3551: [ONTAK2010]Peaks加强版

3551: [ONTAK2010]Peaks加强版

https://www.lydsy.com/JudgeOnline/problem.php?id=3551

分析：

　　kruskal重构树 +  倍增 + 主席树。

　　首先建立kruskal重构树，那么查询就变成了，在kruskal重构树上找倍增找到最上面的权值小于x的点（节点的权值为原图的边权），那么这棵树内的所有点都可以在经过权值小于x的点相互到达，所以在这棵树内查询第k大即可。dfs序后，变成序列上的问题，查询区间的第k大。

代码：

 #include<cstdio>
 #include<algorithm>
 #include<cstring>
 #include<cmath>
 #include<iostream>
 #include<cctype>
 #include<set>
 #include<vector>
 #include<queue>
 #include<map>
 #define fi(s) freopen(s,"r",stdin);
 #define fo(s) freopen(s,"w",stdout);
 using namespace std;
 typedef long long LL;

 inline int read() {
     int x=,f=;char ch=getchar();for(;!isdigit(ch);ch=getchar())if(ch=='-')f=-;
     for(;isdigit(ch);ch=getchar())x=x*+ch-'';return x*f;
 }

 const int N = ;

 struct Edge{
     int u, v, w;
     bool operator < (const Edge &A) const {
         return w < A.w;
     }
 }e[];
 int fa[N << ], f[N << ][], mx[N << ], st[N << ], pos[N << ], en[N << ], val[N], disc[N]; // mx[N<<1]
 int sum[N * ], ls[N * ], rs[N * ], Root[N << ]; // 乘18，不要17
 int n, m, Q, tot, Time_Index, tot_node;
 vector<int> T[N << ];

 #define lson l, mid, rt << 1
 #define rson mid + 1, r, rt << 1 | 1

 int find(int x) {
     return x == fa[x] ? x : fa[x] = find(fa[x]);
 }
 void Kruskal() {
     for (int i=; i<=n+n; ++i) fa[i] = i;
     sort(e + , e + m + );
     int cntedge = ; tot = n;
     for (int i=; i<=m; ++i) {
         int u = find(e[i].u), v = find(e[i].v);
         if (u == v) continue;
         ++tot;
         fa[u] = tot, fa[v] = tot;
         f[u][] = tot, f[v][] = tot;
         mx[tot] = e[i].w;
         T[tot].push_back(u), T[tot].push_back(v);
 //        if (++cntedge == n + n - 1) break; // n + n - 1
     }
 }
 void dfs(int u,int fa) {
     st[u] = ++Time_Index;
     pos[Time_Index] = u;
     for (int sz=T[u].size(),i=; i<sz; ++i) {
         int v = T[u][i];
         if (v == fa) continue;
         dfs(v, u);
     }
     en[u] = Time_Index;
 }
 void update(int l,int r,int &rt,int last,int p) {
     rt = ++tot_node;
     sum[rt] = sum[last] + ;
     ls[rt] = ls[last], rs[rt] = rs[last];
     if (l == r) return ;
     int mid = (l + r) >> ;
     if (p <= mid) update(l, mid, ls[rt], ls[last], p);
     else update(mid + , r, rs[rt], rs[last], p);
 }
 int query(int l,int r,int Head,int Tail,int k) {
     if (sum[Tail] - sum[Head] < k) return -;
     if (l == r) return l;
     int mid = (l + r) >> , cnt = sum[ls[Tail]] - sum[ls[Head]];
     if (cnt >= k) return query(l, mid, ls[Head], ls[Tail], k);
     else return query(mid + , r, rs[Head], rs[Tail], k - cnt);
 }
 int main() {
     n = read(), m = read(), Q = read();
     for (int i=; i<=n; ++i) val[i] = read(), disc[i] = val[i];
     for (int i=; i<=m; ++i)
         e[i].u = read(), e[i].v = read(), e[i].w = read();

     sort(disc + , disc + n + );
     int cnt = ;
     for (int i=; i<=n; ++i) if (disc[i] != disc[cnt]) disc[++cnt] = disc[i]; // i=2
     for (int i=; i<=n; ++i) val[i] = lower_bound(disc + , disc + cnt + , val[i]) - disc;

     Kruskal();
     dfs(tot, );

     for (int j=; j<=; ++j)
         for (int i=; i<=tot; ++i) f[i][j] = f[f[i][j-]][j-];

     for (int i=; i<=tot; ++i) {
         if (pos[i] > n) Root[i] = Root[i - ];
         else update(, cnt, Root[i], Root[i - ], val[pos[i]]); // val[pos[i]] !!!
     }

     int lastans = ;
     while (Q--) {
         int v = read(), x = read(), k = read();
         if (lastans != -) v ^= lastans, x ^= lastans, k ^= lastans;
         for (int i=; i>=; --i)
             if (f[v][i] && mx[f[v][i]] <= x) v = f[v][i];
         int l = st[v], r = en[v];
         k = sum[Root[r]] - sum[Root[l]] - k + ;
         if (k <= ) { puts("-1"); lastans = -; continue; }
         int p = query(, cnt, Root[l], Root[r], k);
         if (p == -) { puts("-1"); lastans = -; continue; }
         printf("%d\n",lastans = disc[p]);
     }
     return ;
 }