oj.uz

Submission #211928

# Submission time Handle Problem Language Result Execution time Memory
211928 2020-03-21T18:33:59 Z Benq Ruins 3 (JOI20_ruins3) C++14
100 / 100
 214 ms 3320 KB 
#include <bits/stdc++.h>
using namespace std;
 
typedef long long ll;
typedef long double ld;
typedef double db; 
typedef string str; 

typedef pair<int,int> pi;
typedef pair<ll,ll> pl; 
typedef pair<db,db> pd; 

typedef vector<int> vi; 
typedef vector<ll> vl; 
typedef vector<db> vd; 
typedef vector<str> vs; 
typedef vector<pi> vpi;
typedef vector<pl> vpl; 
typedef vector<pd> vpd; 

#define mp make_pair 
#define f first
#define s second
#define sz(x) (int)x.size()
#define all(x) begin(x), end(x)
#define rall(x) (x).rbegin(), (x).rend() 
#define rsz resize
#define ins insert 
#define ft front() 
#define bk back()
#define pf push_front 
#define pb push_back
#define eb emplace_back 
#define lb lower_bound 
#define ub upper_bound 

#define FOR(i,a,b) for (int i = (a); i < (b); ++i)
#define F0R(i,a) FOR(i,0,a)
#define ROF(i,a,b) for (int i = (b)-1; i >= (a); --i)
#define R0F(i,a) ROF(i,0,a)
#define trav(a,x) for (auto& a: x)

const int MOD = 1e9+7; // 998244353;
const int MX = 2e5+5; 
const ll INF = 1e18; 
const ld PI = acos((ld)-1);
const int xd[4] = {1,0,-1,0}, yd[4] = {0,1,0,-1}; 

template<class T> bool ckmin(T& a, const T& b) { 
	return b < a ? a = b, 1 : 0; }
template<class T> bool ckmax(T& a, const T& b) { 
	return a < b ? a = b, 1 : 0; } 
int pct(int x) { return __builtin_popcount(x); } 
int bit(int x) { return 31-__builtin_clz(x); } // floor(log2(x)) 
int cdiv(int a, int b) { return a/b+!(a<0||a%b == 0); } // division of a by b rounded up, assumes b > 0 

// INPUT
template<class A> void re(complex<A>& c);
template<class A, class B> void re(pair<A,B>& p);
template<class A> void re(vector<A>& v);
template<class A, size_t SZ> void re(array<A,SZ>& a);

template<class T> void re(T& x) { cin >> x; }
void re(db& d) { str t; re(t); d = stod(t); }
void re(ld& d) { str t; re(t); d = stold(t); }
template<class H, class... T> void re(H& h, T&... t) { re(h); re(t...); }

template<class A> void re(complex<A>& c) { A a,b; re(a,b); c = {a,b}; }
template<class A, class B> void re(pair<A,B>& p) { re(p.f,p.s); }
template<class A> void re(vector<A>& x) { trav(a,x) re(a); }
template<class A, size_t SZ> void re(array<A,SZ>& x) { trav(a,x) re(a); }

// TO_STRING
#define ts to_string
template<class A, class B> str ts(pair<A,B> p);
template<class A> str ts(complex<A> c) { return ts(mp(c.real(),c.imag())); }
str ts(bool b) { return b ? "true" : "false"; }
str ts(char c) { str s = ""; s += c; return s; }
str ts(str s) { return s; }
str ts(const char* s) { return (str)s; }
str ts(vector<bool> v) { 
	bool fst = 1; str res = "{";
	F0R(i,sz(v)) {
		if (!fst) res += ", ";
		fst = 0; res += ts(v[i]);
	}
	res += "}"; return res;
}
template<size_t SZ> str ts(bitset<SZ> b) {
	str res = ""; F0R(i,SZ) res += char('0'+b[i]);
	return res; }
template<class T> str ts(T v) {
	bool fst = 1; str res = "{";
	for (const auto& x: v) {
		if (!fst) res += ", ";
		fst = 0; res += ts(x);
	}
	res += "}"; return res;
}
template<class A, class B> str ts(pair<A,B> p) {
	return "("+ts(p.f)+", "+ts(p.s)+")"; }

// OUTPUT
template<class A> void pr(A x) { cout << ts(x); }
template<class H, class... T> void pr(const H& h, const T&... t) { 
	pr(h); pr(t...); }
void ps() { pr("\n"); } // print w/ spaces
template<class H, class... T> void ps(const H& h, const T&... t) { 
	pr(h); if (sizeof...(t)) pr(" "); ps(t...); }

// DEBUG
void DBG() { cerr << "]" << endl; }
template<class H, class... T> void DBG(H h, T... t) {
	cerr << to_string(h); if (sizeof...(t)) cerr << ", ";
	DBG(t...); }
#ifdef LOCAL // compile with -DLOCAL
#define dbg(...) cerr << "[" << #__VA_ARGS__ << "]: [", DBG(__VA_ARGS__)
#else
#define dbg(...) 42
#endif

// FILE I/O
void setIn(string s) { freopen(s.c_str(),"r",stdin); }
void setOut(string s) { freopen(s.c_str(),"w",stdout); }
void unsyncIO() { ios_base::sync_with_stdio(0); cin.tie(0); }
void setIO(string s = "") {
	unsyncIO();
	// cin.exceptions(cin.failbit); 
	// throws exception when do smth illegal
	// ex. try to read letter into int
	if (sz(s)) { setIn(s+".in"), setOut(s+".out"); } // for USACO
}

mt19937 rng((uint32_t)chrono::steady_clock::now().time_since_epoch().count()); 

/**
 * Description: modular arithmetic operations 
 * Source: 
	* KACTL
	* https://codeforces.com/blog/entry/63903
	* https://codeforces.com/contest/1261/submission/65632855 (tourist)
	* https://codeforces.com/contest/1264/submission/66344993 (ksun)
 * Verification: 
	* https://open.kattis.com/problems/modulararithmetic
 */

struct mi {
	typedef decay<decltype(MOD)>::type T; 
 	/// don't silently convert to T
	T v; explicit operator T() const { return v; }
	mi() { v = 0; }
	mi(ll _v) { 
		v = (-MOD < _v && _v < MOD) ? _v : _v % MOD;
		if (v < 0) v += MOD;
	}
	friend bool operator==(const mi& a, const mi& b) { 
		return a.v == b.v; }
	friend bool operator!=(const mi& a, const mi& b) { 
		return !(a == b); }
	friend bool operator<(const mi& a, const mi& b) { 
		return a.v < b.v; }
	friend void re(mi& a) { ll x; re(x); a = mi(x); }
	friend str to_string(mi a) { return to_string(a.v); }
   
	mi& operator+=(const mi& m) { 
		if ((v += m.v) >= MOD) v -= MOD; 
		return *this; }
	mi& operator-=(const mi& m) { 
		if ((v -= m.v) < 0) v += MOD; 
		return *this; }
	mi& operator*=(const mi& m) { 
		v = (ll)v*m.v%MOD; return *this; }
	mi& operator/=(const mi& m) { return (*this) *= inv(m); }
	friend mi pow(mi a, ll p) {
		mi ans = 1; assert(p >= 0);
		for (; p; p /= 2, a *= a) if (p&1) ans *= a;
		return ans;
	}
	friend mi inv(const mi& a) { assert(a.v != 0); 
		return pow(a,MOD-2); }
		
	mi operator-() const { return mi(-v); }
	mi& operator++() { return *this += 1; }
	mi& operator--() { return *this -= 1; }
	friend mi operator+(mi a, const mi& b) { return a += b; }
	friend mi operator-(mi a, const mi& b) { return a -= b; }
	friend mi operator*(mi a, const mi& b) { return a *= b; }
	friend mi operator/(mi a, const mi& b) { return a /= b; }
};
typedef vector<mi> vmi;
typedef pair<mi,mi> pmi;
typedef vector<pmi> vpmi;

vector<vmi> comb;
void genComb(int SZ) {
	comb.assign(SZ,vmi(SZ)); comb[0][0] = 1;
	FOR(i,1,SZ) F0R(j,i+1) 
		comb[i][j] = comb[i-1][j]+(j?comb[i-1][j-1]:0);
}

mi fac[601];

int N;
bool ok[1201];
mi ways[601];
array<mi,601> dp, DP;
mi precalc[601][601];

int main() {
	setIO(); re(N); genComb(N+1);
	F0R(i,N) {
		int x; re(x);
		ok[x] = 1;
	}
	fac[0] = 1; FOR(i,1,601) fac[i] = i*fac[i-1];
	precalc[0][0] = 1;
	F0R(i,N) {
		FOR(j,i,N+1) {
			if (j+2 <= N) precalc[i+1][j+2] += precalc[i][j];
			if (j+1 <= N) precalc[i+1][j+1] += 2*precalc[i][j];
			precalc[i+1][j] += precalc[i][j];
		}
	}
	FOR(i,1,N+1) {
		ways[i] = precalc[i-1][i-1];
		ways[i] *= fac[i-1];
		ways[i] *= i+1;
		// ps("HA",i,ways[i]);
	}
	dp[0] = 1;
	int yes = 0, no = 0;
	ROF(i,1,2*N+1) {
		DP = array<mi,601>();
		FOR(j,no,yes+1) if (dp[j] != 0) {
			if (ok[i]) {
				DP[j] += dp[j];
				FOR(k,j+1,yes+2) DP[k] += dp[j]*comb[yes-j][k-j-1]*ways[k-j];
			} else {
				DP[j] += dp[j]*(j-no);
			}
		}
		if (ok[i]) yes ++;
		else no ++;
		swap(dp,DP);
	}
	ps(dp[N]/pow(mi(2),N));
	// you should actually read the stuff at the bottom
}

/* stuff you should look for
	* int overflow, array bounds
	* special cases (n=1?)
	* do smth instead of nothing and stay organized
	* WRITE STUFF DOWN
*/

Compilation message

ruins3.cpp: In function 'void setIn(std::__cxx11::string)':
ruins3.cpp:123:31: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
 void setIn(string s) { freopen(s.c_str(),"r",stdin); }
                        ~~~~~~~^~~~~~~~~~~~~~~~~~~~~
ruins3.cpp: In function 'void setOut(std::__cxx11::string)':
ruins3.cpp:124:32: warning: ignoring return value of 'FILE* freopen(const char*, const char*, FILE*)', declared with attribute warn_unused_result [-Wunused-result]
 void setOut(string s) { freopen(s.c_str(),"w",stdout); }
                         ~~~~~~~^~~~~~~~~~~~~~~~~~~~~~

Subtask #1
6.0 / 6.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 1792 KB Output is correct
2 Correct 5 ms 1664 KB Output is correct
3 Correct 5 ms 1792 KB Output is correct
4 Correct 6 ms 1792 KB Output is correct
5 Correct 5 ms 1792 KB Output is correct
6 Correct 6 ms 1792 KB Output is correct
7 Correct 5 ms 1792 KB Output is correct
8 Correct 5 ms 1792 KB Output is correct
9 Correct 5 ms 1792 KB Output is correct
10 Correct 5 ms 1792 KB Output is correct

Subtask #2
52.0 / 52.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 1792 KB Output is correct
2 Correct 5 ms 1664 KB Output is correct
3 Correct 5 ms 1792 KB Output is correct
4 Correct 6 ms 1792 KB Output is correct
5 Correct 5 ms 1792 KB Output is correct
6 Correct 6 ms 1792 KB Output is correct
7 Correct 5 ms 1792 KB Output is correct
8 Correct 5 ms 1792 KB Output is correct
9 Correct 5 ms 1792 KB Output is correct
10 Correct 5 ms 1792 KB Output is correct
11 Correct 6 ms 1792 KB Output is correct
12 Correct 6 ms 1792 KB Output is correct
13 Correct 6 ms 1792 KB Output is correct
14 Correct 6 ms 1792 KB Output is correct
15 Correct 5 ms 1792 KB Output is correct
16 Correct 6 ms 1792 KB Output is correct
17 Correct 6 ms 1792 KB Output is correct
18 Correct 5 ms 1792 KB Output is correct
19 Correct 5 ms 1792 KB Output is correct
20 Correct 5 ms 1792 KB Output is correct

Subtask #3
42.0 / 42.0

# Verdict Execution time Memory Grader output
1 Correct 5 ms 1792 KB Output is correct
2 Correct 5 ms 1664 KB Output is correct
3 Correct 5 ms 1792 KB Output is correct
4 Correct 6 ms 1792 KB Output is correct
5 Correct 5 ms 1792 KB Output is correct
6 Correct 6 ms 1792 KB Output is correct
7 Correct 5 ms 1792 KB Output is correct
8 Correct 5 ms 1792 KB Output is correct
9 Correct 5 ms 1792 KB Output is correct
10 Correct 5 ms 1792 KB Output is correct
11 Correct 6 ms 1792 KB Output is correct
12 Correct 6 ms 1792 KB Output is correct
13 Correct 6 ms 1792 KB Output is correct
14 Correct 6 ms 1792 KB Output is correct
15 Correct 5 ms 1792 KB Output is correct
16 Correct 6 ms 1792 KB Output is correct
17 Correct 6 ms 1792 KB Output is correct
18 Correct 5 ms 1792 KB Output is correct
19 Correct 5 ms 1792 KB Output is correct
20 Correct 5 ms 1792 KB Output is correct
21 Correct 10 ms 3200 KB Output is correct
22 Correct 10 ms 3200 KB Output is correct
23 Correct 10 ms 3200 KB Output is correct
24 Correct 11 ms 3200 KB Output is correct
25 Correct 9 ms 3200 KB Output is correct
26 Correct 13 ms 3200 KB Output is correct
27 Correct 9 ms 3200 KB Output is correct
28 Correct 10 ms 3200 KB Output is correct
29 Correct 10 ms 3200 KB Output is correct
30 Correct 214 ms 3320 KB Output is correct
31 Correct 107 ms 3200 KB Output is correct
32 Correct 157 ms 3200 KB Output is correct
33 Correct 194 ms 3248 KB Output is correct
34 Correct 113 ms 3200 KB Output is correct
35 Correct 161 ms 3200 KB Output is correct
36 Correct 191 ms 3200 KB Output is correct