BZOJ 3091 城市旅行

Description

Input

Output

Sample Input

4 5
1 3 2 5
1 2
1 3
2 4
4 2 4
1 2 4
2 3 4
3 1 4 1
4 1 4

Sample Output

16/3
6/1

HINT

对于所有数据满足 1<=N<=50,000 1<=M<=50,000 1<=Ai<=10^6 1<=D<=100 1<=U,V<=N

Source

维护方法我就不再赘述了，见我博客的 BZOJ 2572 高速公路。这一题和那一题的维护方法其实是一样的，但是数据结构不同，很明显这是lct嘛。

但是那么问题就来，树上的序号id不是一定的，不像线段树一样，怎么办呢？？？

这就是本题的难点——维护id。但是细细想想其实也不是很难。

你想，他是要维护一条链上深度的id，左子树id<右子树，其实我们就是在access操作中对某一条链的id整体加上一个值或者减去一个值，这样来操作(splay维护的都是一条链)。因此，维护id就不成问题。

但是你有没有考虑过这样一种情况：根翻转了，他所在splay的id也全部都要翻转，这怎么办？其实也不难，将其所在splay中所有id都取负，再加上splay的size+1即可。

代码实现有许多的细节要处理：比如初始化连边，他貌似卡了你的link，如果你直接连的话，正确的做法是dfs直接将father连上去(这就是我开始tle了八九发的原因)。

 #include<iostream>
 #include<cstdio>
 #include<cstdlib>
 using namespace std;

 typedef long long ll;
 #define maxn 50010
 int n,m,ch[maxn][],size[maxn],fa[maxn],stack[maxn];
 int side[maxn],next[maxn*],toit[maxn*],cnt;
 ll key[maxn],id[maxn],s1[maxn],s2[maxn],s3[maxn];
 ll lef[maxn],rig[maxn],sign1[maxn],sign2[maxn];
 bool rev[maxn];

 inline int getint()
 {
     int x=,f=;char ch=getchar();
     while(ch<''||ch>''){if(ch=='-')f=-;ch=getchar();}
     while(ch>=''&&ch<=''){x=x*+ch-'';ch=getchar();}
     return x*f;
 }

 inline ll getlong()
 {
     ll x=,f=;char ch=getchar();
     while(ch<''||ch>''){if(ch=='-')f=-;ch=getchar();}
     while(ch>=''&&ch<=''){x=x*+ch-'';ch=getchar();}
     return x*f;
 }

 inline ll gcd(ll a,ll b) { return b?gcd(b,a%b):a; }

 inline void pushdown(int x)
 {
     int lc = ch[x][],rc = ch[x][];
     if (rev[x])
     {
         id[x] = -id[x]; s2[x] = -s2[x];
         swap(lef[x],rig[x]);
         lef[x] = -lef[x]; rig[x] = -rig[x];
         swap(ch[x][],ch[x][]);
         if (lc) rev[lc] ^= ,sign2[lc] = -sign2[lc];
         if (rc) rev[rc] ^= ,sign2[rc] = -sign2[rc];
         rev[x] = false;
     }
     if (sign2[x])
     {
         lef[x] += sign2[x]; rig[x] += sign2[x]; id[x] += sign2[x];
         s3[x] += (sign2[x]*s2[x]<<)+sign2[x]*sign2[x]*s1[x];
         s2[x] += sign2[x]*s1[x];
         if (lc) sign2[lc] += sign2[x];
         if (rc) sign2[rc] += sign2[x];
         sign2[x] = ;
     }
     if (sign1[x])
     {
         s1[x] += sign1[x]*(ll)size[x];
         s2[x] += (ll)size[x]*(lef[x]+rig[x])/*sign1[x];
         s3[x] += (rig[x]*(rig[x]+)*((rig[x]<<)+)/-(lef[x]-)*lef[x]*((lef[x]<<)-)/)*sign1[x];
         key[x] += sign1[x];
         if (lc) sign1[lc] += sign1[x];
         if (rc) sign1[rc] += sign1[x];
         sign1[x] = ;
     }
 }

 inline void updata(int x)
 {
     int lc = ch[x][],rc = ch[x][];
     if (lc) pushdown(lc); if (rc) pushdown(rc);
     size[x] = size[lc]+size[rc]+;
     s1[x] = s1[lc]+s1[rc]+key[x];
     s2[x] = id[x]*key[x]+s2[lc]+s2[rc];
     s3[x] = id[x]*id[x]*key[x]+s3[lc]+s3[rc];
     lef[x] = rig[x] = id[x];
     if (lc) lef[x] = lef[lc];
     if (rc) rig[x] = rig[rc];
 }

 inline bool isroot(int a) { return ch[fa[a]][] != a&&ch[fa[a]][] != a; }

 inline void rotate(int x)
 {
     int y = fa[x],z = fa[y],l = ch[y][]==x,r = l^;
     if (!isroot(y)) ch[z][ch[z][]==y] = x; fa[x] = z;
     if (ch[x][r]) fa[ch[x][r]] = y; ch[y][l] = ch[x][r];
     ch[x][r] = y; fa[y] = x;
     updata(y); updata(x);
 }

 inline void splay(int x)
 {
     int top = ,i;
     for (i = x;!isroot(i);i = fa[i]) stack[++top] = i;
     stack[++top] = i;
     while (top) pushdown(stack[top--]);
     while (!isroot(x))
     {
         int y = fa[x],z = fa[y];
         if (!isroot(y))
         {
             if ((ch[y][]==x)^(ch[z][]==y)) rotate(x);
             else rotate(y);
         }
         rotate(x);
     }
 }

 inline int access(int x)
 {
     int t;
     for (t = ;x;t = x,x = fa[x])
     {
         splay(x);
         if (ch[x][]) sign2[ch[x][]] -= size[ch[x][]]+;
         ch[x][] = t;
         if (t) sign2[t] += size[ch[x][]]+;
         updata(x);
     }
     return t;
 }

 inline void evert(int x)
 {
     x = access(x);  rev[x] ^= ;
     sign2[x] += rev[x]*(size[x]+);
 }

 inline int find(int x)
 {
     x = access(x);
     while (pushdown(x),ch[x][]) x = ch[x][];
     return x;
 }

 inline void cut(int x,int y)
 {
     evert(x); access(y); splay(y);
     if (ch[y][] != x||ch[x][] != ) return;
     ch[y][] = fa[x] = ;
     updata(x);
     sign2[y] -= size[x];
 }

 inline void link(int x,int y)
 {
     if (find(x) == find(y)) return;
     evert(x); fa[x] = y;
 }

 inline void change(int x,int y,ll v)
 {
     if (find(x) != find(y)) return;
     evert(x); x = access(y);
     sign1[x] += v;
     pushdown(x);
 }

 inline void ask(int x,int y)
 {
     if (find(x) != find(y)) { printf("-1\n"); return; }
     evert(x); access(y); splay(x);
     ll up = -s3[x]+(ll)(size[x]+)*s2[x],down = (ll)size[x]*(ll)(size[x]+)>>,d = gcd(up,down);
     up /= d; down /= d;
     printf("%lld/%lld\n",up,down);
 }

 inline void add(int a,int b) { next[++cnt] = side[a]; side[a] = cnt; toit[cnt] = b;  }

 inline void ins(int a,int b) { add(a,b); add(b,a); }

 inline void dfs(int now,int f)
 {
     if (f) fa[now] = f;
     for (int i = side[now];i;i = next[i])
         if (toit[i] != f) dfs(toit[i],now);
 }

 int main()
 {
     freopen("3091.in","r",stdin);
     freopen("3091.out","w",stdout);
     scanf("%d %d",&n,&m);
     for (int i = ;i <= n;++i)
     {
         key[i] = getlong();
         s1[i] = s2[i] = s3[i] = key[i];
         size[i] = lef[i] = rig[i] = id[i] = ;
     }
     for (int i = ;i < n;++i)
     {
         int a = getint(),b = getint();
         ins(a,b);
     }
     dfs(,);
     while (m--)
     {
         int opt = getint();
         if (opt == )
         {
             int u = getint(),v = getint(); ll d = getlong();
             change(u,v,d);
         }
         else
         {
             int u = getint(),v = getint();
             if (opt == ) cut(u,v);
             else if (opt == ) link(u,v);
             else ask(u,v);
         }
     }
     fclose(stdin); fclose(stdout);
     return ;
 }