森林 BZOJ 3123

题解：

第k大直接用主席树解决

合并利用启发式合并，将较小的连接到较大的树上

 #include<cmath>
 #include<cstdio>
 #include<cstdlib>
 #include<cstring>
 #include<iostream>
 #include<algorithm>
 using namespace std;
 const int inf = 2e9;
 const int logn = ;
 const int maxn = 8e4 + ;
 const int maxm = 2e5;
 int t, n, m, q;
 int sum[maxn * ], lc[maxn * ], rc[maxn * ];
 int rt[maxn];
 int tot, nex[maxm], fir[maxm], ver[maxm];
 int num, cnt;
 int ans;
 int disp[maxn];
 int si[maxn], dep[maxn], anc[maxn][logn + ];
 int fat[maxn];
 int val[maxn];
 bool vis[maxn];
 inline int Get()
 {
     int x;
     char c;
     bool o = false;
     while((c = getchar()) < '' || c > '')
         if(c == '-') o = true;
     x = c - '';
     while((c = getchar()) >= '' && c <= '')
         x = x *  + c - '';
     return (o) ? -x : x;
 }
 inline void Reset()
 {
     for(int i = ; i <= n; ++i)
         disp[i] = val[i], fat[i] = i, si[i] = ;
 }
 inline void Disperse()
 {
     sort(disp + , disp +  + n);
     disp[] = -inf;
     for(int i = ; i <= n; ++i)
         if(disp[i] != disp[i - ])
             disp[++num] = disp[i];
     for(int i = ; i <= n; ++i)
         val[i] = lower_bound(disp + , disp +  + num, val[i]) - disp;
 }
 inline void Ins(int x, int y)
 {
     nex[++tot] = fir[x], fir[x] = tot, ver[tot] = y;
 }
 inline int Find(int x)
 {
     return (fat[x] != x) ? fat[x] = Find(fat[x]) : x;
 }
 inline void Edge(int x, int y)
 {
     int a = Find(x), b = Find(y);
     if(a != b) fat[a] = b, si[b] += si[a];
     Ins(x, y), Ins(y, x);
 }
 int Add(int p, int l, int r, int v)
 {
     int k = ++cnt;
     sum[k] = sum[p] + ;
     if(l == r) return k;
     int mi = l + r >> ;
     if(v <= mi) lc[k] = Add(lc[p], l, mi, v), rc[k] = rc[p];
     else lc[k] = lc[p], rc[k] = Add(rc[p], mi + , r, v);
     return k;
 }
 void Build(int u, int f)
 {
     vis[u] = true;
     dep[u] = dep[f] + ;
     anc[u][] = f;
     for(int i = ; i <= logn; ++i)
         anc[u][i] = anc[anc[u][i - ]][i - ];
     rt[u] = Add(rt[f], , num, val[u]);
     for(int i = fir[u]; i; i = nex[i])
     {
         int v = ver[i];
         if(v == f) continue;
         Build(v, u);
     }
 }
 inline void Edge()
 {
     for(int i = ; i <= m; ++i) Edge(Get(), Get());
 }
 inline void Build()
 {
     for(int i = ; i <= n; ++i)
         if(!vis[i])
             Build(i, );
 }
 inline void Link(int x, int y)
 {
     int a = Find(x), b = Find(y);
     if(si[a] < si[b]) swap(x, y);
     dep[y] = dep[x] + ;
     Build(y, x);
     Ins(x, y), Ins(y, x);
 }
 inline int Lca(int x, int y)
 {
     if(dep[x] < dep[y]) swap(x, y);
     for(int i = logn; i >= ; --i)
         if(dep[anc[x][i]] >= dep[y])
             x = anc[x][i];
     if(x == y) return x;
     for(int i = logn; i >= ; --i)
         if(anc[x][i] != anc[y][i])
         {
             x = anc[x][i];
             y = anc[y][i];
         }
     return anc[x][];
 }
 inline int Query(int a, int b, int c, int d, int l, int r, int k)
 {
     if(l == r) return disp[l];
     int res = sum[lc[a]] + sum[lc[b]] - sum[lc[c]] - sum[lc[d]];
     int mi = l + r >> ;
     if(res >= k) return Query(lc[a], lc[b], lc[c], lc[d], l, mi, k);
     return Query(rc[a], rc[b], rc[c], rc[d], mi + , r, k - res);
 }
 inline void Ask()
 {
     while(q--)
     {
         char c;
         while((c = getchar()) != 'L' && c != 'Q');
         switch(c)
         {
             case 'L':
             {
                 int x = Get() ^ ans, y = Get() ^ ans;
                 Link(x, y);
                 break;
             }
             case 'Q':
             {
                 int x = Get() ^ ans, y = Get() ^ ans, k = Get() ^ ans;
                 int lca = Lca(x, y);
                 ans = Query(rt[x], rt[y], rt[lca], rt[anc[lca][]], , num, k);
                 printf("%d\n", ans);
                 break;
             }
         }
     }
 }
 int main()
 {
     t = Get(), n = Get(), m = Get(), q = Get();
     for(int i = ; i <= n; ++i) val[i] = Get();
     Reset();
     Disperse();
     Edge();
     Build();
     Ask();
 }