oj.uz

Submission #777521

# Submission time Handle Problem Language Result Execution time Memory
777521 2023-07-09T10:05:08 Z qwerasdfzxcl Festivals in JOI Kingdom 2 (JOI23_festival2) C++17
87 / 100
 9000 ms 7144 KB 
#include <bits/stdc++.h>

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

ll dpNAIVE[3030][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> karatsuba(const vector<ll> &A, const vector<ll> &B){
	if (A.size()==1){
		return {mul(A[0], B[0])};
	}

	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();

	// naive();
	solve();

	// 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:212:7: warning: ignoring return value of 'int scanf(const char*, ...)' declared with attribute 'warn_unused_result' [-Wunused-result]
  212 |  scanf("%d %d", &n, &MOD);
      |  ~~~~~^~~~~~~~~~~~~~~~~~~

Subtask #1
5.0 / 5.0

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

Subtask #2
5.0 / 5.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 468 KB Output is correct
2 Correct 1 ms 468 KB Output is correct
3 Correct 1 ms 468 KB Output is correct
4 Correct 1 ms 340 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 468 KB Output is correct
8 Correct 1 ms 468 KB Output is correct
9 Correct 1 ms 468 KB Output is correct
10 Correct 1 ms 436 KB Output is correct
11 Correct 1 ms 468 KB Output is correct
12 Correct 1 ms 468 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 468 KB Output is correct
2 Correct 1 ms 468 KB Output is correct
3 Correct 1 ms 468 KB Output is correct
4 Correct 1 ms 340 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 468 KB Output is correct
8 Correct 1 ms 468 KB Output is correct
9 Correct 1 ms 468 KB Output is correct
10 Correct 1 ms 436 KB Output is correct
11 Correct 1 ms 468 KB Output is correct
12 Correct 1 ms 468 KB Output is correct
13 Correct 1 ms 468 KB Output is correct
14 Correct 1 ms 468 KB Output is correct
15 Correct 1 ms 440 KB Output is correct
16 Correct 1 ms 444 KB Output is correct
17 Correct 1 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 1 ms 468 KB Output is correct
2 Correct 1 ms 468 KB Output is correct
3 Correct 1 ms 468 KB Output is correct
4 Correct 1 ms 340 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 468 KB Output is correct
8 Correct 1 ms 468 KB Output is correct
9 Correct 1 ms 468 KB Output is correct
10 Correct 1 ms 436 KB Output is correct
11 Correct 1 ms 468 KB Output is correct
12 Correct 1 ms 468 KB Output is correct
13 Correct 1 ms 468 KB Output is correct
14 Correct 1 ms 468 KB Output is correct
15 Correct 1 ms 440 KB Output is correct
16 Correct 1 ms 444 KB Output is correct
17 Correct 1 ms 468 KB Output is correct
18 Correct 1 ms 468 KB Output is correct
19 Correct 27 ms 596 KB Output is correct
20 Correct 26 ms 576 KB Output is correct
21 Correct 26 ms 592 KB Output is correct
22 Correct 2 ms 444 KB Output is correct
23 Correct 4 ms 436 KB Output is correct

Subtask #5
36.0 / 36.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 468 KB Output is correct
2 Correct 1 ms 468 KB Output is correct
3 Correct 1 ms 468 KB Output is correct
4 Correct 1 ms 340 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 468 KB Output is correct
8 Correct 1 ms 468 KB Output is correct
9 Correct 1 ms 468 KB Output is correct
10 Correct 1 ms 436 KB Output is correct
11 Correct 1 ms 468 KB Output is correct
12 Correct 1 ms 468 KB Output is correct
13 Correct 1 ms 468 KB Output is correct
14 Correct 1 ms 468 KB Output is correct
15 Correct 1 ms 440 KB Output is correct
16 Correct 1 ms 444 KB Output is correct
17 Correct 1 ms 468 KB Output is correct
18 Correct 1 ms 468 KB Output is correct
19 Correct 27 ms 596 KB Output is correct
20 Correct 26 ms 576 KB Output is correct
21 Correct 26 ms 592 KB Output is correct
22 Correct 2 ms 444 KB Output is correct
23 Correct 4 ms 436 KB Output is correct
24 Correct 1024 ms 1564 KB Output is correct
25 Correct 1030 ms 1596 KB Output is correct
26 Correct 996 ms 1740 KB Output is correct
27 Correct 33 ms 596 KB Output is correct
28 Correct 257 ms 976 KB Output is correct
29 Correct 216 ms 920 KB Output is correct

Subtask #6
0 / 13.0

# Verdict Execution time Memory Grader output
1 Correct 1 ms 468 KB Output is correct
2 Correct 1 ms 468 KB Output is correct
3 Correct 1 ms 468 KB Output is correct
4 Correct 1 ms 340 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 468 KB Output is correct
8 Correct 1 ms 468 KB Output is correct
9 Correct 1 ms 468 KB Output is correct
10 Correct 1 ms 436 KB Output is correct
11 Correct 1 ms 468 KB Output is correct
12 Correct 1 ms 468 KB Output is correct
13 Correct 1 ms 468 KB Output is correct
14 Correct 1 ms 468 KB Output is correct
15 Correct 1 ms 440 KB Output is correct
16 Correct 1 ms 444 KB Output is correct
17 Correct 1 ms 468 KB Output is correct
18 Correct 1 ms 468 KB Output is correct
19 Correct 27 ms 596 KB Output is correct
20 Correct 26 ms 576 KB Output is correct
21 Correct 26 ms 592 KB Output is correct
22 Correct 2 ms 444 KB Output is correct
23 Correct 4 ms 436 KB Output is correct
24 Correct 1024 ms 1564 KB Output is correct
25 Correct 1030 ms 1596 KB Output is correct
26 Correct 996 ms 1740 KB Output is correct
27 Correct 33 ms 596 KB Output is correct
28 Correct 257 ms 976 KB Output is correct
29 Correct 216 ms 920 KB Output is correct
30 Execution timed out 9051 ms 7144 KB Time limit exceeded
31 Halted 0 ms 0 KB -