[BZOJ3697] 采药人的路径

来源：互联网发布：幼儿学拼音软件编辑：程序博客网时间：2024/05/17 00:54

传送门

http://www.lydsy.com/JudgeOnline/problem.php?id=3697

题目大意

给定一棵树，找一些路径满足，路径上0,1数量相等，并在路径上找到一个点(休息站)，改点到路径两端上0,1数量也相等，同一条路径点不同，记为不同，询问有多少条路径满足条件

题解

点分治
对于一个点u我们遍历每棵子树中的节点v，求出dis(u,v)，我们记录这条路径上有无节点t使得dis(v,t)=0存在数组里
休息站一定在起点到根的路径上或根到终点的路径上
合并两条路径时选取只有一条有休息站的或者两条都有的

const    maxn=200005;var    w:array[0..3*maxn,1..3]of longint;    size,maxx,vis,dis:array[0..maxn]of longint;    x:array[-maxn..maxn]of longint;    f,g:array[-maxn..maxn,0..1]of int64;    i,j,k:longint;    n,m,len,a,b,c,root,cnt,mx,mxdep:longint;    ans:int64;function max(a,b:longint):longint;begin if a>b then exit(a) else exit(b); end;procedure init(a,b,c:longint);begin    w[len,1]:=b; w[len,2]:=c; w[len,3]:=0;    if (w[a,3]=0) then w[a,3]:=len else w[w[a,1],3]:=len;    w[a,1]:=len; inc(len); end;procedure getroot(a,fa:longint);var tt:longint;begin    tt:=w[a,3]; size[a]:=1; maxx[a]:=0;    while (tt<>0) do    begin        if (w[tt,1]<>fa)and(vis[w[tt,1]]=0) then         begin            getroot(w[tt,1],a);            inc(size[a],size[w[tt,1]]);            maxx[a]:=max(maxx[a],size[w[tt,1]]);        end;        tt:=w[tt,3];    end;    maxx[a]:=max(maxx[a],cnt-size[a]);    if (root=0)or(maxx[a]<maxx[root]) then root:=a;end;procedure getdep(a,fa,b:longint);var tt:longint;begin    tt:=w[a,3]; mxdep:=max(mxdep,b);    if (x[dis[a]]=0) then g[dis[a],0]:=g[dis[a],0]+1 else g[dis[a],1]:=g[dis[a],1]+1;     inc(x[dis[a]]);    while (tt<>0) do    begin        if (w[tt,1]<>fa)and(vis[w[tt,1]]=0) then        begin            dis[w[tt,1]]:=dis[a]+w[tt,2];            getdep(w[tt,1],a,b+1);        end;        tt:=w[tt,3];    end;    dec(x[dis[a]]);end;procedure treedc(a:longint);var tt,i:longint;begin    tt:=w[a,3]; vis[a]:=1; mx:=0; f[0,0]:=1;    while (tt<>0) do    begin        if (vis[w[tt,1]]=0) then         begin            mxdep:=0;            dis[w[tt,1]]:=w[tt,2];             mxdep:=1; getdep(w[tt,1],0,1); mx:=max(mx,mxdep);            ans:=ans+g[0,0]*(f[0,0]-1);            for i:=-mxdep to mxdep do                ans:=ans+g[i,0]*f[-i,1]+g[i,1]*f[-i,0]+g[i,1]*f[-i,1];            for i:=-mxdep to mxdep do            begin                f[i,0]:=f[i,0]+g[i,0]; f[i,1]:=f[i,1]+g[i,1];                g[i,0]:=0; g[i,1]:=0;            end;        end;        tt:=w[tt,3];    end;    for i:=-mx to mx do    begin f[i,0]:=0; f[i,1]:=0; end;    tt:=w[a,3];    while (tt<>0) do    begin        if (vis[w[tt,1]]=0) then         begin            root:=0; cnt:=size[w[tt,1]]; getroot(w[tt,1],0);            treedc(root);        end;        tt:=w[tt,3];    end;end;begin    readln(n); len:=n+1;    for i:=1 to n-1 do    begin readln(a,b,c); if (c=0) then c:=-1; init(a,b,c); init(b,a,c); end;    root:=0; cnt:=n; getroot(1,0);     ans:=0; treedc(root);    writeln(ans);end.

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