#899720 (C++17) No.2405 Minimal Matrix Decomposition

提出ソース

結果

問題	No.2405 Minimal Matrix Decomposition
ユーザー	heno239
提出日時	2023-08-09 02:13:45
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	WA
実行時間	-
コード長	7,561 bytes
コンパイル時間	2,913 ms
コンパイル使用メモリ	179,036 KB
実行使用メモリ	17,536 KB
最終ジャッジ日時	2024-04-26 17:48:27
合計ジャッジ時間	12,722 ms
ジャッジサーバーID （参考情報）	judge4 / judge2

このコードへのチャレンジ
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テストケース

テストケース表示

入力	結果	実行時間実行使用メモリ
testcase_00	AC	10 ms 11,776 KB
testcase_01	AC	10 ms 11,776 KB
testcase_02	AC	10 ms 11,776 KB
testcase_03	AC	10 ms 11,904 KB
testcase_04	WA	-
testcase_05	AC	582 ms 16,768 KB
testcase_06	AC	10 ms 11,776 KB
testcase_07	AC	11 ms 11,776 KB
testcase_08	AC	11 ms 11,904 KB
testcase_09	AC	11 ms 11,776 KB
testcase_10	AC	224 ms 14,720 KB
testcase_11	WA	-
testcase_12	AC	17 ms 12,160 KB
testcase_13	WA	-
testcase_14	AC	87 ms 13,056 KB
testcase_15	WA	-
testcase_16	WA	-
testcase_17	WA	-
testcase_18	AC	146 ms 13,440 KB
testcase_19	AC	180 ms 13,824 KB
testcase_20	WA	-
testcase_21	WA	-
testcase_22	WA	-
testcase_23	AC	13 ms 11,904 KB
testcase_24	WA	-
testcase_25	AC	33 ms 12,416 KB
testcase_26	AC	192 ms 14,208 KB
testcase_27	WA	-
testcase_28	AC	276 ms 14,336 KB
testcase_29	AC	112 ms 13,440 KB
testcase_30	AC	215 ms 14,592 KB
testcase_31	AC	69 ms 12,800 KB
testcase_32	WA	-
testcase_33	WA	-
testcase_34	WA	-
testcase_35	AC	11 ms 11,904 KB
testcase_36	WA	-
testcase_37	WA	-
testcase_38	AC	201 ms 13,824 KB
testcase_39	AC	285 ms 14,464 KB
testcase_40	WA	-
testcase_41	WA	-
testcase_42	WA	-
testcase_43	WA	-
testcase_44	AC	52 ms 12,416 KB
testcase_45	AC	28 ms 12,096 KB
testcase_46	AC	66 ms 12,544 KB
testcase_47	AC	67 ms 12,544 KB
testcase_48	WA	-
testcase_49	WA	-

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ソースコード

raw source code

#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;
//ll mod = 1;
constexpr ll mod = 998244353;
//constexpr ll mod = 1000000007;
const int mod17 = 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;

using ld = double;
typedef pair<ld, ld> LDP;
const ld eps = 1e-10;
const ld pi = acosl(-1.0);

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>
vector<T> vmerge(vector<T>& a, vector<T>& b) {
	vector<T> res;
	int ida = 0, idb = 0;
	while (ida < a.size() || idb < b.size()) {
		if (idb == b.size()) {
			res.push_back(a[ida]); ida++;
		}
		else if (ida == a.size()) {
			res.push_back(b[idb]); idb++;
		}
		else {
			if (a[ida] < b[idb]) {
				res.push_back(a[ida]); ida++;
			}
			else {
				res.push_back(b[idb]); idb++;
			}
		}
	}
	return res;
}
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 << 20;
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;
}
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 };

//------------------------------------



void solve() {
	ll p; cin >> p;
	int n, m; cin >> n >> m;
	vector<vector<ll>> a(n, vector<ll>(m));
	rep(i, n) {
		rep(j, m)cin >> a[i][j];
	}
	vector<vector<vector<ll>>> ans;
	if (n == 1 || m == 1) {
		ans.push_back(a);
	}
	else {
		auto mem = a;
		rep(i, n) {
			a[i].resize(n + m);
			a[i][i + m] = 1;
		}
		int le = 0;
		rep(j, m) {
			if (le == n)break;
			Rep(i, le, n) {
				if (a[i][j]) {
					swap(a[i], a[le]);
					break;
				}
			}
			if (a[le][j]) {
				ll rev = mod_pow(a[le][j], p - 2, p);
				for (int i = le + 1; i < n; i++) {
					ll coef = rev * a[i][j] % p;
					coef = (p - coef) % p;
					for (int k = j; k < n + m; k++) {
						a[i][k] += coef * a[le][k];
						a[i][k] %= p;
					}
				}
				le++;
			}
		}
		if (le == 0) {
			vector<vector<ll>> ans1(n);
			rep(i, n)ans1[i] = { 0 };
			ans.push_back(ans1);
			vector<vector<ll>> ans2(1);
			ans2[0].resize(m, 0);
			ans.push_back(ans2);
		}
		else if (le * (n + m) >= n * m) {
			ans.push_back(mem);
		}
		else {
			//rep(i, n)coutarray(a[i]);
			vector<int> trans(n, -1);
			vector<int> bs;
			rep(i, le)rep(j, n)if (a[i][j + m] != 0)bs.push_back(j);
			sort(all(bs));
			bs.erase(unique(all(bs)), bs.end());
			assert(bs.size() == le);
			bs.erase(unique(all(bs)), bs.end());
			rep(j, bs.size())trans[bs[j]] = j;
			vector<vector<ll>> ans2(le);
			rep(i, le)ans2[i] = mem[bs[i]];
			vector<vector<ll>> ans1(n, vector<ll>(le));
			rep(i, n)if(trans[i]<0) {
				rep(j, le) {
					ans1[i][j] = (p - a[i][bs[j] + m]) % p;
				}
			}
			rep(i, bs.size())ans1[bs[i]][i] = 1;
			ans.push_back(ans1);
			ans.push_back(ans2);
			vector<vector<ll>> t(n, vector<ll>(m));
			rep(i, n)rep(j, le)rep(k, m) {
				t[i][k] += ans1[i][j] * ans2[j][k] % p;
				t[i][k] %= p;
			}
			//rep(i, n)coutarray(t[i]);
		}
	}
	cout << ans.size() << "\n";
	rep(i, ans.size()) {
		auto& sans = ans[i];
		cout << sans.size() << " " << sans[0].size() << "\n";
		rep(j, sans.size())coutarray(sans[j]);
	}
}




signed main() {
	ios::sync_with_stdio(false);
	cin.tie(0);
	//cout << fixed<<setprecision(10);
	//init_f();
	//init();
	//init2();
	//while(true)
	//expr();
	//int t; cin >> t; rep(i, t)
	solve();
	return 0;
}

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結果

テストケース

ソースコード