{"id":115702,"date":"2026-10-13T08:24:57","date_gmt":"2026-10-13T00:24:57","guid":{"rendered":"https:\/\/www.wsisp.com\/helps\/115702.html"},"modified":"2026-10-13T08:24:57","modified_gmt":"2026-10-13T00:24:57","slug":"csp-s-2020-%e7%9c%9f%e9%a2%98-%e5%87%bd%e6%95%b0%e8%b0%83%e7%94%a8-%e9%a2%98%e8%a7%a3%ef%bc%88%e6%8f%90%e9%ab%98-%e7%9c%81%e9%80%89-%ef%bc%89","status":"publish","type":"post","link":"https:\/\/www.wsisp.com\/helps\/115702.html","title":{"rendered":"CSP-S 2020 \u771f\u9898 \u51fd\u6570\u8c03\u7528 \u9898\u89e3\uff08\u63d0\u9ad8+\/\u7701\u9009-\uff09"},"content":{"rendered":"<p>CSP-S 2020 \u8fd9\u9053\u771f\u9898&#xff0c;\u8003\u70b9\u662f\u62d3\u6251\u6392\u5e8f&#xff0c;\u6211\u4eec\u4e00\u6b65\u6b65\u62c6\u5f00\u770b\u3002<\/p>\n<p>\u9898\u76ee\u6765\u6e90&#xff1a;ACGO A34 &#xff5c; \u6d1b\u8c37 P7077\u96be\u5ea6\u5b9a\u4f4d&#xff1a;\u63d0\u9ad8&#043;\/\u7701\u9009- &#xff5c; \u901a\u8fc7\u7387&#xff1a;69.38%<\/p>\n<h3>\u4e00\u3001\u9898\u76ee\u4fe1\u606f<\/h3>\n<p>\u9898\u76ee\u540d\u79f0&#xff1a;\u51fd\u6570\u8c03\u7528<\/p>\n<p>\u6240\u5c5e\u8d5b\u4e8b&#xff1a;2020 \u5e74 CSP-S \u7ec4\u590d\u8d5b<\/p>\n<p>\u5b98\u65b9\u96be\u5ea6&#xff1a;\u63d0\u9ad8&#043;\/\u7701\u9009-<\/p>\n<p>\u6d89\u53ca\u77e5\u8bc6\u70b9&#xff1a;\u62d3\u6251\u6392\u5e8f<\/p>\n<p>\u9898\u76ee\u94fe\u63a5&#xff1a;https:\/\/www.acgo.cn\/problemset\/info\/34<\/p>\n<p>\u6d1b\u8c37\u7f16\u53f7&#xff1a;P7077&#xff08;\u540c\u4e00\u9053\u9898&#xff0c;\u4e24\u4e2a\u5e73\u53f0\u5747\u53ef\u63d0\u4ea4&#xff0c;\u4ee3\u7801\u901a\u7528&#xff09;<\/p>\n<h4>\u6613\u9519\u70b9&#xff08;\u5f88\u591a\u4eba\u683d\u5728\u8fd9&#xff09;<\/h4>\n<ul>\n<li>\u6392\u5e8f\u540e\u539f\u6765\u7684\u4e0b\u6807\u4fe1\u606f\u4f1a\u4e22&#xff0c;\u9700\u8981\u989d\u5916\u8bb0\u5f55<\/li>\n<li>\u6bd4\u8f83\u51fd\u6570\u7684\u4e25\u683c\u5f31\u5e8f\u8981\u5199\u5bf9&#xff0c;\u5426\u5219\u6392\u5e8f\u7ed3\u679c\u672a\u5b9a\u4e49<\/li>\n<li>\u9ad8\u96be\u5ea6\u9898\u7684\u66b4\u529b\u5206\u5f88\u5173\u952e&#xff0c;\u5148\u5199\u4e00\u7248\u80fd\u8fc7\u7684\u90e8\u5206\u5206\u518d\u60f3\u6b63\u89e3<\/li>\n<\/ul>\n<h4>\u9898\u610f\u7b80\u8ff0<\/h4>\n<p>\u9898\u610f\u5176\u5b9e\u5f88\u76f4\u767d&#xff1a;<\/p>\n<p>\u51fd\u6570\u662f\u5404\u79cd\u7f16\u7a0b\u8bed\u8a00\u4e2d\u4e00\u9879\u91cd\u8981\u7684\u6982\u5ff5&#xff0c;\u501f\u52a9\u51fd\u6570&#xff0c;\u6211\u4eec\u603b\u53ef\u4ee5\u5c06\u590d\u6742\u7684\u4efb\u52a1\u5206\u89e3\u6210\u4e00\u4e2a\u4e2a\u76f8\u5bf9\u7b80\u5355\u7684\u5b50\u4efb\u52a1&#xff0c;\u76f4\u5230\u7ec6\u5316\u4e3a\u5341\u5206\u7b80\u5355\u7684\u57fa\u7840\u64cd\u4f5c&#xff0c;\u4ece\u800c\u4f7f\u4ee3\u7801\u7684\u7ec4\u7ec7\u66f4\u52a0\u4e25\u5bc6\u3001\u66f4\u52a0\u6709\u6761\u7406\u3002\u7136\u800c&#xff0c;\u8fc7\u591a\u7684\u51fd\u6570\u8c03\u7528\u4e5f\u4f1a\u5bfc\u81f4\u989d\u5916\u7684\u5f00\u9500&#xff0c;\u5f71\u54cd\u7a0b\u5e8f\u7684\u8fd0\u884c\u6548\u7387\u3002<\/p>\n<p>\u67d0\u6570\u636e\u5e93\u5e94\u7528\u7a0b\u5e8f\u63d0\u4f9b\u4e86\u82e5\u5e72\u51fd\u6570\u7528\u4ee5\u7ef4\u62a4\u6570\u636e\u3002\u5df2\u77e5\u8fd9\u4e9b\u51fd\u6570\u7684\u529f\u80fd\u53ef\u5206\u4e3a\u4e09\u7c7b&#xff1a;<\/p>\n<li>\u5c06\u6570\u636e\u4e2d\u7684\u6307\u5b9a\u5143\u7d20\u52a0\u4e0a\u4e00\u4e2a\u503c&#xff1b;<\/li>\n<li>\u5c06\u6570\u636e\u4e2d\u7684\u6bcf\u4e00\u4e2a\u5143\u7d20\u4e58\u4ee5\u4e00\u4e2a\u76f8\u540c\u503c&#xff1b;<\/li>\n<li>\u4f9d\u6b21\u6267\u884c\u82e5\u5e72\u6b21\u51fd\u6570\u8c03\u7528&#xff0c;\u4fdd\u8bc1\u4e0d\u4f1a\u51fa\u73b0\u9012\u5f52&#xff08;\u5373\u4e0d\u4f1a\u76f4\u63a5\u6216\u95f4\u63a5\u5730\u8c03\u7528\u672c\u8eab&#xff09;\u3002<\/li>\n<p>\u5728\u4f7f\u7528\u8be5\u6570\u636e\u5e93\u5e94\u7528\u65f6&#xff0c;\u7528\u6237\u53ef\u4e00\u6b21\u6027\u8f93\u5165\u8981\u8c03\u7528\u7684\u51fd\u6570\u5e8f\u5217&#xff08;\u4e00\u4e2a\u51fd\u6570\u53ef\u80fd\u88ab\u8c03\u7528\u591a\u6b21&#xff09;&#xff0c;\u5728\u4f9d\u6b21\u6267\u884c\u5b8c\u5e8f\u5217\u4e2d\u7684\u51fd\u6570\u540e&#xff0c;\u7cfb\u7edf\u4e2d\u7684\u6570\u636e\u88ab\u52a0\u4ee5\u66f4\u65b0\u3002\u67d0\u4e00\u5929&#xff0c;\u5c0f A \u5728\u5e94\u7528\u8be5\u6570\u636e\u5e93\u7a0b\u5e8f\u5904\u7406\u6570\u636e\u65f6\u9047\u5230\u4e86\u56f0\u96be&#xff1a;\u7531\u4e8e\u9891\u7e41\u800c\u4f4e\u6548\u7684\u51fd\u6570\u8c03\u7528&#xff0c;\u7cfb\u7edf\u5728\u6267\u884c\u64cd\u4f5c\u65f6\u8fdb\u5165\u4e86\u65e0\u54cd\u5e94\u7684\u72b6\u6001&#xff0c;\u4ed6\u53ea\u597d\u5f3a\u5236\u7ed3\u675f\u4e86\u6570\u636e\u5e93\u7a0b\u5e8f\u3002\u4e3a\u4e86\u8ba1\u7b97\u51fa\u6b63\u786e\u6570\u636e&#xff0c;\u5c0f A \u67e5\u9605\u4e86\u8f6f\u4ef6\u7684\u6587\u6863&#xff0c;\u4e86\u89e3\u5230\u6bcf\u4e2a\u51fd\u6570\u7684\u5177\u4f53\u529f\u80fd\u4fe1\u606f&#xff0c;\u73b0\u5728\u4ed6\u60f3\u8bf7\u4f60\u6839\u636e\u8fd9\u4e9b\u4fe1\u606f\u5e2e\u4ed6\u8ba1\u7b97\u51fa\u66f4\u65b0\u540e\u7684\u6570\u636e\u5e94\u8be5\u662f\u591a\u5c11\u3002<\/p>\n<h4>\u524d\u7f6e\u77e5\u8bc6<\/h4>\n<p>\u8fd9\u9898\u8981\u7528\u5230\u7684\u5de5\u5177\u4e0d\u591a&#xff0c;\u4f46\u6709\u4e00\u4e2a\u5bb9\u6613\u5fd8&#xff0c;\u5148\u8fc7\u4e00\u904d\u3002<\/p>\n<p>\u628a\u6570\u636e\u6392\u597d\u518d\u5904\u7406<\/p>\n<p>\u6392\u5e8f\u672c\u8eab O(n log n)&#xff0c;\u5173\u952e\u662f\u6392\u5b8c\u4e4b\u540e\u80fd\u5229\u7528\u5355\u8c03\u6027\u505a\u7ebf\u6027\u626b\u63cf&#xff0c;\u628a O(n\u00b2) \u964d\u5230 O(n)\u3002<\/p>\n<h3>\u4e8c\u3001\u601d\u8def\u5206\u6790<\/h3>\n<p>\u8fd9\u9898\u5b98\u65b9\u96be\u5ea6\u63d0\u9ad8&#043;\/\u7701\u9009-&#xff0c;\u4e2d\u573a&#xff0c;\u5148\u62ff\u66b4\u529b\u5206\u6bd4\u8f83\u7a33\u59a5\u3002<\/p>\n<p>\u601d\u8def\u7684\u5165\u53e3\u5728\u54ea\u91cc&#xff1f;<\/p>\n<p>\u628a\u6bcf\u4e2a\u64cd\u4f5c\u548c\u5b83\u6240\u6267\u884c\u7684\u64cd\u4f5c\u8fde\u5355\u5411\u8fb9&#xff0c;\u8fd9\u6837\u5c31\u5f62\u6210\u4e86\u4e00\u4e2a dag\u3002<\/p>\n<p>\u5728\u8fd9\u4e2a dag \u4e0a\u9762&#xff0c;\u771f\u6b63\u4f7f\u7b54\u6848\u53d8\u5316\u7684\u662f\u90a3\u4e9b\u51fa\u5ea6\u4e3a 0 \u7684\u70b9&#xff0c;\u5176\u4ed6\u70b9\u53ea\u662f\u53cd\u590d\u5730&#034;\u8c03\u7528&#034;\u5b83\u4eec\u3002<\/p>\n<p>\u90a3\u4e48\u4e0d\u96be\u8054\u60f3\u5230\u8981\u5904\u7406\u51fa\u6bcf\u4e00\u4e2a\u70b9\u6240\u80fd\u4ea7\u751f\u7684\u8d21\u732e\u3002<\/p>\n<p>\u6211\u4eec\u53d1\u73b0&#xff0c;\u5bf9\u4e8e\u4e58\u6cd5\u64cd\u4f5c&#xff0c;\u8d8a\u9760\u540e\u8fdb\u884c\u5b83\u5f71\u54cd\u7684\u8303\u56f4\u5c31\u8d8a\u5e7f&#xff0c;\u800c\u5728\u5b83\u4e4b\u524d\u7684\u6240\u6709\u64cd\u4f5c&#xff0c;\u90fd\u53d7\u8fd9\u4e2a\u4e58\u6cd5\u7684\u5f71\u54cd\u3002<\/p>\n<p>\u8fd9\u6837\u53ef\u4ee5\u6cbf\u62d3\u6251\u5e8f\u5012\u5e8f\u9012\u63a8\u51fa\u6bcf\u4e2a\u8282\u70b9\u7684\u8d21\u732e&#xff0c;\u8fd9\u91cc\u7684\u8d21\u732e\u6307\u8fdb\u884c\u8fd9\u4e2a\u64cd\u4f5c&#xff0c;\u6574\u4e2a\u5e8f\u5217\u8981\u4e58\u4ee5\u591a\u5c11\u3002<\/p>\n<p>\u63a5\u4e0b\u6765\u6211\u4eec\u518d\u8003\u8651\u52a0\u6cd5\u64cd\u4f5c\u3002<\/p>\n<p>\u540c\u7406&#xff0c;\u4f60\u53ef\u4ee5\u7ef4\u62a4\u51fa\u5bf9\u4e8e\u6bcf\u4e2a\u64cd\u4f5c&#xff0c;\u5b83\u5728\u8fd9\u4e2a\u64cd\u4f5c\u4e32\u4e2d\u88ab\u52a0\u4e86\u591a\u5c11\u6b21\u3002<\/p>\n<p>\u6ce8\u610f&#xff1a;\u8fd9\u65f6\u6211\u4eec\u5c31\u8981\u6574\u4f53\u8003\u8651\u4e86&#xff0c;\u5e76\u4e14\u5bf9\u4e8e op\u22601 \u7684\u90a3\u4e9b\u64cd\u4f5c&#xff0c;\u6211\u4eec\u9012\u63a8\u4e0d\u662f\u4e3a\u4e86\u7edf\u8ba1\u7b54\u6848&#xff0c;\u800c\u662f\u8981\u5f97\u5230\u540e\u9762\u72b6\u6001\u7684\u503c\u3002<\/p>\n<p>\u5f88\u663e\u7136&#xff0c;\u6211\u4eec\u8981\u987a\u7740\u62d3\u6251\u5e8f\u53bb\u66f4\u65b0\u3002<\/p>\n<p>\u6b64\u65f6\u4e5f\u8981\u628a\u4e58\u6cd5\u6807\u8bb0\u4e0b\u653e&#xff0c;\u6700\u540e\u5148\u4e58\u518d\u52a0&#xff0c;\u4ee5\u9632\u641e\u6df7\u3002<\/p>\n<h3>\u4e09\u3001\u5b8c\u6574\u4ee3\u7801<\/h3>\n<p>#include &lt;cstdio&gt;<br \/>\n#include &lt;vector&gt;<br \/>\n#include &lt;queue&gt;<br \/>\nusing namespace std;<\/p>\n<p>\/\/ CSP-S 2020 \u51fd\u6570\u8c03\u7528<br \/>\n\/\/ m \u4e2a\u51fd\u6570&#xff0c;\u4e09\u7c7b&#xff1a;<br \/>\n\/\/   1 t v      : a[v] &#043;&#061; t<br \/>\n\/\/   2 t        : \u5168\u4f53 a[i] *&#061; t<br \/>\n\/\/   3 c g1..gc : \u6309\u987a\u5e8f\u8c03\u7528 c \u4e2a\u51fd\u6570&#xff08;\u65e0\u73af&#xff09;<br \/>\n\/\/ \u7ed9\u5b9a\u521d\u59cb a[1..n] \u4e0e\u6267\u884c\u5e8f\u5217 seq[1..q]&#xff0c;\u6c42\u6267\u884c\u540e\u7684 a&#xff08;\u6a21 998244353&#xff09;\u3002<br \/>\n\/\/<br \/>\n\/\/ \u601d\u8def&#xff08;\u7ecf\u5178\u300c\u8d85\u6e90 &#043; \u4e24\u6b21\u62d3\u6251\u6392\u5e8f\u300d&#xff09;&#xff1a;<br \/>\n\/\/   \u6784\u9020 DAG&#xff1a;\u51fd\u6570\u4e3a\u70b9&#xff0c;\u8c03\u7528\u5173\u7cfb\u4e3a\u6709\u5411\u8fb9&#xff08;\u8c03\u7528\u8005 \u2192 \u88ab\u8c03\u7528\u8005&#xff09;\u3002<br \/>\n\/\/   \u989d\u5916\u52a0\u5165\u8d85\u6e90 0 \u53f7\u70b9\u4ee3\u8868\u4e3b\u7a0b\u5e8f&#xff0c;\u5b83\u6309\u987a\u5e8f\u8c03\u7528 seq[1..q]\u3002<br \/>\n\/\/   \u2460 mul[u]&#xff1a;\u6267\u884c\u4e00\u6b21 u \u4f1a\u8ba9\u6574\u4e2a\u5e8f\u5217\u6574\u4f53\u4e58\u4e0a\u591a\u5c11\u3002<br \/>\n\/\/        \u7c7b\u578b 1 \u2192 1&#xff1b;\u7c7b\u578b 2 \u2192 t&#xff1b;\u7c7b\u578b 3 \u2192 \u5b50\u51fd\u6570 mul \u4e4b\u79ef\u3002<br \/>\n\/\/        \u5728\u53cd\u5411\u56fe\u4e0a\u62d3\u6251\u5408\u5e76\u5373\u53ef&#xff08;\u53f6\u5b50\u5148\u51fa\u961f&#xff09;\u3002<br \/>\n\/\/   \u2461 cnt[u]&#xff1a;\u51fd\u6570 u \u5728\u6700\u7ec8\u65b9\u6848\u4e2d\u88ab\u6267\u884c\u7684\u7b49\u6548\u6b21\u6570&#xff08;\u5df2\u542b\u5916\u5c42\u300c\u4f4d\u4e8e\u5176\u540e\u7684\u4e58\u6cd5\u300d&#xff09;\u3002<br \/>\n\/\/        cnt[0] &#061; 1&#xff0c;\u5176\u4f59\u4e3a 0\u3002\u5728\u6b63\u5411\u56fe\u4e0a\u6309\u62d3\u6251\u5e8f\u4e0b\u653e&#xff1a;<br \/>\n\/\/        \u00b7 \u5bf9\u7c7b\u578b 3 \u6216\u8d85\u6e90&#xff1a;**\u5012\u5e8f**\u904d\u5386\u5176\u5b50\u51fd\u6570&#xff1a;<br \/>\n\/\/              run &#061; cnt[u];<br \/>\n\/\/              for j &#061; \u672b..0:  cnt[child[j]] &#043;&#061; run;  run &#061; run * mul[child[j]];<br \/>\n\/\/          \u56e0\u4e3a\u6392\u5728\u540e\u9762\u7684\u5144\u5f1f\u51fd\u6570\u91cc\u7684\u4e58\u6cd5\u4f1a\u653e\u5927\u524d\u9762\u5144\u5f1f\u7684\u6267\u884c\u6548\u679c\u3002<br \/>\n\/\/   \u2462 \u7b54\u6848&#xff1a;a[i] &#061; a[i] * mul[0] &#043; \u03a3_{\u7c7b\u578b 1 \u4e14 pos&#061;i} t * cnt[u]&#xff08;\u6a21&#xff09;\u3002<br \/>\nconst long long MOD &#061; 998244353;<br \/>\nconst int MAXN &#061; 100005;<\/p>\n<p>int n, m, q;<br \/>\nlong long a[MAXN];<br \/>\nint tp[MAXN];               \/\/ \u51fd\u6570\u7c7b\u578b&#xff1b;\u8d85\u6e90 tp[0]&#061;3<br \/>\nint posi[MAXN];             \/\/ \u7c7b\u578b 1 \u7684\u4f4d\u7f6e<br \/>\nlong long val[MAXN];        \/\/ \u7c7b\u578b 1 \u7684\u503c \/ \u7c7b\u578b 2 \u7684\u4e58\u6570<br \/>\nlong long mulv[MAXN];       \/\/ \u6574\u4f53\u4e58\u6570<br \/>\nlong long cntv[MAXN];       \/\/ \u7b49\u6548\u6267\u884c\u6b21\u6570<br \/>\nvector&lt;int&gt; rev_[MAXN];     \/\/ \u53cd\u5411\u56fe&#xff1a;rev_[u] &#061; u \u7684\u6240\u6709\u7236\u8282\u70b9<br \/>\nvector&lt;int&gt; fwd[MAXN];      \/\/ \u6b63\u5411\u56fe&#xff1a;fwd[u] &#061; u \u8c03\u7528\u7684\u5b50\u51fd\u6570<br \/>\nint outdeg[MAXN];           \/\/ \u6b63\u5411\u51fa\u5ea6&#xff08;&#061; \u53cd\u5411\u56fe\u5165\u5ea6&#xff09;<br \/>\nint indeg_[MAXN];           \/\/ \u6b63\u5411\u5165\u5ea6&#xff08;&#061; \u53cd\u5411\u56fe\u51fa\u5ea6&#xff09;<\/p>\n<p>int main() {<br \/>\n    scanf(&#034;%d&#034;, &amp;n);<br \/>\n    for (int i &#061; 1; i &lt;&#061; n; &#043;&#043;i) scanf(&#034;%lld&#034;, &amp;a[i]);<br \/>\n    scanf(&#034;%d&#034;, &amp;m);<br \/>\n    for (int i &#061; 1; i &lt;&#061; m; &#043;&#043;i) {<br \/>\n        scanf(&#034;%d&#034;, &amp;tp[i]);<br \/>\n        mulv[i] &#061; 1;<br \/>\n        if (tp[i] &#061;&#061; 1) {<br \/>\n            scanf(&#034;%d %lld&#034;, &amp;posi[i], &amp;val[i]);<br \/>\n        } else if (tp[i] &#061;&#061; 2) {<br \/>\n            scanf(&#034;%lld&#034;, &amp;val[i]);<br \/>\n            mulv[i] &#061; val[i] % MOD;<br \/>\n        } else {<br \/>\n            int c; scanf(&#034;%d&#034;, &amp;c);<br \/>\n            for (int j &#061; 0; j &lt; c; &#043;&#043;j) {<br \/>\n                int g; scanf(&#034;%d&#034;, &amp;g);<br \/>\n                fwd[i].push_back(g);<br \/>\n                rev_[g].push_back(i);<br \/>\n                outdeg[i]&#043;&#043;; indeg_[g]&#043;&#043;;<br \/>\n            }<br \/>\n        }<br \/>\n    }<br \/>\n    scanf(&#034;%d&#034;, &amp;q);<br \/>\n    tp[0] &#061; 3; mulv[0] &#061; 1; cntv[0] &#061; 1;<br \/>\n    for (int i &#061; 0; i &lt; q; &#043;&#043;i) {<br \/>\n        int f; scanf(&#034;%d&#034;, &amp;f);<br \/>\n        fwd[0].push_back(f);<br \/>\n        rev_[f].push_back(0);<br \/>\n        outdeg[0]&#043;&#043;; indeg_[f]&#043;&#043;;<br \/>\n    }<\/p>\n<p>    \/\/ &#8212;&#8212;&#8212;- \u2460 \u53cd\u5411\u62d3\u6251\u6c42 mul &#8212;&#8212;&#8212;-<br \/>\n    {<br \/>\n        static int deg[MAXN];<br \/>\n        for (int i &#061; 0; i &lt;&#061; m; &#043;&#043;i) deg[i] &#061; outdeg[i];   \/\/ \u53cd\u5411\u56fe\u5165\u5ea6<br \/>\n        queue&lt;int&gt; Q;<br \/>\n        for (int i &#061; 0; i &lt;&#061; m; &#043;&#043;i) if (deg[i] &#061;&#061; 0) Q.push(i);<br \/>\n        while (!Q.empty()) {<br \/>\n            int u &#061; Q.front(); Q.pop();<br \/>\n            for (size_t k &#061; 0; k &lt; rev_[u].size(); &#043;&#043;k) {<br \/>\n                int p &#061; rev_[u][k];<br \/>\n                mulv[p] &#061; mulv[p] * mulv[u] % MOD;          \/\/ \u7236\u8282\u70b9\u7d2f\u4e58\u5b50\u51fd\u6570<br \/>\n                if (&#8211;deg[p] &#061;&#061; 0) Q.push(p);<br \/>\n            }<br \/>\n        }<br \/>\n    }<\/p>\n<p>    \/\/ &#8212;&#8212;&#8212;- \u2461 \u6b63\u5411\u62d3\u6251\u6c42 cnt &#8212;&#8212;&#8212;-<br \/>\n    {<br \/>\n        static int deg[MAXN];<br \/>\n        for (int i &#061; 0; i &lt;&#061; m; &#043;&#043;i) deg[i] &#061; indeg_[i];<br \/>\n        queue&lt;int&gt; Q;<br \/>\n        for (int i &#061; 0; i &lt;&#061; m; &#043;&#043;i) if (deg[i] &#061;&#061; 0) Q.push(i);<br \/>\n        while (!Q.empty()) {<br \/>\n            int u &#061; Q.front(); Q.pop();<br \/>\n            if (u &#061;&#061; 0 || tp[u] &#061;&#061; 3) {<br \/>\n                long long run &#061; cntv[u] % MOD;<br \/>\n                for (int j &#061; (int)fwd[u].size() &#8211; 1; j &gt;&#061; 0; &#8211;j) {<br \/>\n                    int v &#061; fwd[u][j];<br \/>\n                    cntv[v] &#061; (cntv[v] &#043; run) % MOD;<br \/>\n                    run &#061; run * mulv[v] % MOD;<br \/>\n                    if (&#8211;deg[v] &#061;&#061; 0) Q.push(v);<br \/>\n                }<br \/>\n            } else {<br \/>\n                for (size_t j &#061; 0; j &lt; fwd[u].size(); &#043;&#043;j) {<br \/>\n                    int v &#061; fwd[u][j];<br \/>\n                    if (&#8211;deg[v] &#061;&#061; 0) Q.push(v);<br \/>\n                }<br \/>\n            }<br \/>\n        }<br \/>\n    }<\/p>\n<p>    \/\/ &#8212;&#8212;&#8212;- \u2462 \u6c47\u603b &#8212;&#8212;&#8212;-<br \/>\n    for (int i &#061; 1; i &lt;&#061; n; &#043;&#043;i) a[i] &#061; a[i] % MOD * mulv[0] % MOD;<br \/>\n    for (int u &#061; 1; u &lt;&#061; m; &#043;&#043;u)<br \/>\n        if (tp[u] &#061;&#061; 1)<br \/>\n            a[posi[u]] &#061; (a[posi[u]] &#043; val[u] % MOD * cntv[u]) % MOD;<\/p>\n<p>    for (int i &#061; 1; i &lt;&#061; n; &#043;&#043;i) printf(&#034;%lld%c&#034;, a[i], i &#061;&#061; n ? &#039;\\\\n&#039; : &#039; &#039;);<br \/>\n    return 0;<br \/>\n}<\/p>\n<h3>\u56db\u3001\u4ee3\u7801\u5206\u6bb5\u62c6\u89e3<\/h3>\n<p>\u5b8c\u6574\u4ee3\u7801\u5728\u4e0a\u9762&#xff0c;\u4e0b\u9762\u6309\u529f\u80fd\u5206\u5757\u89e3\u91ca\u3002<\/p>\n<h4>\u5934\u6587\u4ef6\u4e0e\u5168\u5c40\u53d8\u91cf<\/h4>\n<p>\u5148\u628a\u7528\u5230\u7684\u5934\u6587\u4ef6\u548c\u5168\u5c40\u53d8\u91cf\u653e\u4e0a\u6765\u3002\u5168\u5c40\u53d8\u91cf\u5728\u7ade\u8d5b\u91cc\u5f88\u5e38\u7528&#xff0c;\u597d\u5904\u662f\u51fd\u6570\u4e4b\u95f4\u5171\u4eab\u65b9\u4fbf&#xff0c;\u4ee3\u4ef7\u662f\u8981\u5c0f\u5fc3\u521d\u59cb\u5316\u548c\u88ab\u610f\u5916\u6539\u5199\u3002<\/p>\n<p>#include &lt;cstdio&gt;<br \/>\n#include &lt;vector&gt;<br \/>\n#include &lt;queue&gt;<br \/>\nusing namespace std;<br \/>\nconst long long MOD &#061; 998244353;<br \/>\nconst int MAXN &#061; 100005;<br \/>\nint n, m, q;<br \/>\nlong long a[MAXN];<br \/>\nint tp[MAXN];               \/\/ \u51fd\u6570\u7c7b\u578b&#xff1b;\u8d85\u6e90 tp[0]&#061;3<br \/>\nint posi[MAXN];             \/\/ \u7c7b\u578b 1 \u7684\u4f4d\u7f6e<br \/>\nlong long val[MAXN];        \/\/ \u7c7b\u578b 1 \u7684\u503c \/ \u7c7b\u578b 2 \u7684\u4e58\u6570<br \/>\nlong long mulv[MAXN];       \/\/ \u6574\u4f53\u4e58\u6570<br \/>\nlong long cntv[MAXN];       \/\/ \u7b49\u6548\u6267\u884c\u6b21\u6570<br \/>\nvector&lt;int&gt; rev_[MAXN];     \/\/ \u53cd\u5411\u56fe&#xff1a;rev_[u] &#061; u \u7684\u6240\u6709\u7236\u8282\u70b9<br \/>\nvector&lt;int&gt; fwd[MAXN];  <\/p>\n<h4>\u4e3b\u4f53\u903b\u8f91<\/h4>\n<p>\u4e3b\u4f53\u90e8\u5206\u6309\u987a\u5e8f\u5b8c\u6210\u8bfb\u5165\u3001\u8ba1\u7b97\u3001\u8f93\u51fa\u3002main \u51fd\u6570\u5c3d\u91cf\u4fdd\u6301\u7ebf\u6027&#xff0c;\u628a\u590d\u6742\u7684\u903b\u8f91\u62c6\u6210\u72ec\u7acb\u51fd\u6570&#xff0c;\u51fa\u95ee\u9898\u65f6\u66f4\u5bb9\u6613\u5b9a\u4f4d\u3002<\/p>\n<h3>\u4e94\u3001\u5b9e\u4f8b\u6a21\u62df<\/h3>\n<p>\u5149\u770b\u4ee3\u7801\u5bb9\u6613\u865a&#xff0c;\u7528\u6837\u4f8b\u5b9e\u6d4b\u4e00\u904d\u6700\u8e0f\u5b9e\u3002<\/p>\n<p>\u6837\u4f8b 1<\/p>\n<p>\u8f93\u5165&#xff1a;<\/p>\n<p>3<br \/>\n1 2 3<br \/>\n3<br \/>\n1 1 1<br \/>\n2 2<br \/>\n3 2 1 2<br \/>\n2<br \/>\n2 3<\/p>\n<p>\u8f93\u51fa&#xff1a;<\/p>\n<p>6 8 12<\/p>\n<p>\u6837\u4f8b 2<\/p>\n<p>\u8f93\u5165&#xff1a;<\/p>\n<p>10<br \/>\n1 2 3 4 5 6 7 8 9 10<br \/>\n8<br \/>\n3 2 2 3<br \/>\n3 2 4 5<br \/>\n3 2 5 8<br \/>\n2 2<br \/>\n3 2 6 7<br \/>\n1 2 5<br \/>\n1 7 6<br \/>\n2 3<br \/>\n3<br \/>\n1 2 3<\/p>\n<p>\u8f93\u51fa&#xff1a;<\/p>\n<p>36 282 108 144 180 216 504 288 324 360<\/p>\n<p>\u4ee5\u7b2c\u4e00\u7ec4\u6837\u4f8b\u4e3a\u4f8b&#xff0c;\u8f93\u5165\u662f 3\u30011 2 3\u30013\u30011 1 1\u30012 2\u30013 2 1 2\u30012\u30012 3&#xff0c;\u6b63\u786e\u8f93\u51fa\u662f 6 8 12\u3002\u5efa\u8bae\u628a\u8fd9\u4e24\u884c\u6570\u636e\u6284\u5728\u7eb8\u4e0a&#xff0c;\u7528\u4e0a\u9762\u7684\u4ee3\u7801\u624b\u52a8\u8d70\u4e00\u904d&#xff0c;\u91cd\u70b9\u770b\u5faa\u73af\u53d8\u91cf\u600e\u4e48\u53d8\u5316\u3001\u7b54\u6848\u5728\u54ea\u4e00\u6b65\u88ab\u66f4\u65b0\u3002\u80fd\u81ea\u5df1\u63a8\u51fa\u6765\u7684\u4e1c\u897f&#xff0c;\u6bd4\u770b\u61c2\u4ee3\u7801\u5370\u8c61\u6df1\u5f97\u591a\u3002<\/p>\n<h3>\u516d\u3001\u8e29\u5751\u603b\u7ed3<\/h3>\n<p>\u6700\u540e\u603b\u7ed3\u51e0\u4e2a\u8981\u70b9\u3002<\/p>\n<li>\u6392\u5e8f\u540e\u539f\u6765\u7684\u4e0b\u6807\u4fe1\u606f\u4f1a\u4e22&#xff0c;\u9700\u8981\u989d\u5916\u8bb0\u5f55<\/li>\n<li>\u6bd4\u8f83\u51fd\u6570\u7684\u4e25\u683c\u5f31\u5e8f\u8981\u5199\u5bf9&#xff0c;\u5426\u5219\u6392\u5e8f\u7ed3\u679c\u672a\u5b9a\u4e49<\/li>\n<li>\u9ad8\u96be\u5ea6\u9898\u7684\u66b4\u529b\u5206\u5f88\u5173\u952e&#xff0c;\u5148\u5199\u4e00\u7248\u80fd\u8fc7\u7684\u90e8\u5206\u5206\u518d\u60f3\u6b63\u89e3<\/li>\n<p>\u53e6\u5916\u63d0\u9192\u4e00\u53e5&#xff1a;\u8fd9\u9898\u5728 CSP-S 2020 \u91cc\u662f\u63d0\u9ad8&#043;\/\u7701\u9009-\u96be\u5ea6&#xff0c;\u8003\u573a\u4e0a\u5982\u679c\u6ca1\u6709\u628a\u63e1\u62ff\u6ee1\u5206&#xff0c;\u5148\u628a\u66b4\u529b\u5199\u6cd5\u4ea4\u4e0a\u53bb\u62ff\u5230\u90e8\u5206\u5206&#xff0c;\u518d\u56de\u5934\u4f18\u5316\u3002CSP \u662f\u6253\u5206\u5236&#xff0c;\u7a7a\u7740\u4e0d\u5199\u624d\u662f\u6700\u4e8f\u7684\u3002<\/p>\n<h3>\u4e03\u3001\u77e5\u8bc6\u70b9\u62d3\u5c55<\/h3>\n<p>\u8fd9\u9898\u7684\u6838\u5fc3\u662f\u6392\u5e8f\u3002<\/p>\n<p>\u6392\u5e8f\u662f\u6240\u6709\u7b97\u6cd5\u7684\u57fa\u7840\u8bbe\u65bd\u3002\u5f88\u591a\u770b\u8d77\u6765\u590d\u6742\u7684\u95ee\u9898&#xff0c;\u6392\u5b8c\u5e8f\u4e4b\u540e\u5c31\u53d8\u6210\u4e86\u7ebf\u6027\u626b\u63cf\u3002<\/p>\n<p>\u5efa\u8bae\u7684\u7ec3\u4e60\u8def\u5f84&#xff1a;<\/p>\n<li>\u5148\u628a\u672c\u9898\u72ec\u7acb\u5199\u4e00\u904d&#xff0c;\u4e0d\u770b\u4ee3\u7801&#xff0c;\u9047\u5230\u5361\u58f3\u518d\u770b\u63d0\u793a<\/li>\n<li>\u6362\u4e2a\u5e73\u53f0\u63d0\u4ea4&#xff08;ACGO \u548c\u6d1b\u8c37\u90fd\u8bd5\u8bd5&#xff09;&#xff0c;\u786e\u4fdd\u4ee3\u7801\u5728\u4e24\u4e2a\u5e73\u53f0\u90fd\u80fd\u8fc7<\/li>\n<li>\u627e\u4e24\u5230\u4e09\u9053\u540c\u7c7b\u578b\u7684\u9898\u7ec3\u624b&#xff0c;\u5de9\u56fa\u8fd9\u7c7b\u95ee\u9898\u7684\u8bc6\u522b\u80fd\u529b<\/li>\n<h3>\u516b\u3001\u9002\u7528\u4eba\u7fa4<\/h3>\n<p>\u8fd9\u9053\u9898\u7684\u9002\u7528\u9762&#xff1a;<\/p>\n<ul>\n<li>\u76ee\u6807\u662f CSP-S \u9ad8\u5206\u6216\u7701\u9009\u7684\u540c\u5b66<\/li>\n<li>\u60f3\u901a\u8fc7\u771f\u9898\u7406\u89e3\u9ad8\u96be\u5ea6\u9898\u5982\u4f55\u4ece\u66b4\u529b\u4f18\u5316\u5230\u6b63\u89e3\u7684\u540c\u5b66<\/li>\n<li>\u60f3\u5f04\u660e\u767d\u6392\u5e8f\u7c7b\u95ee\u9898\u6807\u51c6\u89e3\u6cd5\u7684\u540c\u5b66<\/li>\n<\/ul>\n<p>\u4ee3\u7801\u6709\u4efb\u4f55\u95ee\u9898\u6b22\u8fce\u6307\u6b63&#xff0c;\u6211\u4f1a\u53ca\u65f6\u66f4\u65b0\u3002<\/p>\n<h3>\u5173\u4e8e\u8fd9\u4e2a\u7cfb\u5217<\/h3>\n<p>\u8fd9\u662f\u300cCSP \u771f\u9898\u9010\u9898\u7cbe\u8bb2\u300d\u7684\u7b2c 16 \u7bc7\u3002\u6211\u4f1a\u6309\u5e74\u4efd\u4ece 2019 \u4e00\u8def\u5237\u5230 2025&#xff0c;CSP-J \u548c CSP-S \u5168\u8986\u76d6\u3002\u6bcf\u7bc7\u90fd\u7ed9&#xff1a;\u53cc\u5e73\u53f0\u9898\u53f7&#xff08;ACGO &#043; \u6d1b\u8c37&#xff09;&#043; \u9010\u884c\u4ee3\u7801\u62c6\u89e3 &#043; \u771f\u5b9e\u6837\u4f8b\u6a21\u62df\u3002<\/p>\n<p>\u8ddf\u7740\u5237\u5b8c\u8fd9\u4e00\u5957&#xff0c;CSP \u7b2c\u4e00\u8f6e\u7684\u9009\u62e9\u9898\u548c\u57fa\u7840\u9898\u57fa\u672c\u5c31\u7a33\u4e86\u3002<\/p>\n<p>\u4e0b\u4e00\u7bc7&#xff1a;CSP-S 2020 \u52a8\u7269\u56ed&#xff08;\u666e\u53ca\/\u63d0\u9ad8-&#xff09;<\/p>\n<p>&#x1f449; 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