#240686 (C++17(gcc12)) No.660 家を通り過ぎないランダムウォーク問題

• 問題: No.660 家を通り過ぎないランダムウォーク問題
• ユーザー: mai
• 提出日時: 2018-03-03 00:08:21
• 言語: C++17(gcc12) (gcc 12.3.0 + boost 1.87.0)
• 結果: TLE
• 実行時間: -
• コード長: 9,455 bytes
• コンパイル時間: 12,216 ms
• コンパイル使用メモリ: 275,980 KB
• 最終ジャッジ日時: 2025-01-05 09:02:51
• ジャッジサーバーID （参考情報）: judge5 / judge3

ファイルパターン	結果
other	TLE * 45

ソースコード

#pragma GCC optimize ("O3")
#pragma GCC target ("avx")
#include "bits/stdc++.h" // define macro "/D__MAI"

using namespace std;
typedef long long int ll;

#define debug(v) {printf("L%d %s > ",__LINE__,#v);cout<<(v)<<endl;}
#define debugv(v) {printf("L%d %s > ",__LINE__,#v);for(auto e:(v)){cout<<e<<" ";}cout<<endl;}
#define debuga(m,w) {printf("L%d %s > ",__LINE__,#m);for(int x=0;x<(w);x++){cout<<(m)[x]<<" ";}cout<<endl;}
#define debugaa(m,h,w) {printf("L%d %s >\n",__LINE__,#m);for(int y=0;y<(h);y++){for(int x=0;x<(w);x++){cout<<(m)[y][x]<<" ";}cout<<endl;}}
#define ALL(v) (v).begin(),(v).end()
#define repeat(cnt,l) for(auto cnt=0ll;(cnt)<(l);++(cnt))
#define rrepeat(cnt,l) for(auto cnt=(l)-1;0<=(cnt);--(cnt))
#define iterate(cnt,b,e) for(auto cnt=(b);(cnt)!=(e);++(cnt))
#define diterate(cnt,b,e) for(auto cnt=(b);(cnt)!=(e);--(cnt))
#define MD 1000000007ll
#define PI 3.1415926535897932384626433832795
template<typename T1, typename T2> ostream& operator <<(ostream &o, const pair<T1, T2> p) { o << "(" << p.first << ":" << p.second << ")"; return o; }
template<typename T> T& maxset(T& to, const T& val) { return to = max(to, val); }
template<typename T> T& minset(T& to, const T& val) { return to = min(to, val); }
void bye(string s, int code = 0) { cout << s << endl; exit(code); }
mt19937_64 randdev(8901016);
inline ll rand_range(ll l, ll h) {
    return uniform_int_distribution<ll>(l, h)(randdev);
}

#if defined(_WIN32) || defined(_WIN64)
#define getchar_unlocked _getchar_nolock
#define putchar_unlocked _putchar_nolock
#elif defined(__GNUC__)
#else
#define getchar_unlocked getchar
#define putchar_unlocked putchar
#endif
namespace {
#define isvisiblechar(c) (0x21<=(c)&&(c)<=0x7E)
    class MaiScanner {
    public:
        template<typename T> void input_integer(T& var) {
            var = 0; T sign = 1;
            int cc = getchar_unlocked();
            for (; cc<'0' || '9'<cc; cc = getchar_unlocked())
                if (cc == '-') sign = -1;
            for (; '0' <= cc && cc <= '9'; cc = getchar_unlocked())
                var = (var << 3) + (var << 1) + cc - '0';
            var = var * sign;
        }
        inline int c() { return getchar_unlocked(); }
        inline MaiScanner& operator>>(int& var) { input_integer<int>(var); return *this; }
        inline MaiScanner& operator>>(long long& var) { input_integer<long long>(var); return *this; }
        inline MaiScanner& operator>>(string& var) {
            int cc = getchar_unlocked();
            for (; !isvisiblechar(cc); cc = getchar_unlocked());
            for (; isvisiblechar(cc); cc = getchar_unlocked())
                var.push_back(cc);
            return *this;
        }
        template<typename IT> void in(IT begin, IT end) { for (auto it = begin; it != end; ++it) *this >> *it; }
    };
    class MaiPrinter {
    public:
        template<typename T>
        void output_integer(T var) {
            if (var == 0) { putchar_unlocked('0'); return; }
            if (var < 0)
                putchar_unlocked('-'),
                var = -var;
            char stack[32]; int stack_p = 0;
            while (var)
                stack[stack_p++] = '0' + (var % 10),
                var /= 10;
            while (stack_p)
                putchar_unlocked(stack[--stack_p]);
        }
        inline MaiPrinter& operator<<(char c) { putchar_unlocked(c); return *this; }
        inline MaiPrinter& operator<<(int var) { output_integer<int>(var); return *this; }
        inline MaiPrinter& operator<<(long long var) { output_integer<long long>(var); return *this; }
        inline MaiPrinter& operator<<(char* str_p) { while (*str_p) putchar_unlocked(*(str_p++)); return *this; }
        inline MaiPrinter& operator<<(const string& str) {
            const char* p = str.c_str();
            const char* l = p + str.size();
            while (p < l) putchar_unlocked(*p++);
            return *this;
        }
        template<typename IT> void join(IT begin, IT end, char sep = '\n') { for (auto it = begin; it != end; ++it) *this << *it << sep; }
    };
}
MaiScanner scanner;
MaiPrinter printer;



template<typename T>
// typedef double T;
class Matrix {
public:
    size_t height_, width_;
    valarray<T> data_;
    Matrix(size_t height, size_t width) :height_(height), width_(width), data_(height*width) {}
    Matrix(size_t height, size_t width, const valarray<T>& data) :height_(height), width_(width), data_(data) {}

    inline T& operator()(size_t y, size_t x) { return data_[y*width_ + x]; }
    inline T operator() (size_t y, size_t x) const { return data_[y*width_ + x]; }
    inline T& at(size_t y, size_t x) { return data_[y*width_ + x]; }
    inline T at(size_t y, size_t x) const { return data_[y*width_ + x]; }
    inline void resize(size_t h, size_t w) { height_ = h; width_ = w; data_.resize(h*w); }
    inline void resize(size_t h, size_t w, T val) { height_ = h; width_ = w; data_.resize(h*w, val); }
    inline void fill(T val) { data_ = val; }
    Matrix<T>& setDiag(T val) { for (size_t i = 0, en = min(width_, height_); i < en; ++i)at(i, i) = val; return *this; }

    void print(ostream& os) {
        os << "- - -" << endl; //  << setprecision(3)
        for (size_t y = 0; y < height_; ++y) {
            for (size_t x = 0; x < width_; ++x) {
                os << setw(7) << at(y, x) << ' ';
            }os << endl;
        }
    }
    valarray<valarray<T>> to_valarray() const {
        valarray<valarray<T>> work(height_);
        for (size_t i = 0; i < height_; ++i) {
            auto &v = work[i]; v.resize(height_);
            for (size_t j = 0; j < width_; ++j)
                v[j] = at(i, j);
        } return work;
    }
    // mathematics
    Matrix<T> pow(long long);
    double det() const; T tr();
    Matrix<T>& transpose_self(); Matrix<T> transpose() const;
    struct LU {
        size_t size;
        vector<int> pivot;
        vector<T> elem;
    };
};

// IO
template<typename T> inline ostream& operator << (ostream& os, Matrix<T> mat) { mat.print(os); return os; }

// 掛け算
template<typename T> Matrix<T> multiply(const Matrix<T>& mat1, const Matrix<T>& mat2) {
    assert(mat1.width_ == mat2.height_);
    Matrix<T> result(mat1.height_, mat2.width_);
    for (size_t i = 0; i < mat1.height_; i++) {
        for (size_t j = 0; j < mat2.width_; j++) {
            for (size_t k = 0; k < mat1.width_; k++) {
                result(i, j) += mat1(i, k) * mat2(k, j);
            }
        }
    }
    return result;
}
template<typename T> valarray<T> multiply(const Matrix<T>& mat1, const valarray<T>& vec2) {
    assert(mat1.width_ == vec2.size());
    valarray<T> result(mat1.height_);
    for (size_t i = 0, j; i < mat1.height_; i++) {
        for (j = 0; j < mat1.width_; j++) {
            result[i] += mat1(i, j) * vec2[j];
        }
    }
    return result;
}
template<typename T> inline Matrix<T>& operator*=(Matrix<T>& mat1, Matrix<T>& mat2) { mat1 = multiply(mat1, mat2); return mat1; }
template<typename T> inline Matrix<T> operator*(Matrix<T>& mat1, Matrix<T>& mat2) { return multiply(mat1, mat2); }


// スカラー
template<typename T> inline Matrix<T>& operator+=(Matrix<T>& mat, T val) { mat.data_ += val; return mat; }
template<typename T> inline Matrix<T>& operator*=(Matrix<T>& mat, T val) { mat.data_ *= val; return mat; }
template<typename T> inline Matrix<T>& operator/=(Matrix<T>& mat, T val) { mat.data_ /= val; return mat; }
template<typename T> inline Matrix<T>& operator^=(Matrix<T>& mat, T val) { mat.data_ ^= val; return mat; }

// 行列
template<typename T> inline Matrix<T>& operator+=(Matrix<T>& mat1, Matrix<T>& mat2) { mat1.data_ += mat2.data_; return mat1; }
template<typename T> inline Matrix<T> operator+(Matrix<T>& mat1, Matrix<T>& mat2) { return Matrix<T>(mat1.height_, mat1.width_, mat1.data_ + mat2.data_); }


template<typename T> Matrix<T> Matrix<T>::pow(long long p) {
    assert(height_ == width_);
    Matrix<T> a = *this;
    Matrix<T> b(height_, height_); b.setDiag(1);

    while (0 < p) {
        if (p % 2) {
            b *= a;
        }
        a *= a; p /= 2;
    }
    return b;
}






int height, width, turn;
int starty, startx, goaly, goalx;
int field[10][10];

int main() {

    scanner >> height >> width >> turn;
    scanner >> starty >> startx >> goaly >> goalx;

    Matrix<double> matF(81, 81);

    repeat(i, height) {
        string line;
        scanner >> line;
        repeat(j, width) {
            field[i][j] = line[j] == '.';
        }
    }

    repeat(i, 10) {
        repeat(j, 10) {
            if (!field[i][j]) continue;

            int id = i * 10 + j - 11;
            double sum
                = field[i - 1][j]
                + field[i + 1][j]
                + field[i][j - 1]
                + field[i][j + 1];

            if (sum == 0) {
                matF(id, id) = 1.0;
                continue;
            }

            if (field[i - 1][j])
                matF(id - 10, id) = 1.0 / sum;
            if (field[i + 1][j])
                matF(id + 10, id) = 1.0 / sum;
            if (field[i][j - 1])
                matF(id - 1, id) = 1.0 / sum;
            if (field[i][j + 1])
                matF(id + 1, id) = 1.0 / sum;
        }
    }

    auto matFt = matF.pow(turn);


    Matrix<double> vec1(81, 1);
    vec1(starty * 10 + startx - 1 - 11, 1) = 1.0;

    auto vect = matFt * vec1;
    double ans = vect(goaly * 10 + goalx - 1 - 11, 1);

    printf("%.10f\n", ans);


    return 0;
}