Submission #212293

#	Time	Username	Problem	Language	Result	Execution time	Memory
212293		ksun48	Ruins 3 (JOI20_ruins3)	C++14	100 / 100	1835 ms	10476 KiB

ruins3

#include <bits/stdc++.h>
using namespace std;

template <int MOD_> struct modnum {
	static constexpr int MOD = MOD_;
	static_assert(MOD_ > 0, "MOD must be positive");

private:
	using ll = long long;

	int v;

	static int minv(int a, int m) {
		a %= m;
		assert(a);
		return a == 1 ? 1 : int(m - ll(minv(m, a)) * ll(m) / a);
	}

public:

	modnum() : v(0) {}
	modnum(ll v_) : v(int(v_ % MOD)) { if (v < 0) v += MOD; }
	explicit operator int() const { return v; }
	friend std::ostream& operator << (std::ostream& out, const modnum& n) { return out << int(n); }
	friend std::istream& operator >> (std::istream& in, modnum& n) { ll v_; in >> v_; n = modnum(v_); return in; }

	friend bool operator == (const modnum& a, const modnum& b) { return a.v == b.v; }
	friend bool operator != (const modnum& a, const modnum& b) { return a.v != b.v; }

	modnum inv() const {
		modnum res;
		res.v = minv(v, MOD);
		return res;
	}
	friend modnum inv(const modnum& m) { return m.inv(); }
	modnum neg() const {
		modnum res;
		res.v = v ? MOD-v : 0;
		return res;
	}
	friend modnum neg(const modnum& m) { return m.neg(); }

	modnum operator- () const {
		return neg();
	}
	modnum operator+ () const {
		return modnum(*this);
	}

	modnum& operator ++ () {
		v ++;
		if (v == MOD) v = 0;
		return *this;
	}
	modnum& operator -- () {
		if (v == 0) v = MOD;
		v --;
		return *this;
	}
	modnum& operator += (const modnum& o) {
		v += o.v;
		if (v >= MOD) v -= MOD;
		return *this;
	}
	modnum& operator -= (const modnum& o) {
		v -= o.v;
		if (v < 0) v += MOD;
		return *this;
	}
	modnum& operator *= (const modnum& o) {
		v = int(ll(v) * ll(o.v) % MOD);
		return *this;
	}
	modnum& operator /= (const modnum& o) {
		return *this *= o.inv();
	}

	friend modnum operator ++ (modnum& a, int) { modnum r = a; ++a; return r; }
	friend modnum operator -- (modnum& a, int) { modnum r = a; --a; return r; }
	friend modnum operator + (const modnum& a, const modnum& b) { return modnum(a) += b; }
	friend modnum operator - (const modnum& a, const modnum& b) { return modnum(a) -= b; }
	friend modnum operator * (const modnum& a, const modnum& b) { return modnum(a) *= b; }
	friend modnum operator / (const modnum& a, const modnum& b) { return modnum(a) /= b; }
};

template <typename T> T pow(T a, long long b) {
	assert(b >= 0);
	T r = 1; while (b) { if (b & 1) r *= a; b >>= 1; a *= a; } return r;
}

using num = modnum<int(1e9) + 7>;

vector<num> fact, ifact;

void init(){
	int N = 1100000;
	fact = {1};
	for(int i = 1; i < N; i++) fact.push_back(i * fact[i-1]);
	ifact.resize(N);
	ifact.back() = 1 / fact.back();
	for(int i = N - 1; i > 0; i--) ifact[i-1] = i * ifact[i];
}

num ncr(int n, int k){
	if(k < 0 || k > n) return 0;
	return fact[n] * ifact[k] * ifact[n-k];
}

int main(){
	ios_base::sync_with_stdio(0), cin.tie(0), cout.tie(0);
	init();
	int n;
	cin >> n;
	vector<int> a(n);
	for(int i = 0; i < n; i++){
		cin >> a[i];
		a[i]--;
	}
	vector<vector<num> > dp(n+1, vector<num>(n+1, 0));
	dp[n][0] = 1;
	for(int j = n-1; j >= 0; j--){
		for(int prev_used = 0; prev_used < n-j; prev_used++){
			num F = 0;
			for(int k = j+1; k <= n; k++) F += dp[k][prev_used];
			for(int cur = 1; cur + prev_used <= n-j; cur++){
				if(F == 0) continue;
				num ways = fact[cur] * fact[cur-1];
				ways *= ncr(2*cur, cur);
				dp[j][cur + prev_used] += F * ncr(n - j - prev_used - 1, cur - 1) * ncr(a[j] - j - n + prev_used + cur, cur) * ways;
			}
		}
	}
	cout << dp[0][n] / pow(num(2), n) << '\n';
}

• Subtask 1: 6 / 6
• Subtask 2: 52 / 52
• Subtask 3: 42 / 42