CF455D.Serega and Fun

发表于 | 阅读数

给你一个序列，在线地支持两个操作：

  • 将一个区间循环移位。

  • 查询一个区间中某个数出现的次数。

两个方法

  • 分块 维护块内元素出现次数，修改和更新用双向队列都很显然。$O((n+m)\sqrt{n})=1700ms$
  • 平衡树，第一个操作很好解决，对于第二个操作，首先我们只能维护$t_i$这个数字平衡树出现的相对位置，而不能维护绝对位置。但是我们可以通过一开始构造原序列的平衡树的映射，就可以知道某个值在原序列第几个位置，这里需要$O(\log n)$。我想知道$[1,r]$之间$i$出现了几次，平衡树上通过这个查询二分即可。总复杂度$O(n+m\log^2 n)=300ms$
平衡树 
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#include <bits/stdc++.h>
using namespace std;

#define pii pair<int, int>
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;
}

std::mt19937 rnd(std::chrono::steady_clock::now().time_since_epoch().count());
struct FHQ
{
    int ls[N], rs[N];
    int siz[N], key[N], val[N];
    int fa[N];
    int cor[N];
    // ll sum[N];
    int tcnt;
    int root;
    int Newnode(int x)
    {
        siz[++tcnt] = 1;
        val[tcnt] = x;
        key[tcnt] = rnd(); //精髓所在

        fa[tcnt] = tcnt;
        ls[tcnt] = rs[tcnt] = 0;
        return tcnt;
    }
    void pushup(int pos)
    {
        siz[pos] = siz[ls[pos]] + siz[rs[pos]] + 1;
        // sum[pos] = sum[ls[pos]] + sum[rs[pos]] + val[pos];
        ls[pos] ? (fa[ls[pos]] = pos) : 0;
        rs[pos] ? (fa[rs[pos]] = pos) : 0;
    }

    void split(int pos, int v, int &ll, int &rr)
    {
        if (!pos)
        {
            ll = 0, rr = 0;
            return;
        }

        if (siz[ls[pos]] + 1 <= v)
        {
            ll = pos;
            split(rs[pos], v - siz[ls[pos]] - 1, rs[pos], rr);
        }
        else
        {
            rr = pos;
            split(ls[pos], v, ll, ls[pos]);
        }
        fa[ll] = ll, fa[rr] = rr; //保证头节点
        pushup(pos);
    }
    int merge(int l, int r)
    {
        if (!l || !r)
            return l + r;

        if (key[l] < key[r])
        {
            rs[l] = merge(rs[l], r);
            pushup(l);
            return l;
        }
        else
        {

            ls[r] = merge(l, ls[r]);
            pushup(r);
            return r;
        }
    }
    // int find(int x)
    // {
    //     return fa[x] == x ? x : find(fa[x]);
    // }
    int insert(int &rt, int x)
    {
        int pos = Newnode(x);
        rt = merge(rt, pos);
        return pos;
    }
    int kth(int x)
    {
        int res = siz[ls[x]] + 1;
        while (fa[x] != x)
        {
            if (rs[fa[x]] == x)
            {
                res += siz[ls[fa[x]]] + 1;
            }
            x = fa[x];
        }
        return res;
    }

} t;

int rt[N];

int calc(int k, int r)
{
    int o = rt[k];
    int res = 0;
    while (o)
    {
        if (t.kth(t.cor[o]) <= r)
        {
            res += t.siz[t.ls[o]] + 1;
            o = t.rs[o];
        }
        else
            o = t.ls[o];
    }
    return res;
}
int query(int l, int r, int k)
{
    return calc(k, r) - calc(k, l - 1);
}

void update(int l, int r)
{
    int a, b, c, d;
    t.split(rt[0], l - 1, a, b);
    t.split(b, r - l + 1, b, d);
    t.split(b, r - l, b, c);

    int k = t.val[c];
    rt[0] = t.merge(a, t.merge(c, t.merge(b, d)));
    int ls = calc(k, l - 1);
    int rs = calc(k, r);
    //cout << k << " " << ls << " " << rs << endl;

    t.split(rt[k], ls, a, b);
    t.split(b, rs - ls, b, d);
    t.split(b, rs - ls - 1, b, c);

    rt[k] = t.merge(a, t.merge(c, t.merge(b, d)));
}

int a[N];
int main()
{
    //freopen("1", "r", stdin);
    int n = read();
    for (int i = 1; i <= n; i++)
    {
        a[i] = read();
        int x = t.insert(rt[0], a[i]);
        int y = t.insert(rt[a[i]], a[i]);
        t.cor[x] = y;
        t.cor[y] = x;
    }

    int lst = 0;
    int q = read();
    while (q--)
    {
        int op = read(), l = read(), r = read();

        if (op == 1)
        {
            l = (l + lst - 1) % n + 1, r = (r + lst - 1) % n + 1;
            //cout << op << " " << l << " " << r << " " << endl;
            if (l > r)
                swap(l, r);
            if (l == r)
                continue;
            update(l, r);
        }
        else
        {
            int k = read();
            l = (l + lst - 1) % n + 1, r = (r + lst - 1) % n + 1, k = (k + lst - 1) % n + 1;
            // cout << op << " " << l << " " << r << " "
            //      << " " << k << endl;
            if (l > r)
                swap(l, r);

            printf("%d\n", lst = query(l, r, k));
        }
    }
}
分块 
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  #include <bits/stdc++.h>
using namespace std;
#define ll long long
#define pii pair<ll, int>
const int N = 1e5 + 10;
const int mod = 1e9 + 7;
const int M = 400;

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;
}

struct Bo
{
    int block, tot, bl[N], br[N], fa[N];
    int cnt[M][N];
    int a[N];
    deque<int> q[M];
    ll tag[N];

    void replace(int x, int y, int w)
    {
        cnt[x][y] += w;
    }
    void build(int n)
    {
        block = sqrt(n);
        tot = n / block + (n % block != 0);

        for (int i = 1; i <= tot; i++)
            bl[i] = (i - 1) * block + 1, br[i] = i * block;

        br[tot] = n;

        for (int i = 1; i <= n; i++)
            fa[i] = (i - 1) / (block) + 1;
        for (int i = 1; i <= tot; i++)
        {
            for (int j = bl[i]; j <= br[i]; j++)
            {
                q[i].push_back(a[j]);
                replace(i, a[j], 1);
            }
        }
    }
    void work(int lx, int rx, int l, int r)
    {

        stack<int> le, ri;
        for (int i = 1; i <= l - bl[lx]; i++)
        {
            le.push(q[lx].front());
            q[lx].pop_front();
        }

        for (int i = 1; i <= br[rx] - r; i++)
        {
            ri.push(q[rx].back());
            q[rx].pop_back();
        }
        int u = q[rx].back();
        replace(rx, u, -1);
        q[rx].pop_back();
        replace(lx, u, 1);
        q[lx].push_front(u);
        while (!le.empty())
        {
            q[lx].push_front(le.top());
            le.pop();
        }
        while (!ri.empty())
        {
            q[rx].push_back(ri.top());
            ri.pop();
        }
    }
    int calc(int lx, int rx, int l, int r, int k)
    {

        stack<int> le, ri;
        for (int i = 1; i <= l - bl[lx]; i++)
        {
            le.push(q[lx].front());
            q[lx].pop_front();
        }

        for (int i = 1; i <= br[rx] - r; i++)
        {
            ri.push(q[rx].back());
            q[rx].pop_back();
        }
        int res = 0;
        for (int x : q[lx])
            if (x == k)
                res++;
        if (lx != rx)
        {
            for (int x : q[rx])
                if (x == k)
                    res++;
        }

        while (!le.empty())
        {
            q[lx].push_front(le.top());
            le.pop();
        }
        while (!ri.empty())
        {
            q[rx].push_back(ri.top());
            ri.pop();
        }
        return res;
    }

    void update(int l, int r)
    {
        if (fa[l] == fa[r])
        {
            work(fa[l], fa[l], l, r);
            return;
        }
        int lx = fa[l], rx = fa[r];
        for (int i = lx; i < rx; i++)
        {
            int x = q[i].back();
            q[i].pop_back();
            replace(i, x, -1);
            q[i + 1].push_front(x);
            replace(i + 1, x, 1);
        }
        work(lx, rx, l, r);
    }
    int query(int l, int r, int k)
    {
        if (fa[l] == fa[r])
        {
            return calc(fa[l], fa[l], l, r, k);
        }
        int lx = fa[l], rx = fa[r];
        int res = 0;
        for (int i = lx + 1; i < rx; i++)
        {
            res += cnt[i][k];
        }
        res += calc(lx, rx, l, r, k);
        return res;
    }
} t;

int main()
{
    // freopen("1", "r", stdin);
    int n = read();
    for (int i = 1; i <= n; i++)
        t.a[i] = read();
    t.build(n);
    int q = read();
    int lst = 0;
    while (q--)
    {
        int op = read(), l = read(), r = read();

        if (op == 1)
        {
            l = (l + lst - 1) % n + 1, r = (r + lst - 1) % n + 1;
            //cout << op << " " << l << " " << r << " " << endl;
            if (l > r)
                swap(l, r);
            if (l == r)
                continue;
            t.update(l, r);
        }
        else
        {
            int k = read();
            l = (l + lst - 1) % n + 1, r = (r + lst - 1) % n + 1, k = (k + lst - 1) % n + 1;
            // cout << op << " " << l << " " << r << " "
            //      << " " << k << endl;
            if (l > r)
                swap(l, r);

            printf("%d\n", lst = t.query(l, r, k));
        }
    }
}