oj.uz

Submission #777540

# Submission time Handle Problem Language Result Execution time Memory
777540 2023-07-09T10:18:42 Z qwerasdfzxcl Festivals in JOI Kingdom 2 (JOI23_festival2) C++17
100 / 100
 4133 ms 8116 KB 
#include <bits/stdc++.h>

using namespace std;
typedef long long ll;
int n, MOD;

ll dpNAIVE[100100][2];
ll P[9][100100], Q[9][100100], R[9][100100], dp[100100][2];

ll fact[100100], factINV[100100];

inline void add(ll &x, const ll &y){
	x += y;
	if (x>=MOD) x -= MOD;
}

inline ll mul(const vector<ll> &a){
	ll ret = 1;
	for (auto &x:a) ret = ret * x % MOD;
	return ret;
}

inline ll mul(ll x, ll y){
	return x * y % MOD;
}

vector<ll> operator +(const vector<ll> &A, const vector<ll> &B){
	vector<ll> ret(max(A.size(), B.size()));
	for (int i=0;i<(int)ret.size();i++){
		if (i<(int)A.size()) add(ret[i], A[i]);
		if (i<(int)B.size()) add(ret[i], B[i]);
	}

	return ret;
}

vector<ll> cut(ll a[], int l, int r){
	vector<ll> ret(r-l+1);
	for (int i=0;i<(int)ret.size();i++) ret[i] = a[l+i];
	return ret;
}

vector<ll> cut(const vector<ll> &a, int l, int r){
	vector<ll> ret(r-l+1);
	for (int i=0;i<(int)ret.size();i++) ret[i] = a[l+i];
	return ret;	
}

ll pw(ll a, ll e){
	if (!e) return 1;
	ll ret = pw(a, e/2);
	if (e&1) return ret * ret % MOD * a % MOD;
	return ret * ret % MOD;
}

ll all(){
	ll ret = 1;
	for (int i=1;i<=n;i++) ret = ret * (i*2-1) % MOD;
	return ret;
}

void init(){
	fact[0] = 1;
	for (int i=1;i<=n*3+100;i++) fact[i] = fact[i-1] * i % MOD;
	factINV[n*3+100] = pw(fact[n*3+100], MOD-2);
	for (int i=n*3+99;i>=0;i--) factINV[i] = factINV[i+1] * (i+1) % MOD;
}

void naive(){
	dpNAIVE[2][0] = 1;
	dpNAIVE[1][1] = 1;

	for (int i=1;i<=n;i++){
		for (int j=0;i+j<=n;j++){
			if (i>1) add(dpNAIVE[i+j+2][0], mul({dpNAIVE[i][0], j+2, j+1, fact[2*i-2 + (j-1)], factINV[2*i-3]}));
			if (i>0) add(dpNAIVE[i+j+2][0], mul({dpNAIVE[i][1],      j+1, fact[2*i-1 + (j-1)], factINV[2*i-2]}));
			if (i>1) add(dpNAIVE[i+j+1][1], mul({dpNAIVE[i][0],      j+1, fact[2*i-2 + (j-1)], factINV[2*i-3]}));
			if (i>0) add(dpNAIVE[i+j+1][1], mul({dpNAIVE[i][1],           fact[2*i-1 + (j-1)], factINV[2*i-2]}));
		}
	}
}

vector<ll> naive(const vector<ll> &A, const vector<ll> &B){
	vector<ll> ret(A.size() + B.size() - 1);
	for (int i=0;i<(int)A.size();i++){
		for (int j=0;j<(int)B.size();j++){
			add(ret[i+j], A[i] * B[j] % MOD);
		}
	}

	return ret;
}

vector<ll> karatsuba(const vector<ll> &A, const vector<ll> &B){
	if (A.size() <= 10) return naive(A, B);

	int mid = (int)A.size() / 2;
	auto A2 = cut(A, 0, mid-1), A1 = cut(A, mid, (int)A.size()-1);
	auto B2 = cut(B, 0, mid-1), B1 = cut(B, mid, (int)B.size()-1);
	
	auto C1 = karatsuba(A1, B1), C2 = karatsuba(A2, B2), C3 = karatsuba(A1+A2, B1+B2);
	C2.resize(C1.size());

	assert(C1.size() == C2.size());
	assert(C1.size() == C3.size());
	
	vector<ll> ret(A.size()+B.size()-1);
	for (int i=0;i<(int)C1.size();i++) add(ret[i+mid*2], C1[i]);
	for (int i=0;i<(int)C2.size();i++) add(ret[i], C2[i]);
	for (int i=0;i<(int)C3.size();i++) add(ret[i+mid], (C3[i] - C1[i] - C2[i] + (ll)MOD*2) % MOD);

	return ret;
}

pair<vector<ll>, int> myConv(vector<ll> A, vector<ll> B){
	int ofs = (int)A.size()-1;
	int sz = max(A.size(), B.size());
	assert(A.size() <= B.size());

	reverse(A.begin(), A.end());
	A.resize(sz);

	return {karatsuba(A, B), ofs};
}

void dnc(int l, int r){
	if (l==r){
		if (l==1){
			dp[1][0] = 0;
			dp[1][1] = 1;
		}

		else if (l==2){
			dp[2][0] = 1;
			dp[2][1] = 1;
		}

		else{
			add(dp[l][0], R[1][l]);
			add(dp[l][0], mul(R[2][l], (MOD-l*2+1)));
			add(dp[l][0], mul(R[3][l], mul(l, l)-l+MOD));
			
			add(dp[l][0], R[4][l]);
			add(dp[l][0], mul(R[5][l], l-1));

			add(dp[l][1], R[6][l]);
			add(dp[l][1], mul(R[7][l], l));

			add(dp[l][1], R[8][l]);
		}

		if (l>=2){
			P[1][l] = mul({dp[l][0], l, l, factINV[2*l-3]});
			P[2][l] = mul({dp[l][0], l, factINV[2*l-3]});
			P[3][l] = mul(dp[l][0], factINV[2*l-3]);

			P[6][l] = mul({dp[l][0], MOD-l, factINV[2*l-3]});
			P[7][l] = mul(dp[l][0], factINV[2*l-3]);
		}

		if (l>=1){
			P[4][l] = mul({dp[l][1], MOD-l, factINV[2*l-2]});
			P[5][l] = mul(dp[l][1], factINV[2*l-2]);

			P[8][l] = mul(dp[l][1], factINV[2*l-2]);
		}

		return;
	}

	int m = (l+r)>>1;
	dnc(l, m);

	for (int k=1;k<=8;k++){
		auto [ret, ofs] = myConv(cut(P[k], l, m), cut(Q[k], m+1+l, m+r));

		for (int i=m+1;i<=r;i++) add(R[k][i], ret[ofs+(i-m-1)]);
	}

	dnc(m+1, r);
}

void solve(){
	for (int i=0;i<=n*2+100;i++){
		if (i>=5) Q[1][i] = Q[2][i] = Q[3][i] = fact[i-5];
		if (i>=4) Q[4][i] = Q[5][i] = fact[i-4];
		if (i>=4) Q[6][i] = Q[7][i] = fact[i-4];
		if (i>=3) Q[8][i] = fact[i-3];
	}

	dnc(1, n+1);
}

int main(){
	scanf("%d %d", &n, &MOD);
	
	init();
	solve();

	printf("%lld\n", (all() + MOD - dp[n+1][1]) % MOD);

}

Compilation message

festival2.cpp: In function 'int main()':
festival2.cpp:195:7: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
  195 |  scanf("%d %d", &n, &MOD);
      |  ~~~~~^~~~~~~~~~~~~~~~~~~

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 436 KB Output is correct
2 Correct 1 ms 468 KB Output is correct
3 Correct 1 ms 432 KB Output is correct
4 Correct 1 ms 540 KB Output is correct
5 Correct 1 ms 468 KB Output is correct
6 Correct 1 ms 468 KB Output is correct
7 Correct 1 ms 436 KB Output is correct

Subtask #2
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 436 KB Output is correct
2 Correct 1 ms 468 KB Output is correct
3 Correct 1 ms 432 KB Output is correct
4 Correct 1 ms 540 KB Output is correct
5 Correct 1 ms 468 KB Output is correct
6 Correct 1 ms 468 KB Output is correct
7 Correct 1 ms 436 KB Output is correct
8 Correct 1 ms 432 KB Output is correct
9 Correct 1 ms 468 KB Output is correct
10 Correct 1 ms 468 KB Output is correct
11 Correct 1 ms 436 KB Output is correct
12 Correct 1 ms 432 KB Output is correct
13 Correct 1 ms 468 KB Output is correct

Subtask #3
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 436 KB Output is correct
2 Correct 1 ms 468 KB Output is correct
3 Correct 1 ms 432 KB Output is correct
4 Correct 1 ms 540 KB Output is correct
5 Correct 1 ms 468 KB Output is correct
6 Correct 1 ms 468 KB Output is correct
7 Correct 1 ms 436 KB Output is correct
8 Correct 1 ms 432 KB Output is correct
9 Correct 1 ms 468 KB Output is correct
10 Correct 1 ms 468 KB Output is correct
11 Correct 1 ms 436 KB Output is correct
12 Correct 1 ms 432 KB Output is correct
13 Correct 1 ms 468 KB Output is correct
14 Correct 1 ms 436 KB Output is correct
15 Correct 1 ms 468 KB Output is correct
16 Correct 1 ms 468 KB Output is correct
17 Correct 1 ms 432 KB Output is correct
18 Correct 1 ms 468 KB Output is correct

Subtask #4
14.0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 436 KB Output is correct
2 Correct 1 ms 468 KB Output is correct
3 Correct 1 ms 432 KB Output is correct
4 Correct 1 ms 540 KB Output is correct
5 Correct 1 ms 468 KB Output is correct
6 Correct 1 ms 468 KB Output is correct
7 Correct 1 ms 436 KB Output is correct
8 Correct 1 ms 432 KB Output is correct
9 Correct 1 ms 468 KB Output is correct
10 Correct 1 ms 468 KB Output is correct
11 Correct 1 ms 436 KB Output is correct
12 Correct 1 ms 432 KB Output is correct
13 Correct 1 ms 468 KB Output is correct
14 Correct 1 ms 436 KB Output is correct
15 Correct 1 ms 468 KB Output is correct
16 Correct 1 ms 468 KB Output is correct
17 Correct 1 ms 432 KB Output is correct
18 Correct 1 ms 468 KB Output is correct
19 Correct 6 ms 596 KB Output is correct
20 Correct 6 ms 596 KB Output is correct
21 Correct 6 ms 596 KB Output is correct
22 Correct 1 ms 436 KB Output is correct
23 Correct 2 ms 468 KB Output is correct

Subtask #5
36.0 / 36.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 436 KB Output is correct
2 Correct 1 ms 468 KB Output is correct
3 Correct 1 ms 432 KB Output is correct
4 Correct 1 ms 540 KB Output is correct
5 Correct 1 ms 468 KB Output is correct
6 Correct 1 ms 468 KB Output is correct
7 Correct 1 ms 436 KB Output is correct
8 Correct 1 ms 432 KB Output is correct
9 Correct 1 ms 468 KB Output is correct
10 Correct 1 ms 468 KB Output is correct
11 Correct 1 ms 436 KB Output is correct
12 Correct 1 ms 432 KB Output is correct
13 Correct 1 ms 468 KB Output is correct
14 Correct 1 ms 436 KB Output is correct
15 Correct 1 ms 468 KB Output is correct
16 Correct 1 ms 468 KB Output is correct
17 Correct 1 ms 432 KB Output is correct
18 Correct 1 ms 468 KB Output is correct
19 Correct 6 ms 596 KB Output is correct
20 Correct 6 ms 596 KB Output is correct
21 Correct 6 ms 596 KB Output is correct
22 Correct 1 ms 436 KB Output is correct
23 Correct 2 ms 468 KB Output is correct
24 Correct 206 ms 1532 KB Output is correct
25 Correct 199 ms 1556 KB Output is correct
26 Correct 212 ms 1560 KB Output is correct
27 Correct 7 ms 620 KB Output is correct
28 Correct 49 ms 980 KB Output is correct
29 Correct 44 ms 876 KB Output is correct

Subtask #6
13.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 436 KB Output is correct
2 Correct 1 ms 468 KB Output is correct
3 Correct 1 ms 432 KB Output is correct
4 Correct 1 ms 540 KB Output is correct
5 Correct 1 ms 468 KB Output is correct
6 Correct 1 ms 468 KB Output is correct
7 Correct 1 ms 436 KB Output is correct
8 Correct 1 ms 432 KB Output is correct
9 Correct 1 ms 468 KB Output is correct
10 Correct 1 ms 468 KB Output is correct
11 Correct 1 ms 436 KB Output is correct
12 Correct 1 ms 432 KB Output is correct
13 Correct 1 ms 468 KB Output is correct
14 Correct 1 ms 436 KB Output is correct
15 Correct 1 ms 468 KB Output is correct
16 Correct 1 ms 468 KB Output is correct
17 Correct 1 ms 432 KB Output is correct
18 Correct 1 ms 468 KB Output is correct
19 Correct 6 ms 596 KB Output is correct
20 Correct 6 ms 596 KB Output is correct
21 Correct 6 ms 596 KB Output is correct
22 Correct 1 ms 436 KB Output is correct
23 Correct 2 ms 468 KB Output is correct
24 Correct 206 ms 1532 KB Output is correct
25 Correct 199 ms 1556 KB Output is correct
26 Correct 212 ms 1560 KB Output is correct
27 Correct 7 ms 620 KB Output is correct
28 Correct 49 ms 980 KB Output is correct
29 Correct 44 ms 876 KB Output is correct
30 Correct 4006 ms 8116 KB Output is correct
31 Correct 4133 ms 8088 KB Output is correct
32 Correct 4008 ms 7948 KB Output is correct
33 Correct 2277 ms 6288 KB Output is correct
34 Correct 606 ms 2708 KB Output is correct
35 Correct 571 ms 2536 KB Output is correct