oj.uz

Submission #777532

# Submission time Handle Problem Language Result Execution time Memory
777532 2023-07-09T10:16:51 Z qwerasdfzxcl Festivals in JOI Kingdom 2 (JOI23_festival2) C++17
100 / 100
 5492 ms 7912 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]}));
		}
	}

	// for (int i=1;i<=n+1;i++){
	// 	printf("%d -> %lld %lld (naive)\n", i, dpNAIVE[i][0], dpNAIVE[i][1]);
	// }
}

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() <= 50) 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());

	// printf("ok size %d %d -> %d %d %d\n", (int)A1.size(), (int)A2.size(), (int)C1.size(), (int)C2.size(), (int)C3.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){
	// C[j-i] = \sum A[i] * B[j]
	// ret[ofs+x] = C[x]

	// printf("A: ");
	// for (auto &x:A) printf("%lld ", x);
	// printf("\n");
	// printf("B: ");
	// for (auto &x:B) printf("%lld ", x);
	// printf("\n");

	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]);
			// printf("ok dp[3][1] = %lld\n", dp[3][1]);
			add(dp[l][1], mul(R[7][l], l));
			// printf("ok dp[3][1] = %lld\n", dp[3][1]);

			add(dp[l][1], R[8][l]);
			// printf("ok dp[3][1] = %lld (%lld)\n", dp[3][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]);
		}

		// printf("%d -> %lld %lld\n", l, dp[l][0], dp[l][1]);

		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));

		// printf("Conv: ");
		// for (auto &x:ret) printf("%lld ", x);
		// printf("(ofs = %d)\n\n", ofs);
		for (int i=m+1;i<=r;i++) add(R[k][i], ret[ofs+(i-m-1)]);

		// if (k==8) printf("ok %lld\n", R[8][2]);
	}

	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();

	// printf("naive start\n");
	// auto st = clock();
	// naive();
	// printf("naive end: %fs\n", (double)(clock()-st)/CLOCKS_PER_SEC);
	// st = clock();
	// printf("solve start\n");
	solve();
	// printf("solve end: %fs\n", (double)(clock()-st)/CLOCKS_PER_SEC);

	// printf("ok %lld %lld\n", dpNAIVE[n+1][1], dp[n+1][1]);

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

}

Compilation message

festival2.cpp: In function 'int main()':
festival2.cpp:221:7: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
  221 |  scanf("%d %d", &n, &MOD);
      |  ~~~~~^~~~~~~~~~~~~~~~~~~

Subtask #1
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB Output is correct
2 Correct 0 ms 468 KB Output is correct
3 Correct 0 ms 468 KB Output is correct
4 Correct 0 ms 468 KB Output is correct
5 Correct 0 ms 468 KB Output is correct
6 Correct 0 ms 468 KB Output is correct
7 Correct 0 ms 468 KB Output is correct

Subtask #2
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB Output is correct
2 Correct 0 ms 468 KB Output is correct
3 Correct 0 ms 468 KB Output is correct
4 Correct 0 ms 468 KB Output is correct
5 Correct 0 ms 468 KB Output is correct
6 Correct 0 ms 468 KB Output is correct
7 Correct 0 ms 468 KB Output is correct
8 Correct 0 ms 468 KB Output is correct
9 Correct 1 ms 340 KB Output is correct
10 Correct 0 ms 468 KB Output is correct
11 Correct 1 ms 468 KB Output is correct
12 Correct 1 ms 340 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 340 KB Output is correct
2 Correct 0 ms 468 KB Output is correct
3 Correct 0 ms 468 KB Output is correct
4 Correct 0 ms 468 KB Output is correct
5 Correct 0 ms 468 KB Output is correct
6 Correct 0 ms 468 KB Output is correct
7 Correct 0 ms 468 KB Output is correct
8 Correct 0 ms 468 KB Output is correct
9 Correct 1 ms 340 KB Output is correct
10 Correct 0 ms 468 KB Output is correct
11 Correct 1 ms 468 KB Output is correct
12 Correct 1 ms 340 KB Output is correct
13 Correct 1 ms 468 KB Output is correct
14 Correct 1 ms 340 KB Output is correct
15 Correct 1 ms 468 KB Output is correct
16 Correct 1 ms 468 KB Output is correct
17 Correct 0 ms 468 KB Output is correct
18 Correct 0 ms 468 KB Output is correct

Subtask #4
14.0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB Output is correct
2 Correct 0 ms 468 KB Output is correct
3 Correct 0 ms 468 KB Output is correct
4 Correct 0 ms 468 KB Output is correct
5 Correct 0 ms 468 KB Output is correct
6 Correct 0 ms 468 KB Output is correct
7 Correct 0 ms 468 KB Output is correct
8 Correct 0 ms 468 KB Output is correct
9 Correct 1 ms 340 KB Output is correct
10 Correct 0 ms 468 KB Output is correct
11 Correct 1 ms 468 KB Output is correct
12 Correct 1 ms 340 KB Output is correct
13 Correct 1 ms 468 KB Output is correct
14 Correct 1 ms 340 KB Output is correct
15 Correct 1 ms 468 KB Output is correct
16 Correct 1 ms 468 KB Output is correct
17 Correct 0 ms 468 KB Output is correct
18 Correct 0 ms 468 KB Output is correct
19 Correct 7 ms 596 KB Output is correct
20 Correct 6 ms 576 KB Output is correct
21 Correct 6 ms 596 KB Output is correct
22 Correct 1 ms 468 KB Output is correct
23 Correct 1 ms 468 KB Output is correct

Subtask #5
36.0 / 36.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB Output is correct
2 Correct 0 ms 468 KB Output is correct
3 Correct 0 ms 468 KB Output is correct
4 Correct 0 ms 468 KB Output is correct
5 Correct 0 ms 468 KB Output is correct
6 Correct 0 ms 468 KB Output is correct
7 Correct 0 ms 468 KB Output is correct
8 Correct 0 ms 468 KB Output is correct
9 Correct 1 ms 340 KB Output is correct
10 Correct 0 ms 468 KB Output is correct
11 Correct 1 ms 468 KB Output is correct
12 Correct 1 ms 340 KB Output is correct
13 Correct 1 ms 468 KB Output is correct
14 Correct 1 ms 340 KB Output is correct
15 Correct 1 ms 468 KB Output is correct
16 Correct 1 ms 468 KB Output is correct
17 Correct 0 ms 468 KB Output is correct
18 Correct 0 ms 468 KB Output is correct
19 Correct 7 ms 596 KB Output is correct
20 Correct 6 ms 576 KB Output is correct
21 Correct 6 ms 596 KB Output is correct
22 Correct 1 ms 468 KB Output is correct
23 Correct 1 ms 468 KB Output is correct
24 Correct 278 ms 1524 KB Output is correct
25 Correct 277 ms 1572 KB Output is correct
26 Correct 277 ms 1564 KB Output is correct
27 Correct 7 ms 596 KB Output is correct
28 Correct 62 ms 904 KB Output is correct
29 Correct 51 ms 904 KB Output is correct

Subtask #6
13.0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 340 KB Output is correct
2 Correct 0 ms 468 KB Output is correct
3 Correct 0 ms 468 KB Output is correct
4 Correct 0 ms 468 KB Output is correct
5 Correct 0 ms 468 KB Output is correct
6 Correct 0 ms 468 KB Output is correct
7 Correct 0 ms 468 KB Output is correct
8 Correct 0 ms 468 KB Output is correct
9 Correct 1 ms 340 KB Output is correct
10 Correct 0 ms 468 KB Output is correct
11 Correct 1 ms 468 KB Output is correct
12 Correct 1 ms 340 KB Output is correct
13 Correct 1 ms 468 KB Output is correct
14 Correct 1 ms 340 KB Output is correct
15 Correct 1 ms 468 KB Output is correct
16 Correct 1 ms 468 KB Output is correct
17 Correct 0 ms 468 KB Output is correct
18 Correct 0 ms 468 KB Output is correct
19 Correct 7 ms 596 KB Output is correct
20 Correct 6 ms 576 KB Output is correct
21 Correct 6 ms 596 KB Output is correct
22 Correct 1 ms 468 KB Output is correct
23 Correct 1 ms 468 KB Output is correct
24 Correct 278 ms 1524 KB Output is correct
25 Correct 277 ms 1572 KB Output is correct
26 Correct 277 ms 1564 KB Output is correct
27 Correct 7 ms 596 KB Output is correct
28 Correct 62 ms 904 KB Output is correct
29 Correct 51 ms 904 KB Output is correct
30 Correct 5297 ms 7864 KB Output is correct
31 Correct 5482 ms 7656 KB Output is correct
32 Correct 5492 ms 7912 KB Output is correct
33 Correct 3206 ms 5680 KB Output is correct
34 Correct 881 ms 2688 KB Output is correct
35 Correct 733 ms 2572 KB Output is correct