) , reverse(ALL(b));\r\n\r\n    if (cmp(a , b))\r\n    {\r\n        auto ans = sub(a , b);\r\n        for (auto i : ans) cout &lt;&lt; i;\r\n        cout &lt;&lt; endl;\r\n    }\r\n    else \r\n    {\r\n        cout &lt;&lt; '-';\r\n        auto ans = sub(b , a);\r\n        for (auto i : ans) cout &lt;&lt; i;\r\n        cout &lt;&lt; endl;\r\n    }\r\n}<\/pre>\n<p>&nbsp;<\/p>\n<h2>\u9ad8\u7cbe\u5ea6\u4e58\u6cd5<\/h2>\n<p>\u539f\u9898\u94fe\u63a5\uff1a<a href=\"https:\/\/www.lanqiao.cn\/problems\/1943\/learning\/?page=1&amp;first_category_id=1&amp;name=%E9%AB%98%E7%B2%BE%E5%BA%A6\" target=\"_blank\"  rel=\"nofollow\" >https:\/\/www.lanqiao.cn\/problems\/1943\/learning\/?page=1&amp;first_category_id=1&amp;name=%E9%AB%98%E7%B2%BE%E5%BA%A6<\/a><\/p>\n<h3>\u9898\u76ee\u63cf\u8ff0<\/h3>\n<ul>\n<li>\u7ed9\u5b9a\u4e24\u4e2a\u4f4d\u6570\u4e0d\u8d85\u8fc7100\u4f4d\u7684\u6b63\u6574\u6570\uff0c\u6c42\u5b83\u4eec\u7684\u4e58\u79ef\u3002<\/li>\n<li>\u8f93\u5165\u683c\u5f0f\uff1a\u8f93\u5165\u6587\u4ef6\u4e2d\u5305\u542b\u591a\u4e2a\u6d4b\u8bd5\u6570\u636e\u3002\u6bcf\u4e2a\u6d4b\u8bd5\u6570\u636e\u5360\u4e24\u884c\uff0c\u5206\u522b\u4e3a\u4e00\u4e2a\u6b63\u6574\u6570\uff0c\u6bcf\u4e2a\u6b63\u6574\u6570\u7684\u4f4d\u6570\u4e0d\u8d85\u8fc7100\u4f4d\u3002\u8f93\u5165\u6570\u636e\u4e00\u76f4\u5230\u6587\u4ef6\u5c3e\u3002<\/li>\n<li>\u8f93\u51fa\u683c\u5f0f\uff1a\u5bf9\u6bcf\u4e2a\u6d4b\u8bd5\u6570\u636e\uff0c\u8f93\u51fa\u5176\u4e2d\u4e24\u4e2a\u6b63\u6574\u6570\u7684\u4e58\u79ef\u3002<\/li>\n<\/ul>\n<h3>\u793a\u4f8b<\/h3>\n<ul>\n<li>\u8f93\u5165\uff1a<br \/>\n981567<br \/>\n32976201<br \/>\n123456789<br \/>\n987654321<\/li>\n<li>\u8f93\u51fa\uff1a<br \/>\n32368350686967<br \/>\n121932631112635269<\/li>\n<\/ul>\n<h3>\u4ee3\u7801<\/h3>\n<pre class=\"EnlighterJSRAW\" data-enlighter-language=\"generic\">vector&lt;int&gt; mul(vector&lt;int&gt; &amp;a , vector&lt;int&gt; &amp;b)\r\n{\r\n    vector&lt;int&gt; res(a.size() * b.size());\r\n    \r\n    for (int i = 0 ; i &lt; b.size() ; i ++ )\r\n        for (int j = 0 ; j &lt; a.size() ; j ++ )\r\n            res[i + j] += b[i] * a[j];\r\n\r\n    for (int i = 0 ; i &lt; a.size() + b.size() - 1 ; i ++ )\r\n    {\r\n        if (res[i] &gt; 9)\r\n        {\r\n            res[i + 1] += res[i] \/ 10;\r\n            res[i] %= 10;\r\n        }\r\n    }\r\n\r\n    while (res.size() &gt; 1 &amp;&amp; !res.back()) res.pop_back();\r\n    reverse(ALL(res));\r\n    return res;\r\n}\r\n\r\n\r\nvoid solve()\r\n{\r\n    string s1 , s2;\r\n    while (cin &gt;&gt; s1 &gt;&gt; s2)\r\n    {\r\n        vector&lt;int&gt; a , b;\r\n        for (auto i : s1) a.push_back(i - '0');\r\n        for (auto i : s2) b.push_back(i - '0');\r\n        \r\n        reverse(ALL(a)) , reverse(ALL(b));\r\n        auto ans = mul(a , b);\r\n\r\n        for (auto i : ans) cout &lt;&lt; i;\r\n        cout &lt;&lt; endl;\r\n    }\r\n}<\/pre>\n<p>&nbsp;<\/p>\n","protected":false},"excerpt":{"rendered":"<p>\u8bf4\u660e \u6b64\u6587\u7ae0\u4e3a\u4f5c\u8005\u6574\u7406\u7684\u4e00\u4e9b\u5e38\u89c1\u7684\u57fa\u7840\u7b97\u6cd5\u6a21\u677f\u3002\u5e38\u7528\u4e8e\u5404\u79cd\u9898\u76ee\u7684\u65f6\u95f4\u590d\u6742\u7684\u4f18\u5316\u4e0a\u3002 1.\u5feb\u901f\u5e42 \u76f8\u5173\u9898\u76ee\uff1a \u3010\u6a21\u677f\u3011\u5feb\u901f\u5e42 \u666e\u53ca- &#8230;<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"emotion":"","emotion_color":"","title_style":"","license":"","footnotes":""},"categories":[7],"tags":[12,39],"class_list":["post-332","post","type-post","status-publish","format-standard","hentry","category-algorithm","tag-algorithm","tag-39"],"_links":{"self":[{"href":"https:\/\/m.qzcy2.top\/index.php\/wp-json\/wp\/v2\/posts\/332","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/m.qzcy2.top\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/m.qzcy2.top\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/m.qzcy2.top\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/m.qzcy2.top\/index.php\/wp-json\/wp\/v2\/comments?post=332"}],"version-history":[{"count":2,"href":"https:\/\/m.qzcy2.top\/index.php\/wp-json\/wp\/v2\/posts\/332\/revisions"}],"predecessor-version":[{"id":336,"href":"https:\/\/m.qzcy2.top\/index.php\/wp-json\/wp\/v2\/posts\/332\/revisions\/336"}],"wp:attachment":[{"href":"https:\/\/m.qzcy2.top\/index.php\/wp-json\/wp\/v2\/media?parent=332"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/m.qzcy2.top\/index.php\/wp-json\/wp\/v2\/categories?post=332"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/m.qzcy2.top\/index.php\/wp-json\/wp\/v2\/tags?post=332"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}