oj.uz

답안 #574620

# 제출 시각 아이디 문제 언어 결과 실행 시간 메모리
574620 2022-06-09T00:12:46 Z penguinhacker 힘 센 거북 (IZhO11_turtle) C++14
100 / 100
 243 ms 12108 KB 
#include <bits/stdc++.h>
using namespace std;

#define ll long long
#define ar array

const int mxN=3e5;
int n, m, k, t, z, cnt[2*mxN+1];
ar<int, 2> cells[22];
vector<ar<int, 2>> pf;
ll f[2*mxN+1], iF[2*mxN+1], ways[22][22], dp1[22], dp2[22][22];
vector<ar<int, 2>> ans_set;

ll bp(ll b, int p, int M) {
	ll r=1;
	for (; p; p/=2, b=b*b%M)
		if (p%2)
			r=r*b%M;
	return r;
}

ll C(int a, int b, ar<int, 2> prime, int pp) {
	assert(0<=b&&b<=a&&a<=n+m);
	int pwr=cnt[a]-cnt[b]-cnt[a-b];
	assert(pwr>=0);
	if (pwr>=prime[1])
		return 0;
	ll r=f[a]*iF[b]%pp*iF[a-b]%pp;
	while(pwr--)
		r=r*prime[0]%pp;
	return r;
}

bool ord(int i, int j) {
	return cells[i][0]<=cells[j][0]&&cells[i][1]<=cells[j][1];
}

void solve(ar<int, 2> prime) {
	int pp=1;
	for (int i=0; i<prime[1]; ++i)
		pp*=prime[0];
	f[0]=1, iF[0]=1;
	for (int i=1; i<=n+m; ++i) {
		int x=i;
		cnt[i]=cnt[i-1];
		while(x%prime[0]==0)
			x/=prime[0], ++cnt[i];
		f[i]=f[i-1]*x%pp;
		iF[i]=bp(f[i], pp/prime[0]*(prime[0]-1)-1, pp);
	}
	auto Go=[&](int i, int j) {
		assert(ord(i, j));
		int x=cells[j][0]-cells[i][0];
		int y=cells[j][1]-cells[i][1];
		return C(x+y, x, prime, pp);
	};
	for (int i=0; i<k+2; ++i)
		for (int j=i+1; j<k+2; ++j) {
			assert(cells[i]!=cells[j]&&cells[i][0]<=cells[j][0]);
			if (!ord(i, j)) {
				ways[i][j]=0;
				continue;
			}
			ways[i][j]=Go(i, j);
			for (int a=i+1; a<j; ++a) {
				if (ord(i, a)&&ord(a, j)) {
					dp1[a]=Go(i, a);
					for (int b=i+1; b<a; ++b)
						if (ord(i, b)&&ord(b, a))
							dp1[a]=(dp1[a]-dp1[b]*Go(b, a)%pp+pp)%pp;
					ways[i][j]=(ways[i][j]-dp1[a]*Go(a, j)%pp+pp)%pp;
				}
			}
		}
	memset(dp2, 0, sizeof(dp2));
	dp2[0][0]=1;
	for (int i=1; i<k+2; ++i)
		for (int j=1; j<k+2; ++j)
			for (int a=0; a<i; ++a)
				if (ord(a, i))
					dp2[i][j]=(dp2[i][j]+dp2[a][j-1]*ways[a][i])%pp;
	ll tot=0;
	for (int i=0; i<=t+1; ++i)
		tot=(tot+dp2[k+1][i])%pp;
	//cout << tot << " " << pp << endl;
	ans_set.push_back({(int)tot, pp});
}

ar<int, 2> mrg(ar<int, 2> a, ar<int, 2> b) {
	assert(a[1]<b[1]);
	ar<int, 2> c={b[0], a[1]*b[1]};
	for (int i=1; i<a[1]; ++i) {
		if (c[0]%a[1]==a[0])
			break;
		c[0]+=b[1];
	}
	assert(c[0]%a[1]==a[0]);
	return c;
}

int main() {
	ios::sync_with_stdio(0);
	cin.tie(0);
	cin >> n >> m >> k >> t >> z; // can hit <=t traps
	t=min(t, k);
	if (z==1) {
		cout << 0;
		return 0;
	}
	for (int i=2; i*i<=z; ++i) {
		if (z%i==0) {
			int c=0;
			while(z%i==0)
				z/=i, ++c;
			pf.push_back({i, c});
		}
	}
	if (z>1)
		pf.push_back({z, 1});
	for (int i=0; i<k; ++i)
		cin >> cells[i][0] >> cells[i][1];
	cells[k+1]={n, m};
	sort(cells, cells+k+2);
	for (ar<int, 2> prime : pf)
		solve(prime);
	sort(ans_set.begin(), ans_set.end(), [&](ar<int, 2> a, ar<int, 2> b) { return a[1]<b[1]; });
	while(ans_set.size()>1) {
		ar<int, 2> b=ans_set.back();
		ans_set.pop_back();
		ar<int, 2> a=ans_set.back();
		ans_set.pop_back();
		ans_set.push_back(mrg(a, b));
	}
	cout << ans_set[0][0];
	return 0;
}

Subtask #1
100.0 / 100.0

# 결과 실행 시간 메모리 Grader output
1 Correct 1 ms 340 KB Output is correct
2 Correct 1 ms 340 KB Output is correct
3 Correct 0 ms 340 KB Output is correct
4 Correct 1 ms 276 KB Output is correct
5 Correct 1 ms 340 KB Output is correct
6 Correct 1 ms 340 KB Output is correct
7 Correct 1 ms 340 KB Output is correct
8 Correct 1 ms 340 KB Output is correct
9 Correct 3 ms 468 KB Output is correct
10 Correct 5 ms 724 KB Output is correct
11 Correct 44 ms 4152 KB Output is correct
12 Correct 132 ms 12028 KB Output is correct
13 Correct 215 ms 10104 KB Output is correct
14 Correct 79 ms 4228 KB Output is correct
15 Correct 79 ms 4236 KB Output is correct
16 Correct 227 ms 11428 KB Output is correct
17 Correct 223 ms 11080 KB Output is correct
18 Correct 231 ms 12032 KB Output is correct
19 Correct 236 ms 12052 KB Output is correct
20 Correct 243 ms 12108 KB Output is correct