CF487E Tourists--圆方树

既然有这条性质，这题就很简单了：

\(可能在a->b的简单路径上的点集，就是圆方树上a->b路径上方点代表的点双的并集\)

对每一个方点维护一个\(multiset\)，代表其在圆方树上子结点的最小值，这样更改就只需要改父结点辣。剩下的用树剖乱搞就行了

#include <bits/stdc++.h>

using namespace std;

#define N 200000
#define INF 0x3f3f3f3f
#define lson (o<<1)
#define rson (o<<1|1)
#define mid ((l+r)>>1)

int n, m, q, tot;
int w[N+5], dfn_clk, dfn[N+5], low[N+5], id[N+5];
int stk[N+5], tp;
int sz[N+5], fa[N+5], hson[N+5], rt[N+5], top[N+5], d[N+5];
vector<int> G[N+5], T[N+5];
int minv[4*N+5];
multiset<int> s[N+5];

void tarjan(int u) {
    low[u] = dfn[u] = ++dfn_clk;
    stk[++tp] = u;
    for(int i = 0; i < G[u].size(); ++i) {
        int v = G[u][i];
        if(!dfn[v]) {
            tarjan(v);
            low[u] = min(low[u], low[v]);
            if(low[v] == dfn[u]) {
                ++tot;
                for(int x = 0; x != v; --tp) {
                    x = stk[tp];
                    T[tot].push_back(x);
                    T[x].push_back(tot);
                }
                T[tot].push_back(u);
                T[u].push_back(tot);
            }

        }
        else low[u] = min(low[u], dfn[v]);
    }
}

int minval(int u) {
    if(s[u].size()) return *s[u].begin();
    else return INF;
}

void dfs1(int u, int pa) {
    fa[u] = pa;
    sz[u] = 1;
    d[u] = d[pa]+1;
    for(int i = 0; i < T[u].size(); ++i) {
        int v = T[u][i];
        if(v == pa) continue;
        if(u > n) s[u].insert(w[v]);
        dfs1(v, u);
        if(sz[v] > sz[hson[u]]) hson[u] = v;
        sz[u] += sz[v];
    }
}

void dfs2(int u, int tp) {
    dfn[u] = ++dfn_clk, id[dfn_clk] = u;
    top[u] = tp;
    if(hson[u]) dfs2(hson[u], tp);
    for(int i = 0; i < T[u].size(); ++i) {
        int v = T[u][i];
        if(v == fa[u] || v == hson[u]) continue;
        dfs2(v, v);
    }
    rt[u] = dfn_clk;
}

int lca(int x, int y) {
    while(top[x] != top[y]) d[top[x]] > d[top[y]] ? x = fa[top[x]] : y = fa[top[y]];
    return d[x] < d[y] ? x : y;
}

void pushup(int o) {
    minv[o] = min(minv[lson], minv[rson]);
}

void build(int o, int l, int r) {
    if(l == r) {
        minv[o] = id[l] > n ? minval(id[l]) : INF;
        return ;
    }
    build(lson, l, mid), build(rson, mid+1, r);
    pushup(o);
}

void modify(int o, int l, int r, int x, int k) {
    if(l == r) {
        minv[o] = k;
        return ;
    }
    if(x <= mid) modify(lson, l, mid, x, k);
    else modify(rson, mid+1, r, x, k);
    pushup(o);
}

int queryMin(int o, int l, int r, int L, int R) {
    if(L <= l && r <= R) return minv[o];
    int ret = INF;
    if(L <= mid) ret = min(ret, queryMin(lson, l, mid, L, R));
    if(R > mid) ret = min(ret, queryMin(rson, mid+1, r, L, R));
    return ret;
}

int query(int x, int y) {
    int z = lca(x, y), ret = INF;
    while(top[x] != top[z]) ret = min(ret, queryMin(1, 1, tot, dfn[top[x]], dfn[x])), x = fa[top[x]];
    ret = min(ret, queryMin(1, 1, tot, dfn[z], dfn[x]));
    while(top[y] != top[z]) ret = min(ret, queryMin(1, 1, tot, dfn[top[y]], dfn[y])), y = fa[top[y]];
    ret = min(ret, queryMin(1, 1, tot, dfn[z], dfn[y]));
    if(z > n) ret = min(ret, w[fa[z]]);
    else ret = min(ret, w[z]);
    return ret;
}

int main() {
    scanf("%d%d%d", &n, &m, &q);
    tot = n;
    for(int i = 1; i <= n; ++i) scanf("%d", &w[i]);
    for(int i = 1, x, y; i <= m; ++i) {
        scanf("%d%d", &x, &y);
        G[x].push_back(y), G[y].push_back(x);
    }
    tarjan(1);
    dfn_clk = 0;
    dfs1(1, 0), dfs2(1, 1);
    build(1, 1, tot);
    char type[2];
    for(int i = 1, x, y; i <= q; ++i) {
        scanf("%s%d%d", type, &x, &y);
        if(type[0] == 'C') {
            if(x != 1) {
                int t = minval(fa[x]);
                s[fa[x]].erase(s[fa[x]].lower_bound(w[x]));
                s[fa[x]].insert(y);
                if(minval(fa[x]) != t) modify(1, 1, tot, dfn[fa[x]], minval(fa[x]));
            }
            w[x] = y;
        }
        else {
            printf("%d\n", query(x, y));
        }
    }
    return 0;
}