結果
| 問題 | No.1696 Nonnil |
| ユーザー |
 milanis48663220
|
| 提出日時 | 2021-10-01 23:59:19 |
| 言語 | C++17 (gcc 13.3.0 + boost 1.87.0) |
| 結果 |
AC
|
| 実行時間 | 1,889 ms / 3,500 ms |
| コード長 | 6,685 bytes |
| コンパイル時間 | 1,573 ms |
| コンパイル使用メモリ | 125,512 KB |
| 最終ジャッジ日時 | 2025-01-24 19:38:28 |
|
ジャッジサーバーID （参考情報） |
judge2 / judge2 |
（要ログイン）
| ファイルパターン | 結果 |
|---|---|
| sample | AC * 4 |
| other | AC * 39 |
ソースコード
#include <iostream>
#include <algorithm>
#include <iomanip>
#include <vector>
#include <queue>
#include <set>
#include <map>
#include <tuple>
#include <cmath>
#include <numeric>
#include <functional>
#include <cassert>
#define debug_value(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << #x << "=" << x << endl;
#define debug(x) cerr << "line" << __LINE__ << ":<" << __func__ << ">:" << x << endl;
template<class T> inline bool chmax(T& a, T b) { if (a < b) { a = b; return 1; } return 0; }
template<class T> inline bool chmin(T& a, T b) { if (a > b) { a = b; return 1; } return 0; }
using namespace std;
typedef long long ll;
template<typename T>
vector<vector<T>> vec2d(int n, int m, T v){
return vector<vector<T>>(n, vector<T>(m, v));
}
template<typename T>
vector<vector<vector<T>>> vec3d(int n, int m, int k, T v){
return vector<vector<vector<T>>>(n, vector<vector<T>>(m, vector<T>(k, v)));
}
template<typename T>
void print_vector(vector<T> v, char delimiter=' '){
for(int i = 0; i+1 < v.size(); i++) cout << v[i] << delimiter;
cout << v.back() << endl;
}
const ll MOD = 998244353;
class ModInt{
public:
ll v;
ModInt(ll _v = 0){
if(_v < 0) _v = (_v%MOD)+MOD;
if(_v >= MOD) _v %= MOD;
v = _v;
}
ModInt operator+(ll n){
return ModInt((v+n)%MOD);
}
ModInt operator-(ll n){
return ModInt((v-n+MOD)%MOD);
}
ModInt operator*(ll n){
if(n >= MOD) n %= MOD;
return ModInt((v*n)%MOD);
}
ModInt operator/(ll n){
return ModInt((ModInt(n).inv()*v).v%MOD);
}
void operator+=(ll n){
v = (v+n)%MOD;
}
void operator-=(ll n){
v = (v-n+MOD)%MOD;
}
void operator*=(ll n){
v = (v*n+MOD)%MOD;
}
ModInt operator+(ModInt n){
return ModInt((v+n.v)%MOD);
}
ModInt operator-(ModInt n){
return ModInt((v-n.v+MOD)%MOD);
}
ModInt operator*(ModInt n){
return ModInt((v*n.v)%MOD);
}
ModInt operator/(ModInt n){
return ModInt((n.inv()*v).v%MOD);
}
void operator+=(ModInt n){
v = (v+n.v)%MOD;
}
void operator-=(ModInt n){
v = (v-n.v+MOD)%MOD;
}
void operator*=(ModInt n){
v = (v*n.v)%MOD;
}
void operator=(ModInt n){
v = n.v;
}
bool operator==(ModInt n){
return v == n.v;
}
bool operator!=(ModInt n){
return v != n.v;
}
void operator=(ll n){
v = n%MOD;
}
ModInt inv(){
if(v == 1) return ModInt(1);
else return ModInt(MOD-ModInt(MOD%v).inv().v*(MOD/v)%MOD);
}
};
ostream& operator<<(ostream& os, const ModInt& m){
os << m.v;
return os;
}
istream & operator >> (istream &in, ModInt &m){
in >> m.v;
return in;
}
ModInt pow(ModInt a, ll n) {
assert(n >= 0);
ModInt ans = 1;
ModInt tmp = a;
for (int i = 0; i <= 60; i++) {
ll m = (ll)1 << i;
if (m & n) {
ans *= tmp;
}
tmp *= tmp;
}
return ans;
}
#define N_MAX 200002
ModInt inv[N_MAX],fac[N_MAX],finv[N_MAX];
void init(){
fac[0]=1;fac[1]=1;
finv[0]=1;finv[1]=1;
inv[1]=1;
for(int i=2;i<N_MAX;i++){
inv[i]=ModInt(MOD)-inv[MOD%i]*(MOD/i);
fac[i]=fac[i-1]*(ll) i;
finv[i]=finv[i-1]*inv[i];
}
}
ModInt comb(ll n, ll r){
if(n < r){
return ModInt(0);
}else{
return fac[n]*finv[r]*finv[n-r];
}
}
using mint = ModInt;
using P = pair<int, int>;
const int INF = 1e9;
int main(){
ios::sync_with_stdio(false);
cin.tie(0);
cout << setprecision(10) << fixed;
int n, k; cin >> n >> k;
int m; cin >> m;
vector<int> r(k, INF);
for(int i = 0; i < m; i++) {
int l, x; cin >> l >> x; l--;
chmin(r[l], x);
}
// print_vector(r);
for(int l = 0; l < k; l++){
if(r[l] == INF) continue;
for(int l1 = l+1; l1 < r[l]; l1++){
if(r[l1] <= r[l]) {
r[l] = INF;
// debug_value(l)
break;
}
}
}
auto dp_used = vec3d(k+1, k+1, 2, mint(0));
auto dp_unused = vec3d(k+1, k+1, 2, mint(0));
auto dp_used_cumsum = vec3d(k+2, k+1, 2, mint(0));
auto dp_unused_cumsum = vec3d(k+2, k+1, 2, mint(0));
auto cumsum_used = [&](int l, int r, int len, int x){
if(r <= l) return mint(0);
// mint ans = 0;
// for(int i = l; i < r; i++) ans += dp_used[i][len][x];
// return ans;
return dp_used_cumsum[r][len][x]-dp_used_cumsum[l][len][x];
};
auto cumsum_unused = [&](int l, int r, int len, int x){
if(r <= l) return mint(0);
// mint ans = 0;
// for(int i = l; i < r; i++) ans += dp_unused[i][len][x];
// return ans;
return dp_unused_cumsum[r][len][x]-dp_unused_cumsum[l][len][x];
};
int pre = 0;
for(int l = 0; l < k; l++){
if(r[l] == INF) continue;
// cout << pre << ' ';
for(int rr = pre; rr <= r[l]-1; rr++){
for(int len = 0; len <= k; len++){
dp_used_cumsum[rr+1][len][0] = dp_used_cumsum[rr][len][0] + dp_used[rr][len][0];
dp_used_cumsum[rr+1][len][1] = dp_used_cumsum[rr][len][1] + dp_used[rr][len][1];
dp_unused_cumsum[rr+1][len][0] = dp_unused_cumsum[rr][len][0] + dp_unused[rr][len][0];
dp_unused_cumsum[rr+1][len][1] = dp_unused_cumsum[rr][len][1] + dp_unused[rr][len][1];
}
}
auto cur = vec2d(k+1, 2, mint(0));
for(int len = r[l]-l; len <= r[l]; len++){
cur[len][0] = cumsum_used(0, l+1, len-(r[l]-l), 1) + cumsum_unused(l+1, r[l], r[l]-len, 1);
cur[len][1] = cumsum_used(0, l+1, len-(r[l]-l), 0) + cumsum_unused(l+1, r[l], r[l]-len, 0);
}
cur[r[l]-l][1] += 1;
for(int len = r[l]-l; len <= r[l]; len++){
dp_used[r[l]][len][0] = cur[len][0];
dp_unused[r[l]][r[l]-len][0] = cur[len][0];
dp_used[r[l]][len][1] = cur[len][1];
dp_unused[r[l]][r[l]-len][1] = cur[len][1];
}
pre = r[l];
}
mint ans = pow(mint(k), n);
// debug_value(ans)
for(int r = 1; r <= k; r++){
for(int len = 0; len <= r; len++){
// if(dp_unused[r][len][0].v != 0) cout << r << ' ' << len << ' ' << 0 << ' ' << dp_unused[r][len][0] << endl;
// if(dp_unused[r][len][1].v != 0) cout << r << ' ' << len << ' ' << 1 << ' ' << dp_unused[r][len][1] << endl;
int rem = len+k-r;
ans += pow(mint(rem), n)*dp_unused[r][len][0];
ans -= pow(mint(rem), n)*dp_unused[r][len][1];
}
}
cout << ans << endl;
}