#738897 (C++17) No.1815 K色問題

提出ソース

結果

問題	No.1815 K色問題
ユーザー	heno239
提出日時	2022-02-12 18:46:54
言語	C++17 (gcc 12.3.0 + boost 1.83.0)
結果	AC
実行時間	538 ms / 2,000 ms
コード長	6,395 bytes
コンパイル時間	2,167 ms
コンパイル使用メモリ	152,484 KB
実行使用メモリ	11,716 KB
最終ジャッジ日時	2024-09-29 22:43:49
合計ジャッジ時間	4,536 ms
ジャッジサーバーID （参考情報）	judge3 / judge1

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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	20 ms 11,588 KB
testcase_01	AC	19 ms 11,712 KB
testcase_02	AC	20 ms 11,716 KB
testcase_03	AC	20 ms 11,588 KB
testcase_04	AC	20 ms 11,592 KB
testcase_05	AC	20 ms 11,716 KB
testcase_06	AC	87 ms 11,584 KB
testcase_07	AC	71 ms 11,716 KB
testcase_08	AC	386 ms 11,716 KB
testcase_09	AC	31 ms 11,592 KB
testcase_10	AC	64 ms 11,592 KB
testcase_11	AC	117 ms 11,712 KB
testcase_12	AC	20 ms 11,716 KB
testcase_13	AC	20 ms 11,716 KB
testcase_14	AC	518 ms 11,716 KB
testcase_15	AC	538 ms 11,716 KB

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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;
//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;
}
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; }
modint operator+=(modint& a, modint b) { a.n += b.n; if (a.n >= mod)a.n -= mod; return a; }
modint operator-=(modint& a, modint b) { a.n -= b.n; if (a.n < 0)a.n += 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;
}
typedef long double ld;
typedef pair<ld, ld> LDP;
const ld eps = 1e-8;
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 = 100005;
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>;


int dx[4] = { 1,0,-1,0 };
int dy[4] = { 0,1,0,-1 };
//-----------------------------------------

typedef array<array<modint,2>,2> mat;
typedef array<modint,2> vec;
mat mtmul(mat& A, mat& B) {
	mat C;
	rep(i, 2)rep(j, 2)C[i][j] = 0;
	rep(i, (int)A.size()) {
		rep(k, (int)B.size()) {
			rep(j, (int)B[0].size()) {
				C[i][j] += A[i][k] * B[k][j];
			}
		}
	}
	return C;
}
mat mtpow(mat A, ll n) {
	mat B;
	rep(i, 2)rep(j, 2)B[i][j] = 0;
	rep(i, (int)A.size()) {
		B[i][i] = 1;
	}
	while (n > 0) {
		if (n & (ll)1)B = mtmul(B, A);
		A = mtmul(A, A);
		n >>= 1;
	}
	return B;
}

modint calc(int n, ll m, int k) {
	if (n == 1) {
		modint res = k;
		if (m > 1) {
			if (k - 1 == 0)res = 0;
			else res *= mod_pow(k - 1, m - 1);
		}
		return res;
	}
	else if (n == 2) {
		modint res = k; res *= k - 1;
		if (m > 1) {
			modint coef = 0;
			coef += (ll)(k - 2) * (k - 3);
			coef += k - 2;
			coef += k - 2;
			coef += 1;
			if (coef == (modint)0)res = 0;
			else res *= mod_pow(coef, m - 1);
		}
		return res;
	}
	else {
		vector<modint> ori(2);
		ori[0] = (modint)k * (modint)(k - 1) * (modint)(k - 2);
		ori[1] = (modint)k * (modint)(k - 1);
		mat A;
		rep(i, 2)rep(j, 2)A[i][j] = 0;
		A[0][0] += (modint)(k - 3) * (modint)(k - 4) * (modint)(k - 5);
		A[0][0] += (modint)6*(modint)(k - 3) * (modint)(k - 4);
		A[0][0] += (modint)9 * (modint)(k - 3);
		A[0][0] += 2;
		A[0][1] += (modint)(k - 2) * (modint)(k - 3) * (modint)(k - 4);
		A[0][1] += (modint)3 * (modint)(k - 2) * (modint)(k - 3);
		A[0][1] += (modint)2 * (modint)(k - 2);
		A[1][0] += (modint)(k - 3) * (modint)(k - 4);
		A[1][0] += (modint)3 * (modint)(k - 3);
		A[1][0] += (modint)2;
		A[1][1] += (modint)(k - 2) * (modint)(k - 3);
		A[1][1] += (modint)2 * (modint)(k - 2);
		A[1][1] += 1;
		A = mtpow(A, m - 1);
		modint res = 0;
		rep(i, 2)rep(j, 2) {
			res += A[i][j] * ori[j];
		}
		return res;
	}
}
void solve() {
	int n; ll m; int k; cin >> n >> m >> k;
	modint ans = 0;
	rep1(c, k) {
		modint val = calc(n, m, c);
		val *= comb(k, c);
		if ((k - c) % 2)val *= -1;
		ans += val;
	}
	cout << ans << "\n";
}
signed main(){
	ios::sync_with_stdio(false);
	cin.tie(0);
	//cout << fixed << setprecision(10);
	init_f();
	//init();
	//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