oj.uz

Submission #777531

# Submission time Handle Problem Language Result Execution time Memory
777531 2023-07-09T10:16:26 Z qwerasdfzxcl Festivals in JOI Kingdom 2 (JOI23_festival2) C++17
87 / 100
 9000 ms 7792 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() <= 500) 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 0 ms 468 KB Output is correct
2 Correct 1 ms 340 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 1 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 0 ms 468 KB Output is correct
2 Correct 1 ms 340 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 1 ms 468 KB Output is correct
7 Correct 0 ms 468 KB Output is correct
8 Correct 1 ms 340 KB Output is correct
9 Correct 0 ms 468 KB Output is correct
10 Correct 0 ms 468 KB Output is correct
11 Correct 1 ms 340 KB Output is correct
12 Correct 0 ms 468 KB Output is correct
13 Correct 0 ms 468 KB Output is correct

Subtask #3
27.0 / 27.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 468 KB Output is correct
2 Correct 1 ms 340 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 1 ms 468 KB Output is correct
7 Correct 0 ms 468 KB Output is correct
8 Correct 1 ms 340 KB Output is correct
9 Correct 0 ms 468 KB Output is correct
10 Correct 0 ms 468 KB Output is correct
11 Correct 1 ms 340 KB Output is correct
12 Correct 0 ms 468 KB Output is correct
13 Correct 0 ms 468 KB Output is correct
14 Correct 0 ms 340 KB Output is correct
15 Correct 0 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 1 ms 468 KB Output is correct

Subtask #4
14.0 / 14.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 468 KB Output is correct
2 Correct 1 ms 340 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 1 ms 468 KB Output is correct
7 Correct 0 ms 468 KB Output is correct
8 Correct 1 ms 340 KB Output is correct
9 Correct 0 ms 468 KB Output is correct
10 Correct 0 ms 468 KB Output is correct
11 Correct 1 ms 340 KB Output is correct
12 Correct 0 ms 468 KB Output is correct
13 Correct 0 ms 468 KB Output is correct
14 Correct 0 ms 340 KB Output is correct
15 Correct 0 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 1 ms 468 KB Output is correct
19 Correct 10 ms 468 KB Output is correct
20 Correct 9 ms 468 KB Output is correct
21 Correct 9 ms 468 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 0 ms 468 KB Output is correct
2 Correct 1 ms 340 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 1 ms 468 KB Output is correct
7 Correct 0 ms 468 KB Output is correct
8 Correct 1 ms 340 KB Output is correct
9 Correct 0 ms 468 KB Output is correct
10 Correct 0 ms 468 KB Output is correct
11 Correct 1 ms 340 KB Output is correct
12 Correct 0 ms 468 KB Output is correct
13 Correct 0 ms 468 KB Output is correct
14 Correct 0 ms 340 KB Output is correct
15 Correct 0 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 1 ms 468 KB Output is correct
19 Correct 10 ms 468 KB Output is correct
20 Correct 9 ms 468 KB Output is correct
21 Correct 9 ms 468 KB Output is correct
22 Correct 1 ms 468 KB Output is correct
23 Correct 1 ms 468 KB Output is correct
24 Correct 564 ms 1580 KB Output is correct
25 Correct 561 ms 1480 KB Output is correct
26 Correct 563 ms 1500 KB Output is correct
27 Correct 11 ms 560 KB Output is correct
28 Correct 119 ms 872 KB Output is correct
29 Correct 97 ms 944 KB Output is correct

Subtask #6
0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 0 ms 468 KB Output is correct
2 Correct 1 ms 340 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 1 ms 468 KB Output is correct
7 Correct 0 ms 468 KB Output is correct
8 Correct 1 ms 340 KB Output is correct
9 Correct 0 ms 468 KB Output is correct
10 Correct 0 ms 468 KB Output is correct
11 Correct 1 ms 340 KB Output is correct
12 Correct 0 ms 468 KB Output is correct
13 Correct 0 ms 468 KB Output is correct
14 Correct 0 ms 340 KB Output is correct
15 Correct 0 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 1 ms 468 KB Output is correct
19 Correct 10 ms 468 KB Output is correct
20 Correct 9 ms 468 KB Output is correct
21 Correct 9 ms 468 KB Output is correct
22 Correct 1 ms 468 KB Output is correct
23 Correct 1 ms 468 KB Output is correct
24 Correct 564 ms 1580 KB Output is correct
25 Correct 561 ms 1480 KB Output is correct
26 Correct 563 ms 1500 KB Output is correct
27 Correct 11 ms 560 KB Output is correct
28 Correct 119 ms 872 KB Output is correct
29 Correct 97 ms 944 KB Output is correct
30 Execution timed out 9066 ms 7792 KB Time limit exceeded
31 Halted 0 ms 0 KB -