[SPOJ10628]Count on a tree(主席树)
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题目描述
给你一棵有n个结点的树,节点编号为1~n。
每个节点都有一个权值。
要求执行以下操作:
U V K:求从节点u到节点v的第k小权值。
Solution
树上主席树裸题。
思路和序列差不多,树上前缀和即可。
可持久化时的前一个版本就是它的父亲。
设查询(u,v),值就是u+v-lca-fa[lca]
#include <iostream> #include <cstdio> #include <algorithm> using namespace std; const int N = 100010; struct chairman_tree{ int val; int ls, rs; }tr[N * 20]; int rt[N], tot; struct node{ int pre, to; }edge[N << 1]; int head[N], tt; int n, m, a[N], b[N], nn; int sz[N], bl[N], dep[N], f[N], son[N], tn[N]; int lastans; void ins(int &cur, int pre, int l, int r, int pos) { cur = ++tot; tr[cur] = tr[pre]; tr[cur].val++; if (l == r) return; int mid = (l + r) >> 1; if (pos <= mid) ins(tr[cur].ls, tr[pre].ls, l, mid, pos); else ins(tr[cur].rs, tr[pre].rs, mid + 1, r, pos); } int ask(int o, int p, int q, int s, int l, int r, int k) { if (l == r) return l; int mid = (l + r) >> 1; int num = tr[tr[o].ls].val + tr[tr[p].ls].val - tr[tr[q].ls].val - tr[tr[s].ls].val; if (k <= num) return ask(tr[o].ls, tr[p].ls, tr[q].ls, tr[s].ls, l, mid, k); else return ask(tr[o].rs, tr[p].rs, tr[q].rs, tr[s].rs, mid + 1, r, k - num); } void dfs(int x, int fa) { sz[x] = 1; son[x] = 0; ins(rt[x], rt[fa], 1, nn, a[x]); for (int i = head[x]; i; i = edge[i].pre) { int y = edge[i].to; if (y == fa) continue; dep[y] = dep[x] + 1; f[y] = x; dfs(y, x); sz[x] += sz[y]; if (sz[y] > sz[son[x]]) { son[x] = y; } } } void dfs2(int x, int chain) { bl[x] = chain; if (son[x]) dfs2(son[x], chain); for (int i = head[x]; i; i = edge[i].pre) { int y = edge[i].to; if (y != f[x] && y != son[x]) { dfs2(y, y); } } } int LCA(int u, int v) { while (bl[u] != bl[v]) { if (dep[bl[u]] < dep[bl[v]]) swap(u, v); u = f[bl[u]]; } return dep[u] < dep[v] ? u : v; } void add(int u, int v) { edge[++tt] = node{head[u], v}; head[u] = tt; } int main() { scanf("%d%d", &n, &m); for (int i = 1; i <= n; i++) { scanf("%d", &a[i]); b[++nn] = a[i]; } sort(b + 1, b + nn + 1); nn = unique(b + 1, b + nn + 1) - b - 1; for (int i = 1; i <= n; i++) { int p = lower_bound(b + 1, b + nn + 1, a[i]) - b; tn[p] = a[i]; a[i] = p; } for (int i = 1, u, v; i < n; i++) { scanf("%d%d", &u, &v); add(u, v); add(v, u); } dfs(1, 0); dfs2(1, 1); while (m--) { int u, v, k; scanf("%d%d%d", &u, &v, &k); u ^= lastans; int lca = LCA(u, v); lastans = tn[ask(rt[u], rt[v], rt[lca], rt[f[lca]], 1, nn, k)]; printf("%d ", lastans); } return 0; }
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