結果

問題 No.426 往復漸化式
ユーザー heno239heno239
提出日時 2022-10-12 19:46:15
言語 C++17
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 154 ms / 5,000 ms
コード長 9,701 bytes
コンパイル時間 3,352 ms
コンパイル使用メモリ 186,532 KB
最終ジャッジ日時 2025-02-08 02:08:39
ジャッジサーバーID
(参考情報)
judge3 / 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 * 1
other AC * 22
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#pragma GCC optimize("O3")
#pragma GCC optimize("unroll-loops")
#include<iostream>
#include<string>
#include<cstdio>
#include<vector>
#include<cmath>
#include<algorithm>
#include<functional>
#include<iomanip>
#include<queue>
#include<ciso646>
#include<random>
#include<map>
#include<set>
#include<bitset>
#include<stack>
#include<unordered_map>
#include<unordered_set>
#include<utility>
#include<cassert>
#include<complex>
#include<numeric>
#include<array>
#include<chrono>
using namespace std;
//#define int long long
typedef long long ll;
typedef unsigned long long ul;
typedef unsigned int ui;
//constexpr ll mod = 998244353;
constexpr ll mod = 1000000007;
const ll INF = mod * mod;
typedef pair<int, int>P;
#define rep(i,n) for(int i=0;i<n;i++)
#define per(i,n) for(int i=n-1;i>=0;i--)
#define Rep(i,sta,n) for(int i=sta;i<n;i++)
#define rep1(i,n) for(int i=1;i<=n;i++)
#define per1(i,n) for(int i=n;i>=1;i--)
#define Rep1(i,sta,n) for(int i=sta;i<=n;i++)
#define all(v) (v).begin(),(v).end()
typedef pair<ll, ll> LP;
template<typename T>
void chmin(T& a, T b) {
a = min(a, b);
}
template<typename T>
void chmax(T& a, T b) {
a = max(a, b);
}
template<typename T>
void cinarray(vector<T>& v) {
rep(i, v.size())cin >> v[i];
}
template<typename T>
void coutarray(vector<T>& v) {
rep(i, v.size()) {
if (i > 0)cout << " "; cout << v[i];
}
cout << "\n";
}
ll mod_pow(ll x, ll n, ll m = mod) {
if (n < 0) {
ll res = mod_pow(x, -n, m);
return mod_pow(res, m - 2, m);
}
if (abs(x) >= m)x %= m;
if (x < 0)x += m;
//if (x == 0)return 0;
ll res = 1;
while (n) {
if (n & 1)res = res * x % m;
x = x * x % m; n >>= 1;
}
return res;
}
//mod should be <2^31
struct modint {
int n;
modint() :n(0) { ; }
modint(ll m) {
if (m < 0 || mod <= m) {
m %= mod; if (m < 0)m += mod;
}
n = m;
}
operator int() { return n; }
};
bool operator==(modint a, modint b) { return a.n == b.n; }
bool operator<(modint a, modint b) { return a.n < b.n; }
modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= (int)mod; return a; }
modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += (int)mod; return a; }
modint operator*=(modint& a, modint b) { a.n = ((ll)a.n * b.n) % mod; return a; }
modint operator+(modint a, modint b) { return a += b; }
modint operator-(modint a, modint b) { return a -= b; }
modint operator*(modint a, modint b) { return a *= b; }
modint operator^(modint a, ll n) {
if (n == 0)return modint(1);
modint res = (a * a) ^ (n / 2);
if (n % 2)res = res * a;
return res;
}
ll inv(ll a, ll p) {
return (a == 1 ? 1 : (1 - p * inv(p % a, a)) / a + p);
}
modint operator/(modint a, modint b) { return a * modint(inv(b, mod)); }
modint operator/=(modint& a, modint b) { a = a / b; return a; }
const int max_n = 1 << 21;
modint fact[max_n], factinv[max_n];
void init_f() {
fact[0] = modint(1);
for (int i = 0; i < max_n - 1; i++) {
fact[i + 1] = fact[i] * modint(i + 1);
}
factinv[max_n - 1] = modint(1) / fact[max_n - 1];
for (int i = max_n - 2; i >= 0; i--) {
factinv[i] = factinv[i + 1] * modint(i + 1);
}
}
modint comb(int a, int b) {
if (a < 0 || b < 0 || a < b)return 0;
return fact[a] * factinv[b] * factinv[a - b];
}
modint combP(int a, int b) {
if (a < 0 || b < 0 || a < b)return 0;
return fact[a] * factinv[a - b];
}
ll gcd(ll a, ll b) {
a = abs(a); b = abs(b);
if (a < b)swap(a, b);
while (b) {
ll r = a % b; a = b; b = r;
}
return a;
}
using ld = long double;
//typedef long double ld;
typedef pair<ld, ld> LDP;
const ld eps = 1e-10;
const ld pi = acosl(-1.0);
template<typename T>
void addv(vector<T>& v, int loc, T val) {
if (loc >= v.size())v.resize(loc + 1, 0);
v[loc] += val;
}
/*const int mn = 2000005;
bool isp[mn];
vector<int> ps;
void init() {
fill(isp + 2, isp + mn, true);
for (int i = 2; i < mn; i++) {
if (!isp[i])continue;
ps.push_back(i);
for (int j = 2 * i; j < mn; j += i) {
isp[j] = false;
}
}
}*/
//[,val)
template<typename T>
auto prev_itr(set<T>& st, T val) {
auto res = st.lower_bound(val);
if (res == st.begin())return st.end();
res--; return res;
}
//[val,)
template<typename T>
auto next_itr(set<T>& st, T val) {
auto res = st.lower_bound(val);
return res;
}
using mP = pair<modint, modint>;
mP operator+(mP a, mP b) {
return { a.first + b.first,a.second + b.second };
}
mP operator+=(mP& a, mP b) {
a = a + b; return a;
}
mP operator-(mP a, mP b) {
return { a.first - b.first,a.second - b.second };
}
mP operator-=(mP& a, mP b) {
a = a - b; return a;
}
LP operator+(LP a, LP b) {
return { a.first + b.first,a.second + b.second };
}
LP operator+=(LP& a, LP b) {
a = a + b; return a;
}
LP operator-(LP a, LP b) {
return { a.first - b.first,a.second - b.second };
}
LP operator-=(LP& a, LP b) {
a = a - b; return a;
}
mt19937 mt(time(0));
const string drul = "DRUL";
string senw = "SENW";
//DRUL,or SENW
int dx[4] = { 1,0,-1,0 };
int dy[4] = { 0,1,0,-1 };
//-----------------------------------------
template<typename T>
struct SegT {
private:
int sz; vector<T> node;
T init_c;
function<T(T, T)> f;
public:
SegT(vector<T> v, T _init_c, function<T(T, T)> _f) {
init_c = _init_c; f = _f;
int n = v.size();
sz = 1;
while (sz < n)sz *= 2;
node.resize(2 * sz - 1, init_c);
rep(i, n) {
node[i + sz - 1] = v[i];
}
per(i, sz - 1) {
node[i] = f(node[2 * i + 1], node[2 * i + 2]);
}
}
SegT(int n, T _init_c, function<T(T, T)> _f) {
init_c = _init_c; f = _f;
sz = 1;
while (sz < n)sz *= 2;
node.resize(2 * sz - 1, init_c);
}
void update(int k, T a) {
k += sz - 1;
node[k] = a;
while (k > 0) {
k = (k - 1) / 2;
node[k] = f(node[k * 2 + 1], node[k * 2 + 2]);
}
}
T query(int a, int b, int k = 0, int l = 0, int r = -1) {
if (r < 0)r = sz;
if (r <= a || b <= l)return init_c;
else if (a <= l && r <= b)return node[k];
else {
T vl = query(a, b, k * 2 + 1, l, (l + r) / 2);
T vr = query(a, b, k * 2 + 2, (l + r) / 2, r);
return f(vl, vr);
}
}
//kf(x,node[y+sz-1])truey
int searchloc(int le, T x, function<bool(T, T)> comp) {
int k = le + sz - 1;
if (comp(x, node[k]))return le;
x = f(x, node[k]);
while (k > 0) {
int mem = k;
k = (k - 1) / 2;
if (2 * k + 1 == mem) {
if (comp(x, node[2 * k + 2])) {
k = 2 * k + 2; break;
}
x = f(x, node[2 * k + 2]);
}
}
if (k == 0)return sz;
while (k < sz - 1) {
if (comp(x, node[2 * k + 1])) {
k = 2 * k + 1;
}
else {
x = f(x, node[2 * k + 1]);
k = 2 * k + 2;
}
}
return k - (sz - 1);
}
};
using mat22 = array<array<modint, 2>, 2>;
using mat33 = array<array<modint, 3>, 3>;
using mat23 = array<array<modint, 3>, 2>;
struct Data {
mat22 b; mat33 a; mat23 c;
};
void solve() {
auto f33 = [&](mat33 a, mat33 b) {
mat33 res;
rep(i, 3)rep(j, 3)res[i][j] = 0;
rep(i, 3)rep(k, 3)rep(j, 3) {
res[i][j] += b[i][k] * a[k][j];
}
return res;
};
auto f22 = [&](mat22 a, mat22 b) {
mat22 res;
rep(i, 2)rep(j, 2)res[i][j] = 0;
rep(i, 2)rep(k, 2)rep(j, 2) {
res[i][j] += b[i][k] * a[k][j];
}
return res;
};
auto f223 = [&](mat22 a, mat23 b) {
mat23 res;
rep(i, 2)rep(j, 3)res[i][j] = 0;
rep(i, 2)rep(k, 2)rep(j, 3) {
res[i][j] += a[i][k] * b[k][j];
}
return res;
};
auto f233 = [&](mat23 a, mat33 b) {
mat23 res;
rep(i, 2)rep(j, 3)res[i][j] = 0;
rep(i, 2)rep(k, 3)rep(j, 3) {
res[i][j] += a[i][k] * b[k][j];
}
return res;
};
int n; cin >> n;
vector<modint> p(5);
rep(i, 5) {
int x; cin >> x; p[i] = x;
}
mat33 e33;
rep(j, 3)rep(k, 3) {
if (j == k)e33[j][k] = 1;
else e33[j][k] = 0;
}
mat22 e22;
rep(j, 2)rep(k, 2) {
if (j == k)e22[j][k] = 1;
else e22[j][k] = 0;
}
vector<mat33> a(n,e33);
SegT<mat33> sta(a, e33, f33);
Data e;
e.a = e33;
e.b = e22;
e.c; rep(i, 2)rep(j, 3)e.c[i][j] = 0;
vector<mat22> b(n+1, e22);
vector<Data> orib(n, e);
rep(i, n) {
int tmp = 6 * (n - i);
rep(j, 2)rep(k, 3) {
orib[i].c[j][k] = tmp; tmp++;
}
orib[i].b = b[n - i];
if (i > 0) {
int id = n - i;
orib[i].a = a[id];
}
}
auto f = [&](Data a, Data b) {
Data res;
res.a = f33(b.a, a.a);
res.b = f22(a.b, b.b);
res.c = b.c;
a.c = f223(b.b, a.c);
a.c = f233(a.c, b.a);
rep(i, 2)rep(j, 3)res.c[i][j] += a.c[i][j];
return res;
};
SegT<Data> stb(orib, e, f);
int q; cin >> q;
rep(i, q) {
string ord; cin >> ord;
if (ord == "a") {
int id; cin >> id;
rep(x, 3)rep(y, 3) {
int val; cin >> val;
a[id][x][y] = val;
}
sta.update(id, a[id]);
if (id > 0) {
int nid = n - id;
orib[nid].a = a[id];
stb.update(nid, orib[nid]);
}
}
else if (ord == "b") {
int id; cin >> id;
rep(x, 2)rep(y, 2) {
int val; cin >> val;
b[id][x][y] = val;
}
int nid = n - id;
orib[nid].b = b[id];
stb.update(nid, orib[nid]);
}
else if (ord == "ga") {
int id; cin >> id;
mat33 z = sta.query(0, id);
rep(i, 3) {
if (i > 0)cout << " ";
modint val = 0;
rep(j, 3) {
val += z[i][j] * p[j];
}
cout << val;
}cout << "\n";
}
else {
int id; cin >> id;
if (id == n) {
rep(j, 2) {
if (j > 0)cout << " ";
cout << p[j + 3];
}cout << "\n";
}
else {
Data d = stb.query(0, n - id);
d.c = f233(d.c, sta.query(0, id+1));
vector<modint> ans(2);
rep(i, 2)rep(j, 3) {
ans[i] += d.c[i][j] * p[j];
}
rep(i, 2)rep(j, 2) {
ans[i] += d.b[i][j] * p[j + 3];
}
cout << ans[0] << " " << ans[1] << "\n";
}
}
}
}
signed main() {
ios::sync_with_stdio(false);
cin.tie(0);
cout << fixed << setprecision(10);
//init_f();
//init();
//expr();
//while(true)
//int t; cin >> t; rep(i, t)
solve();
return 0;
}
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