P3241 [HNOI2015]开店

发表于 | 阅读数

在线询问树上$\sum_{i=1}^n dis(x,i),a[i]\in[l,r]$。
$degree\leq 3$

显然$ans=query(x,r)-query(x,l-1)$

查询一颗$u$子树上是,$dis(u,x)\times Num[u][r]+sum[u][r]-u关于x那颗子树$。

由于点的度不大，暴力计算$3$颗子树的贡献。

  • 统计$sum[u][r]$，可以排好序，计算前缀和即可。
  • 需要关系$num[u]+=(a[u]<=r)$
  • 开始的时候需要计算$x$子树的贡献
代码 
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#include <bits/stdc++.h>
using namespace std;
typedef long long ll;
#define pii pair<int, ll>
#define mk make_pair
const int N = 4e5 + 10;
const int mod = 1e9 + 7;

int read()
{
    int x = 0, f = 1;
    char c = getchar();
    while (c < '0' || c > '9')
    {
        if (c == '-')
            f = -1;
        c = getchar();
    }
    while (c >= '0' && c <= '9')
        x = (x << 1) + (x << 3) + c - '0', c = getchar();
    return x * f;
}

vector<pii> g[N];
int vis[N];
int st[N][20], dfn[N], dep[N], tot, lg2[N];
ll dw[N];
void lcadfs(int x, int fa, int d)
{
    st[++tot][0] = x;
    dep[x] = d;
    dfn[x] = tot;
    for (pii now : g[x])
    {
        int to = now.first;
        if (to == fa)
            continue;
        dw[to] = dw[x] + now.second;
        lcadfs(to, x, d + 1);
        st[++tot][0] = x;
    }
}
int lower(int u, int v)
{
    return (dep[u] < dep[v]) ? u : v;
}

void Lca_init()
{
    lcadfs(1, 0, 1);
    for (int i = 2; i <= tot; i++)
        lg2[i] = lg2[i >> 1] + 1;
    for (int l = 1; (1 << l) <= tot; l++)
    {
        for (int i = 1; i + (1 << l) - 1 <= tot; i++)
            st[i][l] = lower(st[i][l - 1], st[i + (1 << (l - 1))][l - 1]);
    }
}

int lca(int u, int v)
{
    u = dfn[u];
    v = dfn[v];
    if (u > v)
        swap(u, v);
    int i = lg2[v - u + 1], w = (1 << i);
    return lower(st[u][i], st[v - w + 1][i]);
}
ll dis(int u, int v)
{
    return dw[u] + dw[v] - 2 * dw[lca(u, v)];
}
int siz[N], f[N];
int father[N], a[N];
int cnt[N], np[N];
int rt, gcnt;
vector<pii> fw[N][3];
vector<ll> sum[N][3];
void GetRoot(int x, int fa)
{
    siz[x] = 1;
    f[x] = 0;
    for (pii now : g[x])
    {
        int to = now.first;
        if (to == fa || vis[to])
            continue;
        GetRoot(to, x);
        siz[x] += siz[to];
        f[x] = max(f[x], siz[to]);
    }
    f[x] = max(f[x], gcnt - siz[x]);
    if (f[x] < f[rt])
        rt = x;
}

void dfs1(int x, int fa, int rt)
{
    fw[rt][cnt[rt]].push_back(mk(a[x], dis(rt, x)));
    for (pii now : g[x])
    {
        int to = now.first;
        if (to == fa || vis[to])
            continue;
        dfs1(to, x, rt);
    }
}
void solve(int x)
{

    vis[x] = 1;

    dfs1(x, 0, father[x]);
    np[x] = cnt[father[x]];
    cnt[father[x]]++;
    for (pii now : g[x])
    {
        int to = now.first;
        if (vis[to])
            continue;
        gcnt = siz[to];
        rt = 0;

        GetRoot(to, x);
        father[rt] = x;
        solve(rt);
    }
}
void Prepare(int n)
{
    for (int i = 0; i <= n; i++)
        if (cnt[i])
        {
            for (int j = 0; j < cnt[i]; j++)
            {

                sort(fw[i][j].begin(), fw[i][j].end());

                sum[i][j].push_back(fw[i][j][0].second);
                for (int t = 1; t < fw[i][j].size(); t++)
                    sum[i][j].push_back(fw[i][j][t].second + sum[i][j][t - 1]);
            }
        }
}
pii calc(int x, int u, int r)
{

    pii res = mk(a[x] <= r, 0);

    for (int i = 0; i < cnt[x]; i++)
    {
        if (i == u)
            continue;

        int it = upper_bound(fw[x][i].begin(), fw[x][i].end(), mk(r + 1, 0ll)) - fw[x][i].begin();
        it--;
        it = min((int)(fw[x][i].size() - 1), it);
        res.first += it + 1;
        if (it >= 0)
            res.second += sum[x][i][it];
    }
    return res;
}
ll query(int u, int r)
{
    if (r < 0)
        return 0;
    int now = u;

    pii o = calc(now, -1, r);
    ll res = o.second;

    while (father[now])
    {

        o = calc(father[now], np[now], r);

        res += o.first * dis(father[now], u);
        res += o.second;
        now = father[now];
    }
    return res;
}
int main()
{
    int n = read(), q = read(), A = read();
    for (int i = 1; i <= n; i++)
        a[i] = read();
    for (int i = 1; i < n; i++)
    {
        int u = read(), v = read(), w = read();
        g[u].push_back(pii(v, w));
        g[v].push_back(mk(u, w));
    }
    Lca_init();
    rt = 0;
    f[0] = 1e9;
    gcnt = n;
    GetRoot(1, 0);

    solve(rt);
    Prepare(n);
    ll ans = 0;
    for (int i = 1; i <= q; i++)
    {
        int u = read(), a = read(), b = read();
        a = (a + ans) % A;
        b = (b + ans) % A;
        if (a > b)
            swap(a, b);
        printf("%lld\n", (ans = (query(u, b) - query(u, a - 1))));
    }
}