算法笔记--圆方树

模板：

struct Circle_Square_Tree {
    const static int N = 2e4 + 10;
    vector<pair<int, LL> > G[N];
    int dp[N], anc[N][18], n;
    LL dis[N], cir[N]; //环的大小
    bool vis[N];//记录到方点的最短距离是否经过回边

    vector<pii> g[N];
    int dfn[N], low[N], fa[N], cnt, tot;
    int a[N];
    inline void solve(int u, int v, int d) {
        int cnt = 0;
        LL sum = d;
        for (int i = v; i != u; i = fa[i]) sum += dis[i] - dis[fa[i]], a[++cnt] = i;
        a[++cnt] = u;
        LL DIS = 0;
        ++tot;
        for (int i = cnt; i >= 1; --i) {
            LL D = min(DIS, sum-DIS);
            if(D == DIS) vis[a[i]] = true;
            else vis[a[i]] = false;
            G[a[i]].pb({tot, D});
            G[tot].pb({a[i], D});
            DIS += dis[a[i-1]]-dis[a[i]];
        }
        cir[tot] = sum;
    }
    inline void tarjan(int u, int o) {
        fa[u] = o;
        dfn[u] = low[u] = ++cnt;
        for (int i = 0; i < g[u].size(); ++i) {
            int v = g[u][i].fi;
            int w = g[u][i].se;
            if(v == o) continue;
            if(!dfn[v]) {
                dis[v] = dis[u] + w;
                tarjan(v, u);
                low[u] = min(low[u], low[v]);
            }
            else low[u] = min(low[u], dfn[v]);
            if(low[v] > dfn[u]) {
                G[u].pb({v, w});
                G[v].pb({u, w});
            }
        }
        for (int i = 0; i < g[u].size(); ++i) {
            int v = g[u][i].fi;
            int w = g[u][i].se;
            if(v == o) continue;
            if(fa[v] != u && dfn[v] > dfn[u]) {
                solve(u, v, w);
            }
        }
    }
    inline void dfs(int u, int o) {
        anc[u][0] = o;
        dp[u] = dp[o] + 1;
        for (int i = 1; i < 18; ++i) anc[u][i] = anc[anc[u][i-1]][i-1];
        for (int i = 0; i < G[u].size(); ++i) {
            int v = G[u][i].fi;
            LL w = G[u][i].se;
            if(v == o) continue;
            dis[v] = dis[u] + w;
            dfs(v, u);
        }
    }
    inline void init(int _n) {
        tot = n = _n;
        cnt = 0;
        dis[0] = dp[1] = 0;
        tarjan(1, 0);
        dfs(1, 1);
    }
    inline int lca(int u, int v) {
        if(dp[u] < dp[v]) swap(u, v);
        for (int i = 17; i >= 0; --i) if(dp[anc[u][i]] >= dp[v]) u = anc[u][i];
        if(u == v) return u;
        for (int i = 17; i >= 0; --i) if(anc[u][i] != anc[v][i]) u = anc[u][i], v = anc[v][i];
        return anc[u][0];
    }
    inline int jump(int u, int lca) {
        for (int i = 17; i >= 0; --i) if(dp[anc[u][i]] > dp[lca]) u = anc[u][i];
        return u;
    }
    inline LL query(int u, int v) {
        int l = lca(u, v);
        if(l <= n) return dis[u]+dis[v]-2*dis[l];
        int uu = jump(u, l), vv = jump(v, l);
        LL d1 = dis[uu]-dis[l], d2 = dis[vv]-dis[l];
        if(!vis[uu]) d1 = cir[l]-d1;
        if(!vis[vv]) d2 = cir[l]-d2;
        return dis[u]-dis[uu]+dis[v]-dis[vv]+min(abs(d1-d2), cir[l]-abs(d1-d2));
    }
}CST;