#include <bits/stdc++.h>
using namespace std;
#define sim template < class c
#define ris return * this
#define dor > debug & operator <<
#define eni(x) sim > typename \
enable_if<sizeof dud<c>(0) x 1, debug&>::type operator<<(c i) {
sim > struct rge { c b, e; };
sim > rge<c> range(c i, c j) { return rge<c>{i, j}; }
sim > auto dud(c* x) -> decltype(cerr << *x, 0);
sim > char dud(...);
struct debug {
#ifdef LOCAL
~debug() { cerr << endl; }
eni(!=) cerr << boolalpha << i; ris; }
eni(==) ris << range(begin(i), end(i)); }
sim, class b dor(pair < b, c > d) {
ris << "(" << d.first << ", " << d.second << ")";
}
sim dor(rge<c> d) {
*this << "[";
for (auto it = d.b; it != d.e; ++it)
*this << ", " + 2 * (it == d.b) << *it;
ris << "]";
}
#else
sim dor(const c&) { ris; }
#endif
};
#define imie(...) " [" << #__VA_ARGS__ ": " << (__VA_ARGS__) << "] "
// debug & operator << (debug & dd, P p) { dd << "(" << p.x << ", " << p.y << ")"; return dd; }
const int M = 65;
unsigned long long C[65][65];
int main() {
for (int i = 0; i < M; i++) {
C[i][0] = C[i][i] = 1;
for (int j = 1; j < i; j++) {
C[i][j] = C[i-1][j] + C[i-1][j-1];
}
}
int h, w;
cin >> h >> w;
vector<string> in(h);
int count_pawns = 0;
for (string& row : in) {
cin >> row;
for (char c : row) {
if (c == 'O') {
count_pawns++;
}
}
}
vector<string> target(h);
for (string& row : target) {
cin >> row;
}
auto getParity = [&](vector<string> grid) {
int p = 0;
for (int row = 0; row < h; row++) {
for (int col = 0; col < w; col++) {
if (grid[row][col] == 'O') {
p += row + col;
}
}
}
return p % 2;
};
if (getParity(in) != getParity(target)) {
puts("0");
return 0;
}
#define in ignore_in
int targetDegree = 0;
for (int row = 0; row < h; row++) {
for (int col = 0; col < w; col++) {
if (row + 1 < h && target[row][col] != target[row+1][col]) {
targetDegree++;
}
if (col + 1 < w && target[row][col] != target[row][col+1]) {
targetDegree++;
}
}
}
debug() << imie(targetDegree);
// answer = targetDegree / (sum of degrees)
unsigned long long ways = ((h - 1) * w + h * (w - 1)) * C[h*w-2][count_pawns-1];
printf("%.15lf\n", (double) targetDegree / ways);
debug() << imie(targetDegree) imie(ways);
// double p = (double) count_pawns / (h * w) * (h * w - count_pawns) / (h * w - 1);
// p *= 2;
// p is probability for a fixed edge to exist
// debug() << imie(p) imie(ways) imie(p * ways) imie(C[h*w][count_pawns]);
}
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 | #include <bits/stdc++.h> using namespace std; #define sim template < class c #define ris return * this #define dor > debug & operator << #define eni(x) sim > typename \ enable_if<sizeof dud<c>(0) x 1, debug&>::type operator<<(c i) { sim > struct rge { c b, e; }; sim > rge<c> range(c i, c j) { return rge<c>{i, j}; } sim > auto dud(c* x) -> decltype(cerr << *x, 0); sim > char dud(...); struct debug { #ifdef LOCAL ~debug() { cerr << endl; } eni(!=) cerr << boolalpha << i; ris; } eni(==) ris << range(begin(i), end(i)); } sim, class b dor(pair < b, c > d) { ris << "(" << d.first << ", " << d.second << ")"; } sim dor(rge<c> d) { *this << "["; for (auto it = d.b; it != d.e; ++it) *this << ", " + 2 * (it == d.b) << *it; ris << "]"; } #else sim dor(const c&) { ris; } #endif }; #define imie(...) " [" << #__VA_ARGS__ ": " << (__VA_ARGS__) << "] " // debug & operator << (debug & dd, P p) { dd << "(" << p.x << ", " << p.y << ")"; return dd; } const int M = 65; unsigned long long C[65][65]; int main() { for (int i = 0; i < M; i++) { C[i][0] = C[i][i] = 1; for (int j = 1; j < i; j++) { C[i][j] = C[i-1][j] + C[i-1][j-1]; } } int h, w; cin >> h >> w; vector<string> in(h); int count_pawns = 0; for (string& row : in) { cin >> row; for (char c : row) { if (c == 'O') { count_pawns++; } } } vector<string> target(h); for (string& row : target) { cin >> row; } auto getParity = [&](vector<string> grid) { int p = 0; for (int row = 0; row < h; row++) { for (int col = 0; col < w; col++) { if (grid[row][col] == 'O') { p += row + col; } } } return p % 2; }; if (getParity(in) != getParity(target)) { puts("0"); return 0; } #define in ignore_in int targetDegree = 0; for (int row = 0; row < h; row++) { for (int col = 0; col < w; col++) { if (row + 1 < h && target[row][col] != target[row+1][col]) { targetDegree++; } if (col + 1 < w && target[row][col] != target[row][col+1]) { targetDegree++; } } } debug() << imie(targetDegree); // answer = targetDegree / (sum of degrees) unsigned long long ways = ((h - 1) * w + h * (w - 1)) * C[h*w-2][count_pawns-1]; printf("%.15lf\n", (double) targetDegree / ways); debug() << imie(targetDegree) imie(ways); // double p = (double) count_pawns / (h * w) * (h * w - count_pawns) / (h * w - 1); // p *= 2; // p is probability for a fixed edge to exist // debug() << imie(p) imie(ways) imie(p * ways) imie(C[h*w][count_pawns]); } |
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