Submission #111343

#	Time	Username	Problem	Language	Result	Execution time	Memory
111343		Benq	Security Gate (JOI18_security_gate)	C++14	100 / 100	756 ms	107268 KiB

securitygate

#pragma GCC optimize ("O3")
#pragma GCC target ("sse4")
 
#include <bits/stdc++.h>
#include <ext/pb_ds/tree_policy.hpp>
#include <ext/pb_ds/assoc_container.hpp>
#include <ext/rope>
 
using namespace std;
using namespace __gnu_pbds;
using namespace __gnu_cxx;
 
typedef long long ll;
typedef long double ld;
typedef complex<ld> cd;
 
typedef pair<int, int> pi;
typedef pair<ll,ll> pl;
typedef pair<ld,ld> pd;
 
typedef vector<int> vi;
typedef vector<ld> vd;
typedef vector<ll> vl;
typedef vector<pi> vpi;
typedef vector<pl> vpl;
typedef vector<cd> vcd;
 
template <class T> using Tree = tree<T, null_type, less<T>, rb_tree_tag,tree_order_statistics_node_update>;
 
#define FOR(i, a, b) for (int i = (a); i < (b); i++)
#define F0R(i, a) for (int i = 0; i < (a); i++)
#define FORd(i,a,b) for (int i = (b)-1; i >= (a); i--)
#define F0Rd(i,a) for (int i = (a)-1; i >= 0; i--)
#define trav(a, x) for (auto& a : x)
 
#define mp make_pair
#define pb push_back
#define f first
#define s second
#define lb lower_bound
#define ub upper_bound
 
#define sz(x) (int)x.size()
#define beg(x) x.begin()
#define en(x) x.end()
#define all(x) beg(x), en(x)
#define resz resize
 
const int MOD = 1000000007; // 998244353
const ll INF = 1e18;
const int MX = 100001;
const ld PI = 4*atan((ld)1);
 
template<class T> void ckmin(T &a, T b) { a = min(a, b); }
template<class T> void ckmax(T &a, T b) { a = max(a, b); }
 
namespace input {
    template<class T> void re(complex<T>& x);
    template<class T1, class T2> void re(pair<T1,T2>& p);
    template<class T> void re(vector<T>& a);
    template<class T, size_t SZ> void re(array<T,SZ>& a);
 
    template<class T> void re(T& x) { cin >> x; }
    void re(double& x) { string t; re(t); x = stod(t); }
    void re(ld& x) { string t; re(t); x = stold(t); }
    template<class Arg, class... Args> void re(Arg& first, Args&... rest) { 
        re(first); re(rest...); 
    }
 
    template<class T> void re(complex<T>& x) { T a,b; re(a,b); x = cd(a,b); }
    template<class T1, class T2> void re(pair<T1,T2>& p) { re(p.f,p.s); }
    template<class T> void re(vector<T>& a) { F0R(i,sz(a)) re(a[i]); }
    template<class T, size_t SZ> void re(array<T,SZ>& a) { F0R(i,SZ) re(a[i]); }
}
 
using namespace input;
 
namespace output {
    template<class T1, class T2> void pr(const pair<T1,T2>& x);
    template<class T, size_t SZ> void pr(const array<T,SZ>& x);
    template<class T> void pr(const vector<T>& x);
    template<class T> void pr(const set<T>& x);
    template<class T1, class T2> void pr(const map<T1,T2>& x);
 
    template<class T> void pr(const T& x) { cout << x; }
    template<class Arg, class... Args> void pr(const Arg& first, const Args&... rest) { 
        pr(first); pr(rest...); 
    }
 
    template<class T1, class T2> void pr(const pair<T1,T2>& x) { 
        pr("{",x.f,", ",x.s,"}"); 
    }
    template<class T> void prContain(const T& x) {
        pr("{");
        bool fst = 1; trav(a,x) pr(!fst?", ":"",a), fst = 0; 
        pr("}");
    }
    template<class T, size_t SZ> void pr(const array<T,SZ>& x) { prContain(x); }
    template<class T> void pr(const vector<T>& x) { prContain(x); }
    template<class T> void pr(const set<T>& x) { prContain(x); }
    template<class T1, class T2> void pr(const map<T1,T2>& x) { prContain(x); }
    
    void ps() { pr("\n"); } 
    template<class Arg, class... Args> void ps(const Arg& first, const Args&... rest) { 
        pr(first," "); ps(rest...); // print w/ spaces
    }
}
 
using namespace output;
 
namespace io {
    void setIn(string s) { freopen(s.c_str(),"r",stdin); }
    void setOut(string s) { freopen(s.c_str(),"w",stdout); }
    void setIO(string s = "") {
        ios_base::sync_with_stdio(0); cin.tie(0); // fast I/O
        if (sz(s)) { setIn(s+".in"), setOut(s+".out"); } // for USACO
    }
}
 
using namespace io;
 
template<class T> T invGeneral(T a, T b) {
    a %= b; if (a == 0) return b == 1 ? 0 : -1;
    T x = invGeneral(b,a); 
    return x == -1 ? -1 : ((1-(ll)b*x)/a+b)%b;
}
 
template<class T> struct modular {
    T val; 
    explicit operator T() const { return val; }
    modular() { val = 0; }
    template<class U> modular(const U& v) {
        val = (-MOD <= v && v <= MOD) ? v : v % MOD;
        if (val < 0) val += MOD;
    }
    friend ostream& operator<<(ostream& os, const modular& a) { return os << a.val; }
    friend bool operator==(const modular& a, const modular& b) { return a.val == b.val; }
    friend bool operator!=(const modular& a, const modular& b) { return !(a == b); }
 
    modular operator-() const { return modular(-val); }
    modular& operator+=(const modular& m) { if ((val += m.val) >= MOD) val -= MOD; return *this; }
    modular& operator-=(const modular& m) { if ((val -= m.val) < 0) val += MOD; return *this; }
    modular& operator*=(const modular& m) { val = (ll)val*m.val%MOD; return *this; }
    friend modular exp(modular a, ll p) {
        modular ans = 1; for (; p; p /= 2, a *= a) if (p&1) ans *= a;
        return ans;
    }
    friend modular inv(const modular& a) { return invGeneral(a.val,MOD); } 
    // inv is equivalent to return exp(b,b.mod-2) if prime
    modular& operator/=(const modular& m) { return (*this) *= inv(m); }
    
    friend modular operator+(modular a, const modular& b) { return a += b; }
    friend modular operator-(modular a, const modular& b) { return a -= b; }
    friend modular operator*(modular a, const modular& b) { return a *= b; }
    
    friend modular operator/(modular a, const modular& b) { return a /= b; }
};
 
typedef modular<int> mi;
typedef pair<mi,mi> pmi;
typedef vector<mi> vmi;
typedef vector<pmi> vpmi;
 
int N;
string S;
mi ans(0);
mi DP[301][301][301];

void gen() {
    F0R(i,sz(S)+1) F0R(j,sz(S)+1) F0R(k,sz(S)+1) DP[i][j][k] = 0;
    DP[sz(S)][0][0] = 1;
    F0Rd(i,sz(S)) {
        char c = S[i];
        F0R(j,sz(S)) FOR(k,j,sz(S)) {
            int e = (int)DP[i+1][j][k];
            if (!e) continue;
            if (c != ')') {
                if (j) DP[i][j-1][k] += e;
            }
            if (c != '(') {
                DP[i][j+1][max(k,j+1)] += e;
            }
        }
    }
    F0R(i,sz(S)+1) F0Rd(j,sz(S)) DP[i][0][j] += DP[i][0][j+1];
}

mi finish(int pos, int need) {
    if (need > sz(S)) return 0;
    /*assert(need >= 0);
    mi res(0); FOR(i,need,sz(S)+1) res += DP[pos][0][i];*/
    // ps("WAT",pos,need,res);
    return DP[pos][0][need];
}
 
void tri(int A, int t) {
    // max1 <= max2-d
    // all in first prefix <= max1 
    // need smth >= t+d in second 
    
    // 0: not yet < 0, not found t 
    // 1: not yet < 0, found t 
    // 2: < 0, but never > 2t
        // if 2d-1 -> 2d maybe go to 3 
    // 3: not found smth >= max1+d 
    // 4: found smth >= max1+d 
    // end: = 2d
    
    // ps("HUH",A,t);
    array<array<mi,3>,601> cur = array<array<mi,3>,601>();
    array<array<mi,3>,601> tmp = array<array<mi,3>,601>();
    cur[N][0 >= A] = 1;
    int par = 0;
    F0R(pos,sz(S)) {
        char c = S[pos];
    	F0R(i,601) F0R(j,3) tmp[i][j] = 0;
        FOR(i,-N,N+1) if ((i-par) % 2 == 0) {
            int e = (int)cur[N+i][0];
            if (e) {
                if (c != ')') tmp[N+i+1][i+1 == A] += e;
                if (c != '(' && i) tmp[N+i-1][0] += e;
            }
            e = (int)cur[N+i][1];
            if (e) {
                if (c != ')' && i+1 <= A) tmp[N+i+1][1] += e;
                if (c != '(') tmp[N+i-1][1+(i == 0)] += e;
            }
            e = (int)cur[N+i][2];
            if (e) {
                if (c != ')') {
                    if (i+1 <= 2*A) {
                    	if ((i-1) % 2 == 0) {
                    		int C = i+1; int B = A+C/2;
                    		ans += e*finish(pos+1,B-C+t);
                    	}
                        tmp[N+i+1][2] += e;
                    }
                } 
                if (c != '(') tmp[N+i-1][2] += e;
            }
        }
        swap(cur,tmp);
        // ps("??",A,t,pos,cur[N-1][2]);
        par ^= 1;
    }
}

void cool(int A) {
    // keep track of current mx: 2*d, current sum 
        // 0: not found 
        // 1: everything must <= 2*(mx-d) until you get to mx-d 
        // 2: found
        
    // csum, mx
    // found A without any > 2*A after 
    // 2d-1 -> 2d <= 2*A 
    array<array<mi,2>,301> cur = array<array<mi,2>,301>();
    array<array<mi,2>,301> tmp = array<array<mi,2>,301>();
    cur[0][0] = 1; int par = 0; 
    F0R(pos,sz(S)) {
        char c = S[pos];
    	F0R(i,301) F0R(j,2) tmp[i][j] = 0;
        F0R(i,N+1) if ((i-par) % 2 == 0) {
            int e = (int)cur[i][0];
            if (e) {
                if (c != ')') {
                    if ((i+1) % 2 == 0 && (i+1 == A || A >= (i+1))) {
                        int C = i+1; int B = A+C/2;
                		ans += e*(finish(pos+1,B-C)-finish(pos+1,B-C+1));
                    }
                    tmp[i+1][(i+1) == A] += e;
                }
                if (c != '(' && i) tmp[i-1][i-1 == A] += e;
            }
            e = (int)cur[i][1];
            if (e) {
                if (c != ')') {
                    if ((i+1) % 2 == 0) {
                        // ps("WAT");
                        int C = i+1; int B = A+C/2;
                		ans += e*(finish(pos+1,B-C)-finish(pos+1,B-C+1));
                    }
                    tmp[i+1][(i+1) <= 2*A] += e;
                } 
                if (c != '(' && i) tmp[i-1][1] += e;
            }
        }
        swap(cur,tmp); // ps("??",A,t,pos,cur[N-1][2]);
        par ^= 1;
    }
}

void balanced() {
    array<mi,301> cur = array<mi,301>(); cur[0] = 1;
    trav(c,S) {
        array<mi,301> tmp = array<mi,301>();
        F0R(i,N+1) {
            int e = (int)cur[i];
            if (e) {
                if (c != ')') tmp[i+1] += e;
                if (c != '(' && i) tmp[i-1] += e;
            }
        }
        swap(cur,tmp);
    }
    // ps("??",cur[0]);
    ans += cur[0];
}

int main() {
    setIO(); re(N,S); assert(sz(S) == N);
    if (N&1) { ps(0); exit(0); }
    // N = 10;
    F0R(i,1) {
        /*ans = 0; S = "";
        F0R(j,N) {
            if (i&(1<<j)) S += '(';
            else S += ')';
        }*/
        balanced();
        gen();
        F0R(i,N/2+1) tri(i,0);
        FOR(i,1,N/2+1) cool(i);
        reverse(all(S));
        trav(t,S) {
            if (t == '(') t = ')';
            else if (t == ')') t = '(';
        }
        gen();
        F0R(i,N/2+1) tri(i,1);
        FOR(i,1,N/2+1) cool(i);
        ps(ans);
    }
}
 
/* stuff you should look for
    * int overflow, array bounds
    * special cases (n=1?), set tle
    * do smth instead of nothing and stay organized
*/

Compilation message (stderr)

securitygate.cpp: In function 'void io::setIn(std::__cxx11::string)':
securitygate.cpp:112:35: 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); }
                            ~~~~~~~^~~~~~~~~~~~~~~~~~~~~
securitygate.cpp: In function 'void io::setOut(std::__cxx11::string)':
securitygate.cpp:113:36: 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: 4 / 4
• Subtask 2: 8 / 8
• Subtask 3: 18 / 18
• Subtask 4: 43 / 43
• Subtask 5: 27 / 27