結果

問題 No.849 yuki国の分割統治
ユーザー sntea
提出日時 2019-07-31 23:17:42
言語 C++14
(gcc 13.3.0 + boost 1.87.0)
結果
AC  
実行時間 125 ms / 2,000 ms
コード長 9,815 bytes
コンパイル時間 2,455 ms
コンパイル使用メモリ 207,992 KB
実行使用メモリ 19,328 KB
最終ジャッジ日時 2024-10-07 02:57:43
合計ジャッジ時間 5,080 ms
ジャッジサーバーID
（参考情報） 		judge4 / judge1
このコードへのチャレンジ
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ファイルパターン 結果
sample AC * 4
other AC * 26
権限があれば一括ダウンロードができます

ソースコード

diff #
プレゼンテーションモードにする

#ifdef LOCAL111
#else
    #pragma GCC optimize ("O3")
    #define NDEBUG
#endif
// #define _USE_MATH_DEFINES
#include <bits/stdc++.h>
const int INF = 1e9;
using namespace std;
template<typename T, typename U> ostream& operator<< (ostream& os, const pair<T,U>& p) { os << '(' << p.first << ' ' << p.second << ')'; return os; }
#define endl '\n'
#define ALL(a)  (a).begin(),(a).end()
#define SZ(a) int((a).size())
#define FOR(i,a,b) for(int i=(a);i<(b);++i)
#define RFOR(i,a,b) for (int i=(b)-1;i>=(a);i--)
#define REP(i,n)  FOR(i,0,n)
#define RREP(i,n) for (int i=(n)-1;i>=0;i--)
#ifdef LOCAL111
    #define DEBUG(x) cout<<#x<<": "<<(x)<<endl
    template<typename T> void dpite(T a, T b){ for(T ite = a; ite != b; ite++) cout << (ite == a ? "" : " ") << *ite; cout << endl;}
#else
    #define DEBUG(x) true
    template<typename T> void dpite(T a, T b){ return; }
#endif
#define F first
#define S second
#define SNP string::npos
#define WRC(hoge) cout << "Case #" << (hoge)+1 << ": "
template<typename T> void pite(T a, T b){ for(T ite = a; ite != b; ite++) cout << (ite == a ? "" : " ") << *ite; cout << endl;}
template<typename T> bool chmax(T& a, T b){if(a < b){a = b; return true;} return false;}
template<typename T> bool chmin(T& a, T b){if(a > b){a = b; return true;} return false;}
template<typename T>
vector<T> make_v(size_t a){return vector<T>(a);}
template<typename T,typename... Ts>
auto make_v(size_t a,Ts... ts){
  return vector<decltype(make_v<T>(ts...))>(a,make_v<T>(ts...));
}
template<typename T,typename U,typename... V>
typename enable_if<is_same<T, U>::value!=0>::type
fill_v(U &u,const V... v){u=U(v...);}
template<typename T,typename U,typename... V>
typename enable_if<is_same<T, U>::value==0>::type
fill_v(U &u,const V... v){
  for(auto &e:u) fill_v<T>(e,v...);
}
const array<int, 4> dx = {0, 1, 0, -1};
const array<int, 4> dy = {1, 0, -1, 0};
typedef long long int LL;
typedef unsigned long long ULL;
typedef pair<int,int> P;
void ios_init(){
    //cout.setf(ios::fixed);
    //cout.precision(12);
#ifdef LOCAL111
    return;
#endif
    ios::sync_with_stdio(false); cin.tie(0);
}
#define EPS 1e-9
//library
template<typename T>
class Matrix {
public:
    vector<vector<T> > v;
    int n,m;
    Matrix(int n){
        this->n = this->m = n;
        v.resize(n,vector<T>(n,0));
    }
    Matrix(int n, int m){
        this -> n = n;
        this -> m = m;
        v.resize(n,vector<T>(m,0));
    }
    size_t size() const {
        return v.size();
    }
    int row() const {
        return n;
    }
    int col() const {
        return m;
    }
    Matrix operator+ (Matrix x) const {
        Matrix res(n,m);
        for(int i = 0; i < n; i++){
            for(int j = 0; j < m; j++){
                res.v[i][j] = x.v[i][j]+v[i][j];
            }
        }
        return res;
    }
    Matrix operator-(Matrix x) const {
        Matrix res(n,m);
        for(int i = 0; i < n; i++){
            for(int j = 0; j < m; j++){
                res.v[i][j] = v[i][j]-x.v[i][j];
            }
        }
    }
    Matrix operator*(Matrix x) const {
        Matrix res(n,x.m);
        for(int i = 0; i < n; i++){
            for(int j = 0; j < x.m; j++){
                for(int k = 0; k < m; k++){
                    res.v[i][j] += v[i][k]*x.v[k][j];
                }
            }
        }
        return res;
    }
    Matrix operator-() const  {
        Matrix res = *this;
        for(int i = 0; i < (int)v.size(); ++i) {
            for(int j = 0; j < (int)v[i].size(); ++j) {
                res [i][j] *= -1;
            }
        }
        return res;
    }
    vector<T> operator*(vector<T> x) const {
        assert(x.size() == v.size());
        vector<T> res(v.size());
        for(int i = 0; i < n; i++){
            T tmp = 0;
            for(int j = 0; j < m; j++){
                tmp += v[i][j]*x[j];
            }
            res[i] = tmp;
        }
        return res;
    }
    Matrix pow(long long x) const {
        assert(n == m);
        Matrix m = (*this);
        Matrix res(n);
        for(int i = 0; i < n; i++) res[i][i] = 1;
        while(x != 0) {
            if(x&1) {
                res = res*m;
            }
            m = m*m;
            x >>= 1;
        }
        return res;
    }
    vector<T>& operator[](int x){
        return v[x];
    }
    const vector<T>& operator[](int x) const {
        return v[x];
    }
    Matrix<T> inverse() const{
        assert(n == m);
        Matrix res(n);
        for(int i = 0; i < n; ++i) {
            res[i][i] = 1;
        }
        
        // vector<pair<int,int>> swap_log;
        Matrix<T> mat = *this;
        for(int k = 0; k < n; ++k) {
            T max_val = abs(mat[k][k]);
            int max_point = k;
            for(int i = k+1; i < n; ++i) {
                if(max_val < abs(mat[i][k])){
                    max_val = abs(mat[i][k]);
                    max_point = i;
                }
            }
            swap(mat[k],mat[max_point]);
            swap(res[k],res[max_point]);
            // swap_log.emplace_back(k,max_point);
            for(int i = k+1; i < n; ++i) {
                T m = mat[i][k]/mat[k][k];
                for(int j = 0; j < n; ++j) {
                    mat[i][j] -= m*mat[k][j];
                    res[i][j] -= m*res[k][j];
                }
            }
        }
        
        for(int k = n-1; k >= 0; --k) {
            for(int i = 0; i < k; ++i) {
                T m = mat[i][k]/mat[k][k];
                for(int j = 0; j < n; ++j) {
                    // mat[i][j] -= mat[k][j]*m;
                    res[i][j] -= res[k][j]*m;
                }
            }
        }
        for(int i = 0; i < n; ++i) {
            for(int j = 0; j < n; ++j) {
                res[i][j] /= mat[i][i];
            }
        }
        // for(auto&& e : swap_log) {
        //  swap(res[e.first],res[e.second]);
        // }
        return res;
    }
    T det() const {
        Matrix<T> mat = *this;
        T res = 1;
        for(int k = 0; k < n; ++k) {
            T max_val = abs(mat[k][k]);
            int max_point = k;
            for(int i = k+1; i < n; ++i) {
                if(max_val < abs(mat[i][k])){
                    max_val = abs(mat[i][k]);
                    max_point = i;
                }
            }
            swap(mat[k],mat[max_point]);
            if(k != max_point) res *= -1;
            for(int i = k+1; i < n; ++i) {
                T m = mat[i][k]/mat[k][k];
                for(int j = 0; j < n; ++j) {
                    mat[i][j] -= m*mat[k][j];
                }
            }
        }
        for(int i = 0; i < n; ++i) {
            res *= mat[i][i];
        }
        return res;
    }
    pair<T, vector<T>> getMaxEigenvalue(int iterNum = 10) const {
        assert(n == m);
        vector<T> xk_(n, 1);
        xk_ = (*this).pow(iterNum)*xk_;
        auto xk = (*this)*xk_;
        T xk_xk = 0, xk_xk_ = 0;
        for(int i = 0; i < n; i++) {
            xk_xk += xk[i]*xk[i];
            xk_xk_ += xk[i]*xk_[i];
        }
        T xkAbs = sqrt(xk_xk);
        auto res = xk;
        for(auto&& e : res) {
            e /= xkAbs;
        }
        return { xk_xk/xk_xk_, res };
    }
    void debug() const {
        for(auto&& ee : v) {
            for(auto&& e : ee) {
                cout << e << ' ';
            }
            cout << endl;
        }
        cout << endl;
    }
};
template<typename T>
Matrix<T> companion_pow(const Matrix<T>& A, long long m) {
    assert(A.col() == A.row());
    int n = A.col();
    Matrix<T> u(1, n), Ak = A;
    u[0][n-1] = 1;
    while(m > 0) {
        if(m&1) {
            u = u*Ak;
        }
        Matrix<T> a(1, n);
        for(int i = 0; i < n; ++i) {
            a[0][i] = Ak[n-1][i];
        }
        a = a*Ak;
        for(int i = n-1; i >= 0; --i) {
            for(int j = 0; j < n; ++j) {
                Ak[i][j] = a[0][j];
            }
            auto a00 = a[0][0];
            for(int j = 0; j < n-1; ++j) {
                a[0][j] = a[0][j+1]+A[0][j]*a00;
            }
            a[0][n-1] = A[0][n-1]*a00;
        }
        m >>= 1;
    }
    Matrix<T> res(n);
    for(int i = n-1; i >= 0; --i) {
        for(int j = 0; j < n; ++j) {
            res[i][j] = u[0][j];
        }
        auto u00 = u[0][0];
        for(int j = 0; j < n-1; ++j) {
            u[0][j] = u[0][j+1]+A[0][j]*u00;
        }
        u[0][n-1] = A[0][n-1]*u00;
    }
    return res;
}
//library
class UFTree {
//private:
public:
    vector<int> par;
    vector<int> rank;
    vector<int> num;
//public:
    UFTree(int n)
    {
        par = vector<int>(n);
        rank = vector<int>(n);
        num = vector<int>(n);
        for(int i = 0; i < n; i++){
            par[i] = i;
            rank[i] = 0;
            num[i] = 1;
        }
    }
    int find(int x)
    {
        if(par[x] == x){
            return x;
        }else{
            return par[x] = find(par[x]);
        }
    }
    void unite(int x, int y)
    {
        x = find(x);
        y = find(y);
        if(x == y) return;
        if(rank[x] < rank[y]){
            par[x] = y;
            num[y] += num[x];
        }else{
            par[y] = x;
            num[x] += num[y];
            if(rank[x] == rank[y])  rank[x]++;
        }
    }
    int count(int x)
    {
        return num[find(x)];
    }
    bool same(int x, int y)
    {
        return find(x) == find(y);
    }
};
//library
template <typename T>
long long gcd(T x, T y){
    return y==0 ? x : gcd(y, x%y);
}
int main()
{
    ios_init();
    LL a, b, c, d;
    while(cin >> a >> b >> c >> d) {
        using P = pair<LL, LL>;
        int n;
        cin >> n;
        vector<LL> x(n), y(n);
        REP(i, n) cin >> x[i] >> y[i];
        const double eps = 1e-15;
        if(a * d == b * c) {
            // if(b == 0) {
            //  assert(d == 0);
            //  int e = gcd(a, c);
            // } else if(a == 0) {
            //  assert(c == 0);
            //  int f = gcd(d, d);
            // } else {
            LL e = gcd(a, c), f = gcd(b, d);
            DEBUG(e); DEBUG(f);
            map<P, vector<int>> ma;
            REP(i, n) {
                int t;
                if(e == 0) {
                    t = y[i] / f;
                } else if(f == 0) {
                    t = x[i] / e;
                } else {
                    t = min(x[i] / e, y[i] / f);
                }
                P ke = {x[i] - t * e, y[i] - t * f};
                DEBUG(ke);
                ma[ke].push_back(i);
            }
            UFTree uf(n);
            for(auto&& e : ma) {
                REP(i, SZ(e.S) - 1) {
                    uf.unite(e.S[i], e.S[i+1]);
                }
            }
            set<int> se;
            REP(i, n) {
                se.insert(uf.find(i));
            }
            cout << se.size() << endl;
            // }
        } else {
            // Matrix<double> mat(2, 2);
            // mat[0] = {a, c};
            // mat[1] = {b, d};
            // mat = mat.inverse();
            // Matrix<LL> mai(2);
            LL det = abs(a * d - c * b);
            // DEBUG(det);
            // REP(i, 2) REP(j, 2) {
            //  mai[i][j] = round(mat[i][j] * det);
            //  DEBUG(mai[i][j]);
            // }
            // DEBUG(det);
            Matrix<LL> mai(2);
            mai[0] = {d,  -c};
            mai[1] = {-b, a};
            if(det < 0) {
                REP(i, 2) REP(j, 2) mai[i][j] *= -1;
            }
            map<P, vector<int>> ma;
            DEBUG(det);
            REP(i, n) {
                DEBUG(i);
                vector<LL> v = {x[i], y[i]};
                DEBUG(x[i]); DEBUG(y[i]);
                auto st = mai * v;
                dpite(ALL(st));
                // {
                //  Matrix<double> mat(2, 2);
                //  mat[0] = {a, c};
                //  mat[1] = {b, d};
                //  vector<double> st0(2);
                //  REP(i, SZ(st)) st0[i] = st[i];
                //  auto v = mat * st0;
                //  dpite(ALL(v));
                // }
                LL mx = st[0] % det;
                if(mx < 0) mx += det;
                LL my = st[1] % det;
                if(my < 0) my += det;
                DEBUG(mx); DEBUG(my);
                ma[{mx, my}].push_back(i);
            }
            UFTree uf(n);
            for(auto&& e : ma) {
                DEBUG(e.F);
                REP(i, SZ(e.S) - 1) {
                    uf.unite(e.S[i], e.S[i+1]);
                }
            }
            set<int> se;
            REP(i, n) {
                se.insert(uf.find(i));
            }
            cout << se.size() << endl;
        }
    }
    return 0;
}
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