#include <bits/stdc++.h>
using namespace std;
typedef vector<int> VI;
typedef pair <int,int> ii;
typedef long long LL;
#define pb push_back
const int INF = 2147483647;
const int N = 10;
int dx[4] = {-1, 1, 0, 0};
int dy[4] = {0, 0, -1, 1};
int n, m, i, j, k, d, par, num, col[N][N], colNum[2], actNum[2], miss[2], mis, l, len, c;
LL sum, act;
char t[N];
ii kol[N * N];
vector<ii> startV, endV, ne;
bool oks(int a, int b) {
return a >= 0 && a < n && b >= 0 && b < m;
}
bool oks(int a, int b, vector<ii>& pos) {
if (a >= 0 && a < n && b >= 0 && b < m) {
for (auto& w : pos) if (w.first == a && w.second == b) return false;
return true;
}
return false;
}
int eval(vector<ii>& pos) {
int res = 0;
for (auto& w : pos) {
for (int k=0;k<4;k++) if (oks(w.first + dx[k], w.second + dy[k], pos)) res++;
}
return res;
}
int evalParity(vector<ii>& pos) {
int res = 0;
for (auto& w : pos) res += col[w.first][w.second];
return res % 2;
}
LL comb(int a, int b) {
LL res = 1;
for (int i=a;i>a-b;i--) res *= i;
for (int i=2;i<=b;i++) res /= i;
return res;
}
int main() {
scanf("%d %d", &n, &m);
for (i=0;i<n;i++) for (j=0;j<m;j++) {
col[i][j] = (i + j) % 2;
colNum[col[i][j]]++;
}
for (i=0;i<n;i++) {
scanf("%s", t);
for (j=0;j<m;j++) if (t[j] == 'O') startV.pb(ii(i, j));
}
for (i=0;i<n;i++) {
scanf("%s", t);
for (j=0;j<m;j++) if (t[j] == 'O') endV.pb(ii(i, j));
}
num = startV.size();
par = evalParity(startV);
if (par != evalParity(endV)) {
printf("0\n");
return 0;
}
sum = 0;
for (i=0;i<n;i++) for (j=0;j<m;j++) {
ne.clear();
for (k=0;k<4;k++) if (oks(i + dx[k], j + dy[k])) ne.pb(ii(i + dx[k], j + dy[k]));
len = ne.size();
for (k=0;k<(1<<len);k++) if (1 + __builtin_popcount(k) <= startV.size()) {
actNum[0] = actNum[1] = 0;
miss[0] = colNum[0];
miss[1] = colNum[1];
actNum[col[i][j]]++;
miss[col[i][j]]--;
for (l=0;l<len;l++) {
c = col[ne[l].first][ne[l].second];
if ((1<<l) & k) actNum[c]++;
miss[c]--;
}
mis = startV.size() - 1 - __builtin_popcount(k);
//printf(" %d %d %d\n", miss[0], miss[1], mis);
for (l=0;l<=mis;l++) if ((actNum[1] + l) % 2 == par && l <= miss[1] && (mis - l) <= miss[0]) {
act = comb(miss[1], l) * comb(miss[0], mis - l) * (len - __builtin_popcount(k));
sum += act;
}
//printf("%d %lld\n", k, sum);
}
//printf("%lld\n", sum);
//return 0;
}
//if (n > 1 && m > 1) sum /= startV.size();
//printf("%lld\n", sum);
printf("%.15lf\n", eval(endV) * 1.0 / sum);
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 | #include <bits/stdc++.h> using namespace std; typedef vector<int> VI; typedef pair <int,int> ii; typedef long long LL; #define pb push_back const int INF = 2147483647; const int N = 10; int dx[4] = {-1, 1, 0, 0}; int dy[4] = {0, 0, -1, 1}; int n, m, i, j, k, d, par, num, col[N][N], colNum[2], actNum[2], miss[2], mis, l, len, c; LL sum, act; char t[N]; ii kol[N * N]; vector<ii> startV, endV, ne; bool oks(int a, int b) { return a >= 0 && a < n && b >= 0 && b < m; } bool oks(int a, int b, vector<ii>& pos) { if (a >= 0 && a < n && b >= 0 && b < m) { for (auto& w : pos) if (w.first == a && w.second == b) return false; return true; } return false; } int eval(vector<ii>& pos) { int res = 0; for (auto& w : pos) { for (int k=0;k<4;k++) if (oks(w.first + dx[k], w.second + dy[k], pos)) res++; } return res; } int evalParity(vector<ii>& pos) { int res = 0; for (auto& w : pos) res += col[w.first][w.second]; return res % 2; } LL comb(int a, int b) { LL res = 1; for (int i=a;i>a-b;i--) res *= i; for (int i=2;i<=b;i++) res /= i; return res; } int main() { scanf("%d %d", &n, &m); for (i=0;i<n;i++) for (j=0;j<m;j++) { col[i][j] = (i + j) % 2; colNum[col[i][j]]++; } for (i=0;i<n;i++) { scanf("%s", t); for (j=0;j<m;j++) if (t[j] == 'O') startV.pb(ii(i, j)); } for (i=0;i<n;i++) { scanf("%s", t); for (j=0;j<m;j++) if (t[j] == 'O') endV.pb(ii(i, j)); } num = startV.size(); par = evalParity(startV); if (par != evalParity(endV)) { printf("0\n"); return 0; } sum = 0; for (i=0;i<n;i++) for (j=0;j<m;j++) { ne.clear(); for (k=0;k<4;k++) if (oks(i + dx[k], j + dy[k])) ne.pb(ii(i + dx[k], j + dy[k])); len = ne.size(); for (k=0;k<(1<<len);k++) if (1 + __builtin_popcount(k) <= startV.size()) { actNum[0] = actNum[1] = 0; miss[0] = colNum[0]; miss[1] = colNum[1]; actNum[col[i][j]]++; miss[col[i][j]]--; for (l=0;l<len;l++) { c = col[ne[l].first][ne[l].second]; if ((1<<l) & k) actNum[c]++; miss[c]--; } mis = startV.size() - 1 - __builtin_popcount(k); //printf(" %d %d %d\n", miss[0], miss[1], mis); for (l=0;l<=mis;l++) if ((actNum[1] + l) % 2 == par && l <= miss[1] && (mis - l) <= miss[0]) { act = comb(miss[1], l) * comb(miss[0], mis - l) * (len - __builtin_popcount(k)); sum += act; } //printf("%d %lld\n", k, sum); } //printf("%lld\n", sum); //return 0; } //if (n > 1 && m > 1) sum /= startV.size(); //printf("%lld\n", sum); printf("%.15lf\n", eval(endV) * 1.0 / sum); return 0; } |
English