結果

問題 No.2230 Good Omen of White Lotus
ユーザー Carpenters-Cat
提出日時 2023-02-25 00:09:15
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 143 ms / 2,000 ms
コード長 16,647 bytes
コンパイル時間 1,783 ms
コンパイル使用メモリ 147,732 KB
最終ジャッジ日時 2025-02-10 22:55:59
ジャッジサーバーID
（参考情報） 		judge4 / judge3
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 3
other AC * 44
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ソースコード

diff #
プレゼンテーションモードにする

#include <algorithm>
#include <bitset>
#include <cassert>
#include <cmath>
#include <deque>
#include <iomanip>
#include <iostream>
#include <map>
#include <queue>
#include <random>
#include <set>
#include <stack>
#include <string>
#include <tuple>
#include <unordered_map>
#include <utility>
#include <vector>
// def_class
using namespace std;
using ll = long long;
using Vi = vector<int>;
using VVi = vector<Vi>;
using Vl = vector<ll>;
using VVl = vector<Vl>;
using Pii = pair<int, int>;
using Vp = vector<Pii>;
using VVp = vector<Vp>;
using Pl = pair<ll, int>;
using Vpl = vector<Pl>;
using VVpl = vector<Vpl>;
using tup = tuple<ll, ll, int>;
using Vt = vector<tuple<int, int, int>>;
using Pll = pair<ll, ll>;
using Vc = vector<char>;
using VVc = vector<Vc>;
template <class U>
using PQmax = priority_queue<U>;
template <class U>
using PQmin = priority_queue<U, vector<U>, greater<U>>;
// func_def
// 再帰で計算するトポロジカルソート
void tprsort(int u, const VVi& gr, Vi& tpr, Vi& par);
void tprsort(int u, const VVpl& gr, Vi& tpr, Vi& par);
// キューで計算するトポロジカルソート
void tprsort(const VVi& gr, Vi& tpr);
ll mpow(ll x, ll n, ll m = 1e9 + 7);
ll comb(int n, int r, const Vl& kai, const Vl& fkai, ll m = 1e9 + 7);
ll gcd(ll a, ll b);
int LCA(const VVi& par, const Vi& depth, int a, int b);
Vi sccResolve(const VVi& gr);
void dijkstra(const VVi& gr, const VVl& cost, Vl& dist, int s);
void dijkstra_prev(const VVi& gr, const VVl& cost, Vl& dist, Vi& prev, int s);
// ax + by = c
struct DLine {
    ll a;
    ll b;
    ll c;
    bool operator<(const DLine l) const;
};
DLine make_dline(ll x1, ll y1, ll x2, ll y2);
double calc_tilt(DLine l1);
bool is_upper(DLine l, ll x, ll y);
bool is_inside(DLine l, ll x, ll y);
class unionfind
{
private:
    Vi par;
    Vi siz;
public:
    unionfind(int N);
    unionfind();
    int root(int v);
    void merge(int a, int b);
    bool same(int a, int b);
    int size(int a);
};
class w_unionfind
{
private:
    Vi par;
    Vi siz;
    Vl val;
    Vi val2;
    ll H;
    Vl ex_val;
public:
    w_unionfind(int N, int H = 0);
    w_unionfind();
    int root(int v);
    bool merge(int a, int b, int z);
    bool same(int a, int b);
    int value(int a);
    void cr_val(int a, ll ex)
    {
        ex_val[a] = ex;
    }
    bool is_cr(int a)
    {
        return ex_val[a] >= 0;
    }
};
class BIT
{
private:
    Vl bit;
    int siz;
public:
    BIT(int N);
    BIT();
    ll& get(int id);
    void add(int id, ll a, ll m);
    ll sum(int id, ll m);
};
class RMQ
{
private:
    Vl val;
    int siz;
    ll e;
    ll prod_sub(int l, int r, int a, int b, int id);
public:
    RMQ(int N, ll e = (ll)1e18);
    RMQ(Vl A, ll e = (ll)1e18);
    RMQ(ll e = (ll)1e18);
    ll& get(int id);
    void set(int id, ll a);
    void add(int id, ll a);
    ll prod(int l, int r);
};
class Fraction
{
public:
    ll mot;
    ll son;
    // a/b を生成
    Fraction(ll a = 0, ll b = 1)
    {
        ll g = gcd(abs(a), abs(b));
        if (b < 0) {
            a *= -1;
            b *= -1;
        }
        mot = b / g;
        son = a / g;
    }
    Fraction(const Fraction& F) : mot(F.mot), son(F.son) {}
    Fraction operator+(const Fraction A) const;
    Fraction operator-(const Fraction A) const;
    Fraction operator*(const Fraction A) const;
    // Fraction operator/(const int& a);
    Fraction operator/(const Fraction A) const;
    Fraction operator=(const Fraction& A);
    bool operator<(const Fraction A) const;
    bool operator>(const Fraction A) const;
};
void chmax(ll& a, ll b)
{
    if (a < b) {
        a = b;
    }
}
int calc_LIS(const Vi& X)
{
    int N = X.size();
    Vi dp(N, 1e9 + 7);
    for (auto x : X) {
        int& pt = *(upper_bound(dp.begin(), dp.end(), x));
        pt = x;
    }
    int fl = 0;
    while (fl < N && dp[fl] < 1e9 + 7) {
        fl++;
    }
    return fl;
}
// sの部分木のsizeを返す
int dfs_hld(const VVi& gr, Vi& hld_son, Vi& hld_id, Vi& hld_root, int s, int p = -1)
{
    hld_son[s] = -1;
    int ma = 0;
    int siz = 1;
    for (auto v : gr[s]) {
        if (v == p) {
            continue;
        }
        int n = dfs_hld(gr, hld_son, hld_id, hld_root, v, s);
        siz += n;
        if (ma < n) {
            ma = n;
            hld_son[s] = v;
        }
    }
    return siz;
}
void hld_b(const VVi& gr, Vi& hld_son, Vi& hld_id, Vi& hld_root, Vi& hld_num, int s, int p = -1)
{
    for (auto v : gr[s]) {
        if (v == p) {
            continue;
        }
        if (v != hld_son[s]) {
            hld_id[v] = hld_root.size();
            hld_root.push_back(v);
            hld_num[v] = 0;
        } else {
            hld_id[v] = hld_id[s];
            hld_num[v] = hld_num[s] + 1;
        }
        hld_b(gr, hld_son, hld_id, hld_root, hld_num, v, s);
    }
}
void HLD(const VVi& gr, Vi& hld_son, Vi& hld_id, Vi& hld_root, Vi& hld_num, int s = 0)
{
    hld_son.assign(gr.size(), -1);
    hld_id.resize(gr.size());
    hld_num.resize(gr.size());
    dfs_hld(gr, hld_son, hld_id, hld_root, s);
    hld_root.push_back(s);
    hld_id[s] = 0;
    hld_num[s] = 0;
    hld_b(gr, hld_son, hld_id, hld_root, hld_num, s);
}
int dfs(const VVi& gr, Vi& vis, int s)
{
    int r = 1;
    vis[s] = 1;
    for (auto v : gr[s]) {
        if (vis[v]) {
            continue;
        }
        r += dfs(gr, vis, v);
        if (r >= 1000000) {
            return 1000000;
        }
    }
    vis[s] = 0;
    return r;
}
ll const m = 998244353;
int main () {
    ll H, W, N, P;
    cin >> H >> W >> N >> P;
    ll Q = mpow(P, m - 2, m);
    Vpl A(N);
    for (auto& [a, b] : A) {
        cin >> a >> b;
    }
    sort(A.begin(), A.end());
    Vi X;
    for (auto [a, b] : A) {
        X.push_back(b);
    }
    int n = calc_LIS(X);
    ll ans = mpow(P - 2, n, m);
    ans *= mpow(P - 1, H + W - 3 - n, m);
    ans %= m;
    /*if (!((H + W) & 1)) {
        ans = m - ans;
        ans %= m;
    }*/
    // cout << ans << endl;
    ans *= mpow(Q, H + W - 3, m);
    ans %= m;
    cout << (m - ans + 1) % m << endl;
}
// 再帰型
void tprsort(int u, const VVi& gr, Vi& tpr, Vi& par)
{
    // idx[u] = tpr.size();
    /*for (int v : gr[u]) {
        if (par[v] == u || par[v] == -1) {
            par[v] = u;
            tprsort(v, gr, tpr, par);
        }
    }
    tpr.push_back(u);*/
    stack<int> st;
    st.push(u);
    bool vis[2000020];
    par.assign(gr.size(), -1);
    par[u] = -2;
    tpr.clear();
    for (int i = 0; i <= gr.size(); i++) {
        vis[i] = false;
    }
    while (!st.empty()) {
        int v = st.top();
        if (!vis[v]) {
            vis[v] = true;
            for (int p : gr[v]) {
                if (par[p] == -1) {
                    par[p] = v;
                    st.push(p);
                }
            }
        } else {
            tpr.push_back(v);
            st.pop();
        }
    }
}
Vi sccResolve(const VVi& gr)
{
    int N = gr.size();
    Vi tpr;
    Vi par(N, -1);
    for (int i = 0; i < N; i++) {
        if (par[i] == -1) {
            tprsort(i, gr, tpr, par);
        }
    }
    Vi ret(N, -1);
    int now = 0;
    for (int i = N - 1; i >= 0; i--) {
        int u = tpr[i];
        if (ret[u] != -1) {
            continue;
        }
        ret[u] = now;
        stack<int> st;
        st.push(u);
        while (!st.empty()) {
            int v = st.top();
            st.pop();
            for (int p : gr[v]) {
                if (ret[p] == -1) {
                    st.push(p);
                    ret[p] = now;
                }
            }
        }
        now++;
    }
    return ret;
}
ll gcd(ll a, ll b)
{
    while (b) {
        a %= b;
        swap(a, b);
    }
    return a;
}
ll mpow(ll x, ll n, ll m)
{
    ll ret = 1;
    while (n) {
        if (n % 2) {
            ret *= x;
            ret %= m;
        }
        x = (x * x) % m;
        n /= 2;
    }
    return ret;
}
ll comb(int n, int r, const Vl& kai, const Vl& fkai, ll m)
{
    if (n < 0 || r < 0 || n < r) {
        return 0;
    }
    ll ret = kai[n];
    ret *= fkai[r];
    ret %= m;
    ret *= fkai[n - r];
    ret %= m;
    return ret;
}
int LCA(const VVi& par, const Vi& depth, int a, int b)
{
    if (depth[a] < depth[b]) {
        swap(a, b);
    }
    int dis = depth[a] - depth[b];
    for (int i = 19; i >= 0; i--) {
        if ((dis >> i) & 1) {
            a = par[i][a];
        }
    }
    if (a == b) {
        return a;
    }
    for (int i = 19; i >= 0; i--) {
        if (par[i][a] != par[i][b]) {
            a = par[i][a];
            b = par[i][b];
        }
    }
    return par[0][a];
}
void dijkstra(const VVi& gr, const VVl& cost, Vl& dist, int s)
{
    ll INF = (ll)1e18;
    dist.assign(gr.size(), INF);
    dist[s] = 0;
    PQmin<Pl> pque;
    pque.push(make_pair(0, s));
    while (!pque.empty()) {
        auto [L, u] = pque.top();
        pque.pop();
        while (L != dist[u] && !pque.empty()) {
            tie(L, u) = pque.top();
            pque.pop();
        }
        for (int i = 0; i < gr[u].size(); i++) {
            int v = gr[u][i];
            ll c = cost[u][i];
            if (dist[v] > c + L) {
                dist[v] = c + L;
                pque.push(make_pair(dist[v], v));
            }
        }
    }
    return;
}
void dijkstra_prev(const VVi& gr, const VVl& cost, Vl& dist, Vi& prev, int s)
{
    ll INF = (ll)1e18;
    dist.assign(gr.size(), INF);
    dist[s] = 0;
    PQmin<Pl> pque;
    pque.push(make_pair(0, s));
    while (!pque.empty()) {
        auto [L, u] = pque.top();
        pque.pop();
        while (L != dist[u] && !pque.empty()) {
            tie(L, u) = pque.top();
            pque.pop();
        }
        for (int i = 0; i < gr[u].size(); i++) {
            int v = gr[u][i];
            ll c = cost[u][i];
            if (dist[v] > c + L) {
                dist[v] = c + L;
                prev[v] = u;
                pque.push(make_pair(dist[v], v));
            }
        }
    }
    return;
}
DLine make_dline(ll x1, ll y1, ll x2, ll y2)
{
    ll dx = x1 - x2;
    ll dy = y2 - y1;
    if (dy < 0) {
        dx *= -1;
        dy *= -1;
    }
    if (dy == 0) {
        dx = abs(dx);
    }
    ll g = gcd(dy, abs(dx));
    dx /= g;
    dy /= g;
    ll c = dx * y1 + dy * x1;
    return DLine{dy, dx, c};
}
double calc_tilt(DLine l)
{
    return atan2(l.a, l.b);
}
bool is_upper(DLine l, ll x, ll y)
{
    return x * l.a + y * l.b > l.c;
}
bool is_inside(DLine l, ll x, ll y)
{
    return x * l.a + y * l.b == l.c;
}
unionfind::unionfind(int N)
{
    par.resize(N);
    siz.assign(N, 1);
    for (int i = 0; i < N; i++) {
        par[i] = i;
    }
}
unionfind::unionfind()
{
    par.resize(100010);
    siz.assign(100010, 1);
    for (int i = 0; i <= 100010; i++) {
        par[i] = i;
    }
}
int unionfind::root(int v)
{
    if (v == par[v]) {
        return v;
    }
    return par[v] = root(par[v]);
}
void unionfind::merge(int a, int b)
{
    a = root(a);
    b = root(b);
    if (a == b) {
        return;
    }
    if (siz[a] < siz[b]) {
        int t = a;
        a = b;
        b = t;
    }
    par[b] = a;
    siz[a] += siz[b];
}
bool unionfind::same(int a, int b)
{
    a = root(a);
    b = root(b);
    return a == b;
}
int unionfind::size(int a)
{
    return siz[this->root(a)];
}
w_unionfind::w_unionfind(int N, int H) : H(H)
{
    par.resize(N);
    siz.assign(N, 1);
    val.assign(N, 0);
    val2.assign(N, 1);
    ex_val.assign(N, -1);
    for (int i = 0; i < N; i++) {
        par[i] = i;
    }
}
w_unionfind::w_unionfind()
{
    par.resize(100010);
    siz.assign(100010, 1);
    val.assign(100010, 0);
    for (int i = 0; i <= 100010; i++) {
        par[i] = i;
    }
}
int w_unionfind::root(int v)
{
    if (v == par[v]) {
        return v;
    }
    int p = par[v];
    int q = root(par[v]);
    val[v] += val2[v] * val[p];
    val[v] += H;
    val[v] %= H;
    val2[v] *= val2[p];
    if (ex_val[q] >= 0) {
        ex_val[v] = ex_val[q] * val2[v] + val[v];
        ex_val[v] += H;
        ex_val[v] %= H;
    }
    return par[v] = q;
}
bool w_unionfind::merge(int a, int b, int z)
{
    // z -= this->value(b);
    // z += this->value(a);
    int pa = root(a);
    int pb = root(b);
    if (ex_val[a] >= 0 && ex_val[b] >= 0) {
        return ((ex_val[a] + ex_val[b]) % H) == z;
    }
    if (pa == pb) {
        z += H - (val[a] - val[b]);
        z %= H;
        if (val2[a] == -1) {
            z = H - z;
            z %= H;
        }
        if (H % 2 == 0 && z % 2 == 1) {
            return false;
        }
        if (z % 2 == 0) {
            z /= 2;
        } else {
            z *= ((H + 1) / 2);
        }
        if (ex_val[pa] >= 0 && ex_val[pa] != z) {
            return false;
        }
        ex_val[pa] = z;
        return true;
    }
    if (siz[pa] < siz[pb]) {
        swap(pa, pb);
        swap(a, b);
    }
    if (ex_val[pb] >= 0) {
        swap(pa, pb);
        swap(a, b);
    }
    par[pb] = pa;
    siz[pa] += siz[pb];
    val[pb] = (-val2[b]) * (val[a] + val[b] - z);
    val[pb] += H * 3;
    val[pb] %= H;
    val2[pb] *= (-val2[a]);
    return true;
}
bool w_unionfind::same(int a, int b)
{
    a = root(a);
    b = root(b);
    return a == b;
}
int w_unionfind::value(int a)
{
    root(a);
    return val[a];
}
BIT::BIT(int N)
{
    siz = N;
    bit.assign(N + 1, 0);
}
BIT::BIT()
{
    siz = 0;
}
ll& BIT::get(int id)
{
    return bit[id];
}
void BIT::add(int id, ll a, ll m)
{
    while (id <= siz) {
        bit[id] += a;
        if (m > 0) {
            bit[id] %= m;
        }
        id += (id & (-id));
    }
}
ll BIT::sum(int id, ll m)
{
    ll ret = 0;
    while (id) {
        ret += bit[id];
        if (m > 0) {
            ret %= m;
        }
        id -= (id & (-id));
    }
    return ret;
}
RMQ::RMQ(int N, ll e)
{
    siz = 1;
    this->e = e;
    while (siz < N) {
        siz *= 2;
    }
    val.assign(siz * 2, e);
}
RMQ::RMQ(Vl A, ll e)
{
    siz = 1;
    this->e = e;
    while (siz < A.size()) {
        siz *= 2;
    }
    val.assign(siz * 2, e);
    for (int i = 0; i < A.size(); i++) {
        val[i + siz - 1] = A[i];
    }
    for (int i = siz - 2; i >= 0; i--) {
        int l = i * 2 + 1;
        int r = i * 2 + 2;
        val[i] = min(val[l], val[r]);
    }
}
RMQ::RMQ(ll e)
{
    siz = (1 << 20);
    this->e = e;
    val.assign(siz * 2, e);
}
ll& RMQ::get(int id)
{
    return val[id + siz - 1];
}
void RMQ::set(int id, ll a)
{
    id += siz - 1;
    val[id] = a;
    while (id > 0) {
        id = (id - 1) / 2;
        int l = id * 2 + 1;
        int r = id * 2 + 2;
        ll v = min(val[l], val[r]);
        /*if (val[id] == v) {
            break;
        }*/
        val[id] = v;
    }
}
void RMQ::add(int id, ll a)
{
    ll n = a + val[id + siz - 1];
    this->set(id, n);
}
ll RMQ::prod_sub(int l, int r, int a, int b, int id)
{
    if (b <= l || r <= a) {
        return this->e;
    }
    if (l <= a && b <= r) {
        return val[id];
    }
    return min(this->prod_sub(l, r, a, (a + b) / 2, id * 2 + 1),
        this->prod_sub(l, r, (a + b) / 2, b, id * 2 + 2));
}
ll RMQ::prod(int l, int r)
{
    return prod_sub(l, r, 0, siz, 0);
}
Fraction Fraction::operator+(const Fraction A) const
{
    return Fraction{this->son * A.mot + A.son * this->mot, this->mot * A.mot};
}
Fraction Fraction::operator-(const Fraction A) const
{
    return Fraction{this->son * A.mot - A.son * this->mot, this->mot * A.mot};
}
Fraction Fraction::operator*(const Fraction A) const
{
    return Fraction{this->son * A.son, this->mot * A.mot};
}
// Fraction Fraction::operator/(const int& a)
// {
//     return *this / (ll)a;
// }
Fraction Fraction::operator/(const Fraction A) const
{
    return Fraction{this->son * A.mot, this->mot * A.son};
}
Fraction Fraction::operator=(const Fraction& A)
{
    this->mot = A.mot;
    this->son = A.son;
    return *this;
}
bool Fraction::operator<(const Fraction A) const
{
    if (A.son < 0 && this->son > 0) {
        return false;
    }
    if (A.son > 0 && this->son < 0) {
        return true;
    }
    if (A.son < 0) {
        return (A * -1) < (*this * -1);
    }
    if (max({this->son, A.son, A.mot, this->mot}) < 3000000000ll) {
        return this->son * A.mot < this->mot * A.son;
    } else if (this->son / this->mot != A.son / A.mot) {
        return this->son / this->mot < A.son / A.mot;
    } else {
        ll f = this->son / this->mot;
        return (*this - f) < (A - f);
    }
}
bool Fraction::operator>(const Fraction A) const
{
    return A < *this;
}
bool DLine::operator<(const DLine l) const
{
    if (a == l.a && b == l.b) {
        return c < l.c;
    }
    return Fraction{a, -b} < Fraction{l.a, -l.b};
}
הההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההההה
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0