double dfs(state &u) {
if (u.c.size() == 1) return 0;
sort(u.c.begin() + 1, u.c.end());
int h = u.hash();
if (hash[h].find(u) != hash[h].end())
return hash[h][u];
double &ret = hash[h][u];
double self = 0, total = 0;
ret = 0;
for (int i = 0; i < u.c.size(); i++)
total += u.c[i];
total = total - 1, self = u.c[0] - 1;
for (int i = 1; i < u.c.size(); i++) {
state v = u;
v.c[0] += v.c[i];
v.c.erase(v.c.begin() + i);
ret += u.c[i] * dfs(v);
}
// E[u] = 1 + E[v] * p + E[u] * q
ret = (ret / total) + 1;
ret = ret / (1 - self / total);
return ret;
}
int bfs(state init) {
for (int i = 0; i < hash_mod; i++)
hash[i].clear();
int h = init.hash(), ti, tj;
state u, v;
queue<state> Q;
Q.push(init), hash[h][init] = 0;
while (!Q.empty()) {
u = Q.front(), Q.pop();
h = u.hash();
int step = hash[h][u];
if (u.g[2][4] == 'w' && u.g[2][5] == 'w') {
// u.print();
return step;
}
for (int i = 0; i < 6; i++) {
for (int j = 0; j < 6; j++) {
if (u.g[i][j] < 'a' || u.g[i][j] > 'z')
continue;
ti = i, tj = j;
v = u;
while (ti-1 >= 0 && v.g[ti-1][tj] == ' ' && ti+1 < 6 && v.g[ti][tj] == v.g[ti+1][tj]) { // shift up
v = shiftup(v, ti, tj);
ti--;
h = v.hash();
if (hash[h].find(v) == hash[h].end()) {
hash[h][v] = step+1;
Q.push(v);
}
// v.print();
}
ti = i, tj = j;
v = u;
while (ti-1 >= 0 && v.g[ti-1][tj] == v.g[ti][tj] && ti+1 < 6 && v.g[ti+1][tj] == ' ') { // shift down
v = shiftdown(v, ti, tj);
ti++;
h = v.hash();
if (hash[h].find(v) == hash[h].end()) {
hash[h][v] = step+1;
Q.push(v);
}
// v.print();
}
ti = i, tj = j;
v = u;
while (tj-1 >= 0 && v.g[ti][tj-1] == ' ' && tj+1 < 6 && v.g[ti][tj] == v.g[ti][tj+1]) { // shift left
v = shiftleft(v, ti, tj);
tj--;
h = v.hash();
if (hash[h].find(v) == hash[h].end()) {
hash[h][v] = step+1;
Q.push(v);
}
// v.print();
}
ti = i, tj = j;
v = u;
while (tj-1 >= 0 && v.g[ti][tj-1] == v.g[ti][tj] && tj+1 < 6 && v.g[ti][tj+1] == ' ') { // shift right
v = shiftright(v, ti, tj);
tj++;
h = v.hash();
if (hash[h].find(v) == hash[h].end()) {
hash[h][v] = step+1;
Q.push(v);
}
// v.print();
}
}
}
}
return -1;
}
