Submission #111293

#	Time	Username	Problem	Language	Result	Execution time	Memory
111293		Benq	Security Gate (JOI18_security_gate)	C++14	73 / 100	3149 ms	760 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);

void tri0(int d, 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
    
    array<array<mi,5>,201> cur = array<array<mi,5>,201>();
    array<array<mi,5>,201> tmp = array<array<mi,5>,201>();
    cur[N][0 >= t] = 1;
    int par = 0;
    trav(c,S) {
    	F0R(i,201) F0R(j,5) 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 >= t] += e;
                if (c != '(' && i) tmp[N+i-1][0] += e;
            }
            e = (int)cur[N+i][1];
            if (e) {
                if (c != ')' && i+1 <= t) tmp[N+i+1][1] += e;
                if (c != '(') {
                    assert(i >= 0);
                    tmp[N+i-1][1+(i == 0)] += e;
                }
            }
            e = (int)cur[N+i][2];
            if (e) {
                if (c != ')') {
                    if (i == 2*d-1) tmp[N+i+1][3+(i+1 >= t+d)] += e;
                    if (i+1 <= 2*t) tmp[N+i+1][2] += e;
                } 
                if (c != '(') tmp[N+i-1][2] += e;
            }
            e = (int)cur[N+i][3];
            if (e) {
                if (c != ')') tmp[N+i+1][3+(i+1 >= t+d)] += e;
                if (c != '(' && i-1 >= 2*d) tmp[N+i-1][3] += e;
            }
            e = (int)cur[N+i][4];
            if (e) {
                if (c != ')') tmp[N+i+1][4] += e;
                if (c != '(' && i-1 >= 2*d) tmp[N+i-1][4] += e;
            }
        }
        swap(cur,tmp);
        par ^= 1;
    }
    ans += cur[N+2*d][4];
}

void tri1(int d, int t) {
    // max1 > max2-d 
    // need smth > t in first prefix 
    // all in second prefix <= t+d, need occurrence of t+d
    
    array<array<mi,5>,201> cur = array<array<mi,5>,201>();
    array<array<mi,5>,201> tmp = array<array<mi,5>,201>();
    cur[N][0] = 1;
    int par = 0;
    trav(c,S) {
    	F0R(i,201) F0R(j,5) 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 > t] += e;
                if (c != '(' && i) tmp[N+i-1][0] += e;
            }
            e = (int)cur[N+i][1];
            if (e) {
                if (c != ')') tmp[N+i+1][1] += e;
                if (c != '(') {
                    assert(i >= 0);
                    tmp[N+i-1][1+(i == 0)] += e;
                }
            }
            e = (int)cur[N+i][2];
            if (e) {
                if (c != ')') {
                    if (i == 2*d-1) tmp[N+i+1][3+(i+1 >= t+d)] += e;
                    if (i+1 <= 2*t) tmp[N+i+1][2] += e;
                } 
                if (c != '(') tmp[N+i-1][2] += e;
            }
            e = (int)cur[N+i][3];
            if (e) {
                if (c != ')') tmp[N+i+1][3+(i+1 >= t+d)] += e;
                if (c != '(' && i-1 >= 2*d) tmp[N+i-1][3] += e;
            }
            e = (int)cur[N+i][4];
            if (e) {
                if (c != ')' && i+1 <= t+d) tmp[N+i+1][4] += e;
                if (c != '(' && i-1 >= 2*d) tmp[N+i-1][4] += e;
            }
        }
        swap(cur,tmp);
        par ^= 1;
    }
    ans += cur[N+2*d][4];
}

void balanced() {
    array<mi,201> cur = array<mi,201>(); cur[0] = 1;
    trav(c,S) {
        array<mi,201> tmp = array<mi,201>();
        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];
}

void cool(int d) {
    // 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
    array<array<array<mi,3>,101>,101> cur = array<array<array<mi,3>,101>,101>(); 
    cur[2*d][2*d][0] = 1;
    trav(c,S) {
        array<array<array<mi,3>,101>,101> tmp = array<array<array<mi,3>,101>,101>(); 
        F0R(i,N+1) F0R(j,N+1) {
            int e = (int)cur[i][j][0];
            if (e) {
                if (c != ')') {
                    if (i+1 <= N) tmp[i+1][max(i+1,j)][0] += e;
                }
                if (c != '(') {
                    if (i-1 >= 0) {
                        if (j-d == i-1) tmp[i-1][j][1] += e;
                        else if (i-1 < 2*d) tmp[i-1][j][2] += e;
                        else tmp[i-1][j][0] += e;
                    }
                }
            }
            e = (int)cur[i][j][1];
            if (e) {
                if (c != ')') {
                    if (i+1 <= N) tmp[i+1][j][1] += e;
                }
                if (c != '(') {
                    if (i-1 >= 0) tmp[i-1][j][1] += e;
                }
            }
            e = (int)cur[i][j][2];
            if (e) {
                if (c != ')') {
                    if (i+1 <= min(N,2*(j-d))) tmp[i+1][j][2] += e;
                }
                if (c != '(') {
                    if (i-1 >= 0) {
                        if (j-d == i-1) tmp[i-1][j][1] += e;
                        else tmp[i-1][j][2] += e;
                    }
                }
            }
        }
        swap(cur,tmp);
    }
    F0R(i,N+1) ans += cur[0][i][1];
}

void solve(int d) {
    FOR(t,d,N-d+1) {
        tri0(d,t); // 1.6
        tri1(d,t); // 1.47
    }
    if (d == 0) balanced();
    else cool(d); // 0.95s
}

int main() {
    setIO(); re(N,S); assert(sz(S) == N);
    if (N&1) { ps(0); exit(0); }
    solve(0); 
    FOR(d,1,N/2+1) solve(d);
    reverse(all(S));
    trav(t,S) {
        if (t == '(') t = ')';
        else if (t == ')') t = '(';
    }
    FOR(d,1,N/2+1) solve(d);
    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: 0 / 27