#include <bits/stdc++.h> using namespace std; using LL = long long; #define FOR(i, l, r) for(int i = (l); i <= (r); ++i) #define REP(i, n) FOR(i, 0, (n) - 1) #define ssize(x) int(x.size()) template<class A, class B> auto &operator<<(ostream &o, pair<A, B> p) { return o << '(' << p.first << ", " << p.second << ')'; } template<class T> auto operator<<(ostream &o, T x) -> decltype(x.end(), o) { o << '{'; int i = 0; for (auto e : x) o << (", ")+2*!i++ << e; return o << '}'; } #ifdef DEBUG #define debug(x...) cerr << "[" #x "]: ", [](auto... $) {((cerr << $ << "; "), ...); }(x), cerr << '\n'; #else #define debug(...) {} #endif int main() { ios_base::sync_with_stdio(false); cin.tie(nullptr); int n, m; cin >> n >> m; vector<vector<char>> vs(n, vector<char>(m)), ve(n, vector<char>(m)); int coord_s = 0, coord_e = 0, k = 0; vector<int> dx = {-1, 0, 1, 0}, dy = {0, -1, 0, 1}; REP(i, n) { REP(j, m) { cin >> vs[i][j]; if (vs[i][j] == 'O') { coord_s += i + j; k += 1; } } } REP(i, n) { REP(j, m) { cin >> ve[i][j]; if (ve[i][j] == 'O') coord_e += i + j; } } if (coord_s % 2 != coord_e % 2) { cout << "0.0\n"; return 0; } auto valid = [&](int x, int y) { return x >= 0 and y >= 0 and x < n and y < m; }; auto possible_moves = [&](int x, int y) { int ans = 0; REP(i, 4) { auto nx = x + dx[i], ny = y + dy[i]; ans += valid(nx, ny) and ve[nx][ny] == '.'; } return ans; }; int deg = 0; REP(i, n) { REP(j, m) { if (ve[i][j] == 'O') deg += possible_moves(i, j); } } auto choose = [&](LL x, LL y) { if (x < 0 || y < 0 || x < y) return 0LL; LL ret = 1; for (LL i = 1; i <= y; i++) { ret *= x - i + 1; ret /= i; } return ret;; }; auto add_1D = [&](int neighbours) { int d = max(n, m); if (neighbours == 1) return choose(d - 2, k - 1); return choose(d - 3, k - 2) * 2 + choose(d - 3, k - 1) * 2; }; auto add = [&](int neighbours) { if (n == 1 or m == 1) return add_1D(neighbours); LL ret = 0; FOR(i, 1, neighbours) { ret += choose(n * m - neighbours - 1, k - neighbours + i - 1) * choose(neighbours, i) * (LL) i; } return ret; }; LL ev = 0; if (n == 1 or m == 1) { ev = add(1) * 2 + add(2) * (LL) (max(n, m) - 2); } else { ev = add(2) * 4 + add(3) * (LL) (2 * (n + m - 4)) + add(4) * (LL) ((n - 2) * (m - 2)); } cout << fixed << setprecision(15); cout << (long double) (2 * deg) / (long double) (ev) << '\n'; return 0; }
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 | #include <bits/stdc++.h> using namespace std; using LL = long long; #define FOR(i, l, r) for(int i = (l); i <= (r); ++i) #define REP(i, n) FOR(i, 0, (n) - 1) #define ssize(x) int(x.size()) template<class A, class B> auto &operator<<(ostream &o, pair<A, B> p) { return o << '(' << p.first << ", " << p.second << ')'; } template<class T> auto operator<<(ostream &o, T x) -> decltype(x.end(), o) { o << '{'; int i = 0; for (auto e : x) o << (", ")+2*!i++ << e; return o << '}'; } #ifdef DEBUG #define debug(x...) cerr << "[" #x "]: ", [](auto... $) {((cerr << $ << "; "), ...); }(x), cerr << '\n'; #else #define debug(...) {} #endif int main() { ios_base::sync_with_stdio(false); cin.tie(nullptr); int n, m; cin >> n >> m; vector<vector<char>> vs(n, vector<char>(m)), ve(n, vector<char>(m)); int coord_s = 0, coord_e = 0, k = 0; vector<int> dx = {-1, 0, 1, 0}, dy = {0, -1, 0, 1}; REP(i, n) { REP(j, m) { cin >> vs[i][j]; if (vs[i][j] == 'O') { coord_s += i + j; k += 1; } } } REP(i, n) { REP(j, m) { cin >> ve[i][j]; if (ve[i][j] == 'O') coord_e += i + j; } } if (coord_s % 2 != coord_e % 2) { cout << "0.0\n"; return 0; } auto valid = [&](int x, int y) { return x >= 0 and y >= 0 and x < n and y < m; }; auto possible_moves = [&](int x, int y) { int ans = 0; REP(i, 4) { auto nx = x + dx[i], ny = y + dy[i]; ans += valid(nx, ny) and ve[nx][ny] == '.'; } return ans; }; int deg = 0; REP(i, n) { REP(j, m) { if (ve[i][j] == 'O') deg += possible_moves(i, j); } } auto choose = [&](LL x, LL y) { if (x < 0 || y < 0 || x < y) return 0LL; LL ret = 1; for (LL i = 1; i <= y; i++) { ret *= x - i + 1; ret /= i; } return ret;; }; auto add_1D = [&](int neighbours) { int d = max(n, m); if (neighbours == 1) return choose(d - 2, k - 1); return choose(d - 3, k - 2) * 2 + choose(d - 3, k - 1) * 2; }; auto add = [&](int neighbours) { if (n == 1 or m == 1) return add_1D(neighbours); LL ret = 0; FOR(i, 1, neighbours) { ret += choose(n * m - neighbours - 1, k - neighbours + i - 1) * choose(neighbours, i) * (LL) i; } return ret; }; LL ev = 0; if (n == 1 or m == 1) { ev = add(1) * 2 + add(2) * (LL) (max(n, m) - 2); } else { ev = add(2) * 4 + add(3) * (LL) (2 * (n + m - 4)) + add(4) * (LL) ((n - 2) * (m - 2)); } cout << fixed << setprecision(15); cout << (long double) (2 * deg) / (long double) (ev) << '\n'; return 0; } |