{"id":346,"date":"2013-03-07T13:23:00","date_gmt":"2013-03-07T05:23:00","guid":{"rendered":"http:\/\/nike0good.jp1.rpvhost.net\/250"},"modified":"2013-03-07T13:23:00","modified_gmt":"2013-03-07T05:23:00","slug":"bzoj_1977_beijing2010_team_small_spanning_tree_tree-lca-bit_operation","status":"publish","type":"post","link":"https:\/\/nike0good.com\/?p=346","title":{"rendered":"BZOJ 1977([BeiJing2010\u7ec4\u961f]\u6b21\u5c0f\u751f\u6210\u6811 Tree-LCA\u7684\u4f4d\u8fd0\u7b97)"},"content":{"rendered":"

<\/p>\n

1977: [BeiJing2010\u7ec4\u961f]\u6b21\u5c0f\u751f\u6210\u6811 Tree<\/h2>\n

Time Limit: <\/span>10 Sec  Memory Limit: <\/span>64 MB
\nSubmit: <\/span>1176  Solved: <\/span>234
\n[Submit<\/a>][Status<\/a>][Discuss<\/a>]<\/center><\/p>\n

Description<\/h2>\n
\n\u5c0f C \u6700\u8fd1\u5b66\u4e86\u5f88\u591a\u6700\u5c0f\u751f\u6210\u6811\u7684\u7b97\u6cd5\uff0cPrim \u7b97\u6cd5\u3001Kurskal \u7b97\u6cd5\u3001\u6d88\u5708\u7b97\u6cd5 \u7b49\u7b49\u3002 \u6b63\u5f53\u5c0f C \u6d0b\u6d0b\u5f97\u610f\u4e4b\u65f6\uff0c\u5c0f P \u53c8\u6765\u6cfc\u5c0f C \u51b7\u6c34\u4e86\u3002\u5c0f P \u8bf4\uff0c\u8ba9\u5c0f C \u6c42\u51fa\u4e00 \u4e2a\u65e0\u5411\u56fe\u7684\u6b21\u5c0f\u751f\u6210\u6811\uff0c\u800c\u4e14\u8fd9\u4e2a\u6b21\u5c0f\u751f\u6210\u6811\u8fd8\u5f97\u662f\u4e25格\u6b21\u5c0f\u7684\uff0c\u4e5f\u5c31\u662f\u8bf4\uff1a \u5982\u679c\u6700\u5c0f\u751f\u6210\u6811\u9009\u62e9\u7684\u8fb9\u96c6\u662f EM\uff0c\u4e25格\u6b21\u5c0f\u751f\u6210\u6811\u9009\u62e9\u7684\u8fb9\u96c6\u662f ES\uff0c\u90a3\u4e48 \u9700\u8981\u6ee1\u8db3\uff1a(value(e) \u8868\u793a\u8fb9 e\u7684\u6743值)\"\" \u8fd9\u4e0b\u5c0f
\n C \u8499\u4e86\uff0c\u4ed6\u627e\u5230\u4e86\u4f60\uff0c\u5e0c\u671b\u4f60\u5e2e\u4ed6\u89e3\u51b3\u8fd9\u4e2a\u95ee\u9898\u3002<\/div>\n

Input<\/h2>\n
\n\u7b2c\u4e00\u884c\u5305\u542b\u4e24\u4e2a\u6574\u6570N \u548cM\uff0c\u8868\u793a\u65e0\u5411\u56fe\u7684\u70b9\u6570\u4e0e\u8fb9\u6570\u3002 \u63a5\u4e0b\u6765 M\u884c\uff0c\u6bcf\u884c 3\u4e2a\u6570x y z \u8868\u793a\uff0c\u70b9 x \u548c\u70b9y\u4e4b\u95f4\u6709\u4e00\u6761\u8fb9\uff0c\u8fb9\u7684\u6743值 \u4e3az\u3002<\/div>\n

Output<\/h2>\n
\n\u5305\u542b\u4e00\u884c\uff0c\u4ec5\u4e00\u4e2a\u6570\uff0c\u8868\u793a\u4e25格\u6b21\u5c0f\u751f\u6210\u6811\u7684\u8fb9\u6743\u548c\u3002(\u6570 \u636e\u4fdd\u8bc1\u5fc5\u5b9a\u5b58\u5728\u4e25格\u6b21\u5c0f\u751f\u6210\u6811)<\/div>\n

Sample Input<\/h2>\n
\n5 6

\n1 2 1

\n1 3 2

\n2 4 3

\n3 5 4

\n3 4 3

\n4 5 6 <\/span><\/div>\n

Sample Output<\/h2>\n
\n11<\/span><\/div>\n

HINT<\/h2>\n
\n

\u6570\u636e\u4e2d\u65e0\u5411\u56fe\u65e0\u81ea\u73af\uff1b 
\n50% \u7684\u6570\u636eN\u22642 000 M\u22643 000\uff1b 
\n80% \u7684\u6570\u636eN\u226450 000 M\u2264100 000\uff1b 
\n100% \u7684\u6570\u636eN\u2264100 000 M\u2264300 000 \uff0c\u8fb9\u6743值\u975e\u8d1f\u4e14\u4e0d\u8d85\u8fc7 10^9
\n\u3002<\/p>\n<\/div>\n

Source<\/h2>\n
\n

<\/a><\/p>\n<\/div>\n

\u8fd9\u9898\u7684\u5173\u952e\u5c31\u5728\u4e8e\u6c42Lca,\u8bb0\u5f55\u8def\u5f84\u4e0a\u7684\u6700\u5c0f\u4e0e\u4e25格\u6b21\u5c0f值.<\/span><\/p>\n

\u7528f[i][j]\u8868\u793ai\u7684\u7b2c2^j\u4e2a\u513f\u5b50(0 \u8868\u793a \u4e0d\u5b58\u5728)<\/span><\/p>\n

\u90a3\u4e48f[i][j]=f[ f[i][ j-1]<\/strong> ][j-1<\/strong>]<\/span><\/p>\n

dp[i][j]\u548cdp0[i][j]\u8868\u793a\u70b9i\u5230f[i][j]\u7684\u6700\u5c0f\u548c\u4e25格\u6b21\u5c0f值\uff08\u4e0d\u5b58\u5728=-1\uff09\uff0c\u90a3\u4e48\u53ea\u9700\u7279\u5224\u5373\u53ef.<\/span><\/span><\/p>\n

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

int lca(int x,int y,int &nowdp,int &nowdp0)\n{\n\tif (deep[x]<deep[y]) swap(x,y);\n\tint t=deep[x]-deep[y]; \/\/\u5dee\u7684\u6570\u91cf\n\tfor (int i=0;t;i++)\n\t\tif (t&bin[i])   \/\/\u8f6c\u5316\u4e3a\u4f4d\u8fd0\u7b97 bin[i]\u8868\u793a2<<i \u628at\u770b\u62102\u8fdb\u5236\n\t\t{\n\t\t\tx=f[x][i];\n\t\t\tt-=bin[i];\n\t\t}\n\tint i=Li-1; \/\/Li \u8868\u793a \u6700\u9ad8\u5b58\u52302^(Li-1)\u4e2a\u7236\u4eb2\n\twhile (x^y) \/\/x\u548cy\u4e0d\u76f8\u7b49\u65f6\n\t{\n\t\twhile (f[x][i]==f[y][i]&&i) i--; \/\/\u5f53i==0\u65f6\u53ea\u80fd\u5411\u4e0a\u8df3\n\t\tx=f[x][i];y=f[y][i];\n\t}\n}\n<\/pre>\n
\u7a0b\u5e8f\uff1a<\/p>\n
#include<cstdio>\n#include<cstdlib>\n#include<cstring>\n#include<iostream>\n#include<algorithm>\n#include<functional>\nusing namespace std;\n#define MAXN (100000+10)\n#define MAXM (600000+10)\n#define Li (17)\n#define INF (2000000000)\nint edge[MAXM],pre[MAXM],weight[MAXM],next[MAXM],size=0;\nint addedge(int u,int v,int w)\n{\n\tedge[++size]=v;\n\tweight[size]=w;\n\tnext[size]=pre[u];\n\tpre[u]=size;\n}\nint addedge2(int u,int v,int w)\n{\n\taddedge(u,v,w);\n\taddedge(v,u,w);\n}\nint f[MAXN][Li]={0},dp[MAXN][Li]={0},dp0[MAXN][Li]={0},deep[MAXN],n,m;\nstruct E\n{\n\tint u,v,w;\n\tfriend bool operator<(E a,E b){return a.w<b.w;\t}\n}e[MAXM];\nbool b[MAXM],vis[MAXN];\nint queue[MAXN],head,tail;\nvoid bfs()\n{\n\tmemset(vis,0,sizeof(vis));\n\thead=tail=1;queue[1]=1;vis[1]=1;deep[1]=0;\n\twhile (head<=tail)\n\t{\n\t\tint &u=queue[head];\n\t\tif (u!=1)\n\t\t{\n\t\t\tfor (int i=1;i<17;i++)\n\t\t\t{\n\t\t\t\tif (f[u][i-1])\n\t\t\t\t{\n\t\t\t\t\tf[u][i]=f[f[u][i-1]][i-1];\n\t\t\t\t}\n\t\t\t\tif (f[u][i]==0) break;\n\t\t\t\tif (f[u][i])\n\t\t\t\t{\n\t\t\t\t\tdp[u][i]=max(dp[u][i-1],dp[f[u][i-1]][i-1]);\n\t\t\t\t}\n\t\t\t\tif (i==1)\n\t\t\t\t{\n\t\t\t\t\tif (dp[u][0]!=dp[f[u][0]][0]) dp0[u][1]=min(dp[u][0],dp[f[u][0]][0]);\n\t\t\t\t\telse dp0[u][1]=-1;\n\t\t\t\t}\n\t\t\t\telse\n\t\t\t\t{\n\t\t\t\t\tdp0[u][i]=max(dp0[u][i-1],dp0[f[u][i-1]][i-1]);\n\t\t\t\t\tif (dp[u][i-1]!=dp[f[u][i-1]][i-1]) dp0[u][i]=max(dp0[u][i],min(dp[u][i-1],dp[f[u][i-1]][i-1]));\n\t\t\t\t}\n\t\t\t}\n\t\t}\n\t\tfor (int p=pre[u];p;p=next[p])\n\t\t{\n\t\t\tint &v=edge[p];\n\t\t\tif (!vis[v])\n\t\t\t{\n\t\t\t\tqueue[++tail]=v;\n\t\t\t\tvis[v]=1;deep[v]=deep[u]+1;\n\t\t\t\tf[v][0]=u;dp[v][0]=weight[p];dp0[v][0]=-1;\n\t\t\t}\n\t\t}\n\t\thead++;\n\t}\n}\nint bin[Li];\nvoid check(int &nowdp,int &nowdp0,int c)\n{\n\tif (c<=nowdp0) return;\n\telse if (nowdp0<c&&c<nowdp) nowdp0=c;\n\telse  if (c==nowdp) return;\n\telse if (nowdp<c) {nowdp0=nowdp;nowdp=c;}\n}\nint lca(int x,int y,int &nowdp,int &nowdp0)\n{\n\tnowdp=nowdp0=-1;\n\tif (deep[x]<deep[y]) swap(x,y);\n\tint t=deep[x]-deep[y];\n\tfor (int i=0;t;i++)\n\t\tif (t&bin[i])\n\t\t{\n\t\t\tcheck(nowdp,nowdp0,dp[x][i]);\n\t\t\tcheck(nowdp,nowdp0,dp0[x][i]);\n\t\t\tx=f[x][i];\n\t\t\tt-=bin[i];\n\t\t}\n\tint i=Li-1;\n\twhile (x^y)\n\t{\n\t\twhile (f[x][i]==f[y][i]&&i) i--;\n\t\tcheck(nowdp,nowdp0,dp[x][i]);\n\t\tcheck(nowdp,nowdp0,dp0[x][i]);\n\t\tcheck(nowdp,nowdp0,dp[y][i]);\n\t\tcheck(nowdp,nowdp0,dp0[y][i]);\n\t\tx=f[x][i];y=f[y][i];\n\t}\n}\nint father[MAXN];\nlong long sum_edge=0;\nint getfather(int x)\n{\n\tif (father[x]==x) return x;\n\tfather[x]=getfather(father[x]);\n\treturn father[x];\n}\nvoid union2(int x,int y)\n{\n\tfather[father[x]]=father[father[y]];\n}\nint main()\n{\n\tscanf("%d%d",&n,&m);\n\tfor (int i=1;i<=n;i++) father[i]=i;\n\tmemset(b,0,sizeof(b));\n\tmemset(next,0,sizeof(next));\n\tfor (int i=0;i<Li;i++) bin[i]=1<<i;\n\tfor (int i=1;i<=m;i++)\n\t{\n\t\tscanf("%d%d%d",&e[i].u,&e[i].v,&e[i].w);\n\t}\n\tsort(e+1,e+1+m);\n\tfor (int i=1;i<=m;i++)\n\t{\n\t\tif (getfather(e[i].u)!=getfather(e[i].v)) {union2(e[i].u,e[i].v);addedge2(e[i].u,e[i].v,e[i].w);sum_edge+=e[i].w;\t}\n\t\telse b[i]=1;\n\t}\n\tbfs();\n\n\tlong long mindec=-1;\n\tfor (int i=1;i<=m;i++)\n\t\tif (b[i])\n\t\t{\n\t\t\tint nowdp,nowdp0;\n\t\t\tlca(e[i].u,e[i].v,nowdp,nowdp0);\n\t\t\tif (nowdp==e[i].w) nowdp=nowdp0;\n\t\t\tif (nowdp==-1) continue;\n\t\t\tif (mindec==-1||mindec>e[i].w-nowdp) mindec=e[i].w-nowdp;\n\t\t}\n\tprintf("%lldn",sum_edge+mindec);\n\treturn 0;\n}\n<\/pre>\n<\/p>\n

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

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

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

\n<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"
1977: [BeiJing2010\u7ec4\u961f]\u6b21\u5c0f\u751f\u6210\u6811 Tree Time Limit: 10 Sec […]<\/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":[35,85],"class_list":["post-346","post","type-post","status-publish","format-standard","hentry","category-defaultcategory","tag-lca","tag-minimum_spanning_tree"],"yoast_head":"\nBZOJ 1977([BeiJing2010\u7ec4\u961f]\u6b21\u5c0f\u751f\u6210\u6811 Tree-LCA\u7684\u4f4d\u8fd0\u7b97) - 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=346\" \/>\n<meta property=\"og:locale\" content=\"zh_CN\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"BZOJ 1977([BeiJing2010\u7ec4\u961f]\u6b21\u5c0f\u751f\u6210\u6811 Tree-LCA\u7684\u4f4d\u8fd0\u7b97) - 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