Codeforces 916E Jamie and Tree 线段树

Jamie and Tree

我们按 1 号点为根建dfs序线段树。即使换了根， 我们也能通过分类讨论去更新求答案。

#include<bits/stdc++.h>
#define LL long long
#define LD long double
#define ull unsigned long long
#define fi first
#define se second
#define mk make_pair
#define PLL pair<LL, LL>
#define PLI pair<LL, int>
#define PII pair<int, int>
#define SZ(x) ((int)x.size())
#define ALL(x) (x).begin(), (x).end()
#define fio ios::sync_with_stdio(false); cin.tie(0);

using namespace std;

const int N = 5e5 + 7;
const int inf = 0x3f3f3f3f;
const LL INF = 0x3f3f3f3f3f3f3f3f;
const int mod = 1e9 + 7;
const double eps = 1e-8;
const double PI = acos(-1);

template<class T, class S> inline void add(T& a, S b) {a += b; if(a >= mod) a -= mod;}
template<class T, class S> inline void sub(T& a, S b) {a -= b; if(a < 0) a += mod;}
template<class T, class S> inline bool chkmax(T& a, S b) {return a < b ? a = b, true : false;}
template<class T, class S> inline bool chkmin(T& a, S b) {return a > b ? a = b, true : false;}

int n, q, a[N];
int idx, dfn[N], in[N], ot[N];
int depth[N], pa[N][20];
vector<int> G[N];

struct SegmentTree {
#define lson l, mid, rt << 1
#define rson mid + 1, r, rt << 1 | 1
    LL sum[N << 2], lazy[N << 2];
    inline void pull(int rt) {
        sum[rt] = sum[rt << 1] + sum[rt << 1 | 1];
    }
    inline void push(int rt, int l, int r) {
        if(lazy[rt]) {
            int mid = l + r >> 1;
            sum[rt << 1] += lazy[rt] * (mid - l + 1);
            sum[rt << 1 | 1] += lazy[rt] * (r - mid);
            lazy[rt << 1] += lazy[rt];
            lazy[rt << 1 | 1] += lazy[rt];
            lazy[rt] = 0;
        }
    }
    void update(int L, int R, LL val, int l, int r, int rt) {
        if(R < l || r < L || R < L) return;
        if(L <= l && r <= R) {
            sum[rt] += val * (r - l + 1);
            lazy[rt] += val;
            return;
        }
        push(rt, l, r);
        int mid = l + r >> 1;
        update(L, R, val, lson);
        update(L, R, val, rson);
        pull(rt);
    }
    LL query(int L, int R, int l, int r, int rt) {
        if(R < l || r < L || R < L) return 0;
        if(L <= l && r <= R) return sum[rt];
        push(rt, l, r);
        int mid = l + r >> 1;
        return query(L, R, lson) + query(L, R, rson);
    }
} Tree;

void dfs(int u, int fa) {
    in[u] = ++idx;
    depth[u] = depth[fa] + 1;
    pa[u][0] = fa;
    for(int i = 1; i < 20; i++)
        pa[u][i] = pa[pa[u][i - 1]][i - 1];
    for(auto& v : G[u])
        if(v != fa) dfs(v, u);
    ot[u] = idx;
}
int getLca(int u, int v) {
    if(depth[u] < depth[v]) swap(u, v);
    int dis = depth[u] - depth[v];
    for(int i = 19; i >= 0; i--)
        if(dis >> i & 1) u = pa[u][i];
    if(u == v) return u;
    for(int i = 19; i >= 0; i--)
        if(pa[u][i] != pa[v][i])
            u = pa[u][i], v = pa[v][i];
    return pa[u][0];
}

int go(int u, int dis) {
    for(int i = 19; i >= 0; i--)
        if(dis >> i & 1) u = pa[u][i];
    return u;
}

bool ok(int i, int j) {
    return in[i] <= in[j] && ot[j] <= ot[i];
}

int main() {
    scanf("%d%d", &n, &q);
    for(int i = 1; i <= n; i++) scanf("%d", &a[i]);
    for(int i = 2; i <= n; i++) {
        int u, v; scanf("%d%d", &u, &v);
        G[u].push_back(v);
        G[v].push_back(u);
    }
    dfs(1, 0);
    for(int i = 1; i <= n; i++)
        Tree.update(in[i], in[i], a[i], 1, n, 1);
    int Rt = 1;
    while(q--) {
        int op, u, v, w, x;
        scanf("%d", &op);
        if(op == 1) {
            scanf("%d", &v);
            Rt = v;
        } else if(op == 2) {
            scanf("%d%d%d", &u, &v, &x);
            if(ok(Rt, u) && ok(Rt, v)) {
                int lca = getLca(u, v);
                if(lca != Rt) Tree.update(in[lca], ot[lca], x, 1, n, 1);
                else Tree.update(1, n, x, 1, n, 1);
            } else if(ok(Rt, u)) {
                Tree.update(1, n, x, 1, n, 1);
            } else if(ok(Rt, v)) {
                Tree.update(1, n, x, 1, n, 1);
            } else {
                w = getLca(u, v);
                int lca = getLca(Rt, w);
                if(lca == w) {
                    int p1 = getLca(Rt, u);
                    int p2 = getLca(Rt, v);
                    if(depth[p1] > depth[p2])  w = p1;
                    else w = p2;
                    int who = go(Rt, depth[Rt] - depth[w] - 1);
                    Tree.update(1, in[who] - 1, x, 1, n, 1);
                    Tree.update(ot[who] + 1, n, x, 1, n, 1);
                } else {
                    Tree.update(in[w], ot[w], x, 1, n, 1);
                }
            }
        } else {
            scanf("%d", &w);
            LL ans = 0;
            if(w == Rt) ans = Tree.query(1, n, 1, n, 1);
            else {
                if(ok(w, Rt)) {
                    int who = go(Rt, depth[Rt] - depth[w] - 1);
                    ans += Tree.query(1, in[who] - 1, 1, n, 1);
                    ans += Tree.query(ot[who] + 1, n, 1, n, 1);
                } else {
                    ans = Tree.query(in[w], ot[w], 1, n, 1);
                }
            }
            printf("%lld
", ans);
        }
    }
    return 0;
}

/*
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