bzoj3669

不难想到从小到大穷举a，判断在携带不超过a个B型精灵的情况下最少携带多少个B型精灵
这是一个经典的问题，显然要求出最小生成树，树上1到N路径上最大的边即是答案
所以我们要动态维护一个最小生成树可以用link cut tree维护
根据最小生成树的回路性质，我们加入一条边(u,v)，保留树上u-v路径上最大边和新边中小的那个
由于这里维护的是边权，我们可以把每条边当做一个点p(u,v)，连接(u,v)时，即是连接(u,p)和（v,p)
然后记录下路径上最大点权的编号即可

 var son:array[..,..] of longint;
     q,f,w,fa,v:array[..] of longint;
     rev:array[..] of boolean;
     s,e,a,b:array[..] of longint;
     ans,i,n,m:longint;

 function min(a,b:longint):longint;
   begin
     if a>b then exit(b) else exit(a);
   end;

 function getf(x:longint):longint;
   begin
     if f[x]<>x then f[x]:=getf(f[x]);
     exit(f[x]);
   end;

 procedure swap(var a,b:longint);
   var c:longint;
   begin
     c:=a;
     a:=b;
     b:=c;
   end;

 function root(x:longint):boolean;
   begin
     exit((son[fa[x],]<>x) and (son[fa[x],]<>x));
   end;

 procedure update(x:longint);
   begin
     w[x]:=x;
     if v[w[son[x,]]]>v[w[x]] then w[x]:=w[son[x,]];
     if v[w[son[x,]]]>v[w[x]] then w[x]:=w[son[x,]];
   end;

 procedure push(x:longint);
   begin
     if rev[x] then
     begin
       rev[son[x,]]:=not rev[son[x,]];
       rev[son[x,]]:=not rev[son[x,]];
       swap(son[x,],son[x,]);
       rev[x]:=false;
     end;
   end;

 procedure rotate(x,w:longint);
   var y:longint;
   begin
     y:=fa[x];
     if not root(y) then
     begin
       if son[fa[y],]=y then son[fa[y],]:=x
       else son[fa[y],]:=x;
     end;
     fa[x]:=fa[y];
     son[y,-w]:=son[x,w];
     if son[x,w]<> then fa[son[x,w]]:=y;
     son[x,w]:=y;
     fa[y]:=x;
     update(y);
   end;

 procedure splay(x:longint);
   var y,t,i:longint;
   begin
     t:=;
     i:=x;
     while not root(i) do
     begin
       inc(t);
       q[t]:=i;
       i:=fa[i];
     end;
     inc(t);
     q[t]:=i;
     for i:=t downto  do
       push(q[i]);
     while not root(x) do
     begin
       y:=fa[x];
       if root(y) then
       begin
         if son[y,]=x then rotate(x,)
         else rotate(x,);
       end
       else begin
         if son[fa[y],]=y then
         begin
           if son[y,]=x then rotate(y,)
           else rotate(x,);
           rotate(x,);
         end
         else begin
           if son[y,]=x then rotate(x,)
           else rotate(y,);
           rotate(x,);
         end;
       end;
     end;
     update(x);
   end;

 procedure access(x:longint);
   var y:longint;
   begin
     y:=;
     repeat
       splay(x);
       son[x,]:=y;
       update(x);
       y:=x;
       x:=fa[x];
     until x=;
   end;

 procedure sort(l,r: longint);
   var i,j,x,y: longint;
   begin
     i:=l;
     j:=r;
     x:=a[(l+r) div ];
     repeat
       while a[i]<x do inc(i);
       while x<a[j] do dec(j);
       if not(i>j) then
       begin
         swap(s[i],s[j]);
         swap(e[i],e[j]);
         swap(a[i],a[j]);
         swap(b[i],b[j]);
         inc(i);
         j:=j-;
       end;
     until i>j;
     if l<j then sort(l,j);
     if i<r then sort(i,r);
   end;

 procedure makeroot(x:longint);
   begin
     access(x);
     splay(x);
     rev[x]:=not rev[x];
   end;

 procedure path(x,y:longint);
   begin
     makeroot(x);
     access(y);
     splay(y);
   end;

 procedure link(x,y:longint);
   begin
     makeroot(x);
     fa[x]:=y;
   end;

 procedure cut(x,y:longint);
   begin
     makeroot(x);
     access(y);
     splay(y);
     son[y,]:=;
     fa[x]:=;
   end;

 procedure deal(i:longint);
   var x,y,z:longint;
   begin
     x:=getf(s[i]);
     y:=getf(e[i]);
     if x<>y then
     begin
       f[x]:=y;
       link(s[i],n+i);
       link(e[i],n+i);
     end
     else begin
       x:=s[i];
       y:=e[i];
       path(x,y);
       z:=w[y];
       if v[z]>b[i] then
       begin
         cut(s[z-n],z);
         cut(e[z-n],z);
         link(s[i],n+i);
         link(e[i],n+i);
       end;
     end;
   end;

 begin
   readln(n,m);
   for i:= to m do
     readln(s[i],e[i],a[i],b[i]);
   for i:= to n do
     f[i]:=i;
   sort(,m);
   for i:= to m do
   begin
     v[n+i]:=b[i];
     w[n+i]:=n+i;
   end;
   ans:=;
   i:=;
   while i<m do
   begin
     inc(i);
     deal(i);
     while a[i]=a[i+] do
     begin
       inc(i);
       deal(i);
     end;
     if getf()=getf(n) then
     begin
       path(,n);
       ans:=min(ans,a[i]+v[w[n]]);
     end;
   end;
   if ans= then writeln(-)
   else writeln(ans);
 end.