{"id":384,"date":"2013-04-10T11:56:00","date_gmt":"2013-04-10T03:56:00","guid":{"rendered":"http:\/\/nike0good.jp1.rpvhost.net\/288"},"modified":"2013-04-10T11:56:00","modified_gmt":"2013-04-10T03:56:00","slug":"school_routes_recursive_sap-incomplete","status":"publish","type":"post","link":"https:\/\/nike0good.com\/?p=384","title":{"rendered":"\u4e0a\u5b66\u8def\u7ebf(\u9012\u5f52sap-\u4e0d\u5b8c\u5168)"},"content":{"rendered":"

Problem 2 \u4e0a\u5b66\u8def\u7ebf(route.cpp\/c\/pas)<\/p>\n

\u3010\u9898\u76ee\u63cf\u8ff0\u3011<\/p>\n

\u53ef\u53ef\u548c\u5361\u5361\u5bb6\u4f4f\u9a6c\u8d5b\u514b\u5e02\u7684\u4e1c\u90ca\uff0c\u6bcf\u5929\u4e0a\u5b66\u4ed6\u4eec\u90fd\u8981\u8f6c\u8f66\u591a\u6b21\u624d\u80fd\u5230\u8fbe\u5e02\u533a\u897f\u7aef\u7684\u5b66\u6821\u3002\u76f4\u5230\u6709\u4e00\u5929\u4ed6\u4eec\u4e24\u4eba\u53c2\u52a0\u4e86\u5b66\u6821\u7684\u4fe1\u606f\u5b66\u5965\u6797\u5339\u514b\u7ade\u8d5b\u5c0f\u7ec4\u624d\u53d1\u73b0\u6bcf\u5929\u4e0a\u5b66\u7684\u4e58\u8f66\u8def\u7ebf\u4e0d\u4e00\u5b9a\u662f\u6700\u4f18\u7684\u3002<\/p>\n

\u9a6c\u8d5b\u514b\u5e02\u4e00\u5171\u8bbe\u6709N\u4e2a\u516c\u4ea4\u8f66\u7ad9\uff0c\u4e0d\u59a8\u5c06\u5b83\u4eec\u7f16\u53f7\u4e3a1\u2026N\u7684\u81ea\u7136\u6570\uff0c\u5e76\u8ba4\u4e3a\u53ef\u53ef\u548c\u5361\u5361\u5bb6\u4f4f\u57281\u53f7\u6c7d\u8f66\u7ad9\u9644\u8fd1\uff0c\u800c\u4ed6\u4eec\u5b66\u6821\u5728N\u53f7\u6c7d\u8f66\u7ad9\u3002\u5e02\u5185\u6709M\u6761\u76f4\u8fbe\u6c7d\u8f66\u8def\u7ebf\uff0c\u6267\u884c\u7b2ci\u6761\u8def\u7ebf\u7684\u516c\u4ea4\u8f66\u5f80\u8fd4\u4e8e\u7ad9\u70b9pi\u548cqi\u4e4b\u95f4\uff0c\u4ece\u8d77\u70b9\u5230\u7ec8\u70b9\u9700\u8981\u82b1\u8d39\u7684\u65f6\u95f4\u4e3ati\u3002(1<=i<=M, 1<=pi, qi<=N)<\/p>\n

\u4e24\u4e2a\u4eba\u5750\u5728\u7535\u8111\u524d\uff0c\u6839\u636e\u4e0a\u9762\u7684\u4fe1\u606f\u5f88\u5feb\u5c31\u7f16\u7a0b\u7b97\u51fa\u4e86\u6700\u4f18\u7684\u4e58\u8f66\u65b9\u6848\u3002\u7136\u800c\u53ef\u53ef\u5ffd\u7136\u6709\u4e86\u4e00\u4e2a鬼\u70b9\u5b50\uff0c\u4ed6\u60f3\u8d81\u5361\u5361\u4e0d\u5907\uff0c\u5728\u5361\u5361\u7684\u8f93\u5165\u6570\u636e\u4e2d\u5220\u53bb\u4e00\u4e9b\u8def\u7ebf\uff0c\u4ece\u800c\u8ba9\u5361\u5361\u7684\u7a0b\u5e8f\u5f97\u51fa\u7684\u7b54\u6848\u5927\u4e8e\u5b9e\u9645\u7684\u6700\u77ed\u65f6\u95f4\u3002\u800c\u5bf9\u4e8e\u6bcf\u4e00\u6761\u8def\u7ebfi\u4e8b\u5b9e\u4e0a\u90fd\u6709\u4e00\u4e2a\u4ee3\u4ef7ci\uff1a\u5220\u53bb\u8def\u7ebf\u7684ci\u8d8a\u5927\u5361\u5361\u5c31\u8d8a\u5bb9\u6613\u53d1\u73b0\u8fd9\u4e2a\u73a9\u7b11\uff0c\u53ef\u53ef\u60f3\u77e5\u9053\u4ec0\u4e48\u6837\u7684\u5220\u9664\u65b9\u6848\u53ef\u4ee5\u8fbe\u5230\u4ed6\u7684\u76ee\u7684\u800c\u8ba9\u88ab\u5220\u9664\u7684\u516c\u4ea4\u8f66\u8def\u7ebfci\u4e4b\u548c\u6700\u5c0f\u3002<\/p>\n

\u9a6c\u8d5b\u514b\u5e02\u7684\u516c\u4ea4\u7f51\u7edc\u5341\u5206\u53d1\u8fbe\uff0c\u4f60\u53ef\u4ee5\u8ba4\u4e3a\u4efb\u610f\u4e24\u4e2a\u8f66\u7ad9\u95f4\u90fd\u53ef\u4ee5\u901a\u8fc7\u76f4\u8fbe\u6216\u8f6c\u8f66\u4e92\u76f8\u5230\u8fbe\uff0c\u5f53\u7136\u5982\u679c\u5728\u4f60\u63d0\u4f9b\u7684\u5220\u9664\u65b9\u6848\u4e2d\uff0c\u5bb6\u548c\u5b66\u6821\u65e0\u6cd5\u4e92\u76f8\u5230\u8fbe\uff0c\u90a3\u4e48\u5219\u8ba4\u4e3a\u4e0a\u5b66\u9700\u8981\u7684\u6700\u77ed\u4e3a\u6b63\u65e0\u7a77\u5927\uff1a\u8fd9\u663e\u7136\u662f\u4e00\u4e2a\u5408\u6cd5\u7684\u65b9\u6848\u3002<\/p>\n

 <\/p>\n

\u3010\u8f93\u5165格\u5f0f\u3011<\/p>\n

\u8f93\u5165\u6587\u4ef6\u4e2d\u7b2c\u4e00\u884c\u6709\u4e24\u4e2a\u6b63\u6574\u6570N\u548cM\uff0c\u5206\u522b\u8868\u793a\u9a6c\u8d5b\u514b\u5e02\u516c\u4ea4\u8f66\u7ad9\u548c\u516c\u4ea4\u6c7d\u8f66\u8def\u7ebf\u7684\u4e2a\u6570\u3002\u4ee5\u4e0bM\u884c\uff0c\u6bcf\u884c\uff08\u7b2ci\u884c\uff0c\u603b\u7b2c(i+1)\u884c\uff09\u7528\u56db\u4e2a\u6b63\u6574\u6570\uff08\u4e4b\u95f4\u7531\u4e00\u4e2a\u7a7a格\u9694\u5f00\uff09\u63cf\u8ff0\u7b2ci\u6761\u8def\u7ebf\uff1api, qi, ti, ci\uff1b\u5177\u4f53\u542b\u4e49\u89c1\u4e0a\u6587\u63cf\u8ff0\u3002<\/p>\n

\u3010\u8f93\u51fa格\u5f0f\u3011<\/p>\n

\u8f93\u51fa\u6587\u4ef6\u6700\u591a\u6709\u4e24\u884c\u3002 \u7b2c\u4e00\u884c\u4e2d\u4ec5\u6709\u4e00\u4e2a\u6574\u6570\uff0c\u8868\u793a\u4ece\u53ef\u53ef\u548c\u5361\u5361\u5bb6\u5230\u5b66\u6821\u9700\u8981\u7684\u6700\u77ed\u65f6\u95f4\u3002\u7b2c\u4e8c\u884c\u8f93\u51fa\u4e00\u4e2a\u6574\u6570C,\u8868\u793aCi\u4e4b\u548c <\/p>\n

\u3010\u6837\u4f8b\u8f93\u5165\u3011<\/p>\n

6 7<\/p>\n

1 21 3<\/p>\n

2 61 5<\/p>\n

1 31 1<\/p>\n

3 41 1<\/p>\n

4 61 1<\/p>\n

5 61 2<\/p>\n

1 51 4<\/p>\n

\u3010\u6837\u4f8b\u8f93\u51fa\u3011<\/p>\n

2<\/p>\n

5<\/p>\n

\u3010\u6570\u636e\u8303\u56f4\u3011<\/p>\n

    <\/p>\n

2<=N<=500,1<=M<=124 750, 1<=ti, ci<=10 000<\/p>\n

 <\/p>\n

\n<\/p>\n

\u8fd9\u9898\u6211\u7528\u7684\u662f\u9012\u5f52sap()\uff0c\u8c01\u77e5\u9053\u72c2Wa\u3002<\/p>\n

\u5927\u5bb6\u7528\u9012\u5f52sap\u7684\u65f6\u5019\u60f3\u5fc5\u7ecf\u5e38\u4f1a\u83ab\u540dNTR\u3002<\/p>\n

\u7ed3\u8bba:\/\/dfs_sap()\u7684Z\u6b63\u786e\u6027\u76ee\u524d\u6709\u5f85\u8003\u8bc1\u3002\u3002\u3002<\/p>\n

\u6839\u636e\u6211\u7684\u7814\u7a76\uff0c\u7ecf\u9a8c\u603b\u7ed3\u5982\u4e0b\uff1a<\/p>\n

1.\u9000\u51fa\u6761\u4ef6\uff1a<\/p>\n

<\/span>-PS\uff1a\u6709\u53ef\u80fd\u67d0\u6b21\u589e\u5e7fflow=0\uff0c\u4f46\u662f\u6539\u8ddd\u79bb\u6807\u53f7\u53ef\u4ee5\u7ee7\u7eedflow<\/p>\n

<\/span>-PS\uff1a\u6709\u65f6\u5019\u65e0\u9650\u589e\u5e7f\uff0c\u8f93\u7b54\u6848\u80fd\u770b\u51fa\u4e0a\u9762\u7684\u9519\u8bef<\/p>\n

2.\u4fee\u6539\u8ddd\u79bb\u6807\u53f7\uff1a<\/p>\n

<\/span>-PS\uff1a\u8ddd\u79bb\u6807\u53f7\u6700\u597d\u76f4\u63a5+1\uff0cminj\u7b49\u624b\u6bb5\u6781\u6709\u53ef\u80fd\u9020\u6210\u2248\u6ca1\u6709\u8ddd\u79bb\u6807\u53f7\u4f18\u5316\u7684\u72b6\u51b5<\/p>\n

3.dfs\u65f6\u7684flow<\/p>\n

<\/span>-PS\uff1a\u4e00\u5b9a\u8981\u63d0\u524dreturn\uff0c\u8981\u4e0d\u7136\u6539\u8ddd\u79bb\u6807\u53f7a~<\/p>\n

4.\u91cd\u6784\u56fe:<\/p>\n

<\/span>-PS\uff1a\u8fd9\u6837\u662f\u8d28\u7684\u5dee\u522b\uff0c\u9012\u5f52\u4e0d\u5361\u65f6\u95f4\uff1f<\/p>\n

5.\u552f\u4e00\u91cd\u70b9\uff1a<\/p>\n

<\/span>PS\uff1a\u5b9e\u5728\u4e0d\u884c\u65f6\uff0c\u53bb\u6389\u8ddd\u79bb\u6807\u53f7\u4f18\u5316\uff01\u53e6\u53efT\u5230\u6b7b\uff0c\u4e0d\u80fdWA\u5230\u7206<\/p>\n

6.\u7528\u9012\u5f52sap\u552f\u4e00\u7684\u597d\u5904\u662f\u7701\u4e8b\u2026\u2026\uff08\u4ec0\u4e48\u4f601\u5206\u949fBFS_sap()?\u5f53\u6211\u6ca1\u8bf4\uff09<\/p>\n

\n<\/p>\n<\/p>\n

#include<cstdio>\n#include<cstring>\n#include<cstdlib>\n#include<iostream>\n#include<algorithm>\n#include<functional>\n#define MAXN (500+10)\n#define MAXM (124750+10)\n#define MAXCi (10000+10)\n#define INF (2139062143)\n#define For(i,n) for(int i=1;i<=n;i++)\n#define Forp(p,u) for (int p=pre[u];p;p=next[p])\nusing namespace std;\nint n,m,edge[2*MAXM],weight[2*MAXM],c[2*MAXM],next[2*MAXM],pre[MAXN],size=1;\nvoid addedge(int u,int v,int w,int w2)\n{\n\tedge[++size]=v;\n\tweight[size]=w;\n\tc[size]=w2;\n\tnext[size]=pre[u];\n\tpre[u]=size;\n}\nint d[MAXN],q[MAXN*8];\nvoid spfa()\n{\n\tmemset(d,127,sizeof(d));\n\td[1]=0;\n\tint head=1,tail=1;q[1]=1;\n\twhile (head<=tail)\n\t{\n\t\tint &u=q[head];\n\t\tForp(p,u)\n\t\t{\n\t\t\tint &v=edge[p];\n\t\t\tif (d[v]==INF||d[u]+weight[p]<d[v])\n\t\t\t{\n\t\t\t\tq[++tail]=v;d[v]=d[u]+weight[p];\n\t\t\t}\n\t\t}\n\t\thead++;\n\t}\n}\nint d2[MAXN],cnt[MAXN];\nvoid spfa2()\n{\n\tmemset(d2,127,sizeof(d2));\n\tmemset(cnt,0,sizeof(cnt));\n\td2[n]=0;cnt[0]=1;\n\tint head=1,tail=1;q[1]=n;\n\twhile (head<=tail)\n\t{\n\t\tint &u=q[head];\n\t\tForp(p,u)\n\t\t{\n\t\t\tint &v=edge[p];\n\t\t\tif (d[u]-weight[p]!=d[v]) continue;\n\t\t\tif (d2[v]==INF)\n\t\t\t{\n\t\t\t\tq[++tail]=v;d2[v]=d2[u]+1;\n\t\t\t\tcnt[d2[v]]++;\n\t\t\t}\n\t\t}\n\t\thead++;\n\t}\n}\nbool sap_T=1,b[2*MAXM]={0};\nint sap(int u,int flow)\n{\n\tif (u==n) return flow;\n\tint tot=0,minj=INF;\n\tForp(p,u)\n\t{\n\t\tint &v=edge[p];\n\t\/*\n\t\tif (d2[v]==INF) continue;\n\t\tif (!(d[u]+weight[p]==d[v]||d[u]-weight[p]==d[v])) continue;\n\t*\/\n\t\tif (!b[p]) continue;\n\t\tif (c[p]>0&&d2[u]==d2[v]+1)\n\t\t{\n\t\t\tint w=sap(v,min(flow-tot,c[p]));\n\t\t\tc[p]-=w;c[p^1]+=w;tot+=w;\n\t\t\tif (flow==tot) return tot;\n\t\t}else if (c[p]) minj=min(minj,d2[v]);\n\t}\n\tif (--cnt[d2[u]]==0)\n\t\t{\n\t\t\td2[1]=n,sap_T=0;\/*return tot;*\/\n\t\t}\/\/d2[1]=n+1;\n\/\/\tif (minj^INF) cnt[d2[u]=minj+1]++;\n\/*\telse*\/ cnt[++d2[u]]++;\n\treturn tot;\n}\nint main()\n{\n\tfreopen("route.in","r",stdin);\n\tfreopen("route.out","w",stdout);\n\tmemset(pre,0,sizeof(pre));\n\tscanf("%d%d",&n,&m);\n\tFor(i,m)\n\t{\n\t\tint u,v,w1,w2;\n\t\tscanf("%d%d%d%d",&u,&v,&w1,&w2);\n\t\taddedge(u,v,w1,w2);\n\t\taddedge(v,u,w1,w2);\n\t}\n\tspfa();\n\/\/\tfor (int i=1;i<=n;i++) cout<<d[i]<<' ';cout<<endl;\n\tcout<<d[n]<<endl;\n\tint ans=0;\n\tspfa2();\n\tint de_bug_1=0;\n\tFor(i,n)\n\t\tForp(p,i)\n\t\t{\n\t\t\tif (d[i]>d[edge[p]]) c[p]=0;\n\t\t\/\/*0\n\t\t\/\/\tif (d2[i]!=INF&&d2[edge[p]]!=INF&&c[p]) cout<<i<<' '<<edge[p]<<endl,de_bug_1++;\n\t\t\tif (d[i]+weight[p]==d[edge[p]]) b[p]=b[p^1]=1,\/*cout<<i<<' '<<edge[p]<<endl,*\/de_bug_1++;\n\t\t}\n\/\/\tcout<<de_bug_1<<endl;\n\tb[0]=1;\n\tFor(i,n)\n\t\tForp(p,i)\n\t\t{\n\t\t\twhile (next[p]&&!b[next[p]]) next[p]=next[next[p]];\n\t\t}\n\n\twhile(\/*sap_T*\/1)\n\t{\n\t\tif (d2[1]>=n) break;\n\t\tint w=sap(1,INF);\n\t\/\/\tif (!w) break;\n\/\/\t\tcout<<ans<<' '<<d2[1]<<endl;\n\t\tans+=w;\n\t}\n\tcout<<ans<<endl;\n\treturn 0;\n}<\/pre>\n<\/p>\n
\n<\/p>\n
<\/p>\n","protected":false},"excerpt":{"rendered":"
Problem 2 \u4e0a\u5b66\u8def\u7ebf(route.cpp\/c\/pas) \u3010\u9898\u76ee\u63cf\u8ff0\u3011 \u53ef\u53ef\u548c\u5361\u5361\u5bb6\u4f4f\u9a6c\u8d5b\u514b\u5e02\u7684\u4e1c\u90ca\uff0c\u6bcf […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_coblocks_attr":"","_coblocks_dimensions":"","_coblocks_responsive_height":"","_coblocks_accordion_ie_support":"","footnotes":""},"categories":[3],"tags":[113],"class_list":["post-384","post","type-post","status-publish","format-standard","hentry","category-defaultcategory","tag-network_flow"],"yoast_head":"\n\u4e0a\u5b66\u8def\u7ebf(\u9012\u5f52sap-\u4e0d\u5b8c\u5168) - nike0good<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/nike0good.com\/?p=384\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"\u4e0a\u5b66\u8def\u7ebf(\u9012\u5f52sap-\u4e0d\u5b8c\u5168) - 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