// Time: O(MN * 2^(MN))
// Space: O(2^(MN))
class Solution {
public:
int minFlips(vector<vector<int>>& A) {
int start = 0, M = A.size(), N = A[0].size(), step = 0, dirs[5] = {1,0,-1,0,1};
for (int i = 0; i < M; ++i) {
for (int j = 0; j < N; ++j) {
start |= (A[i][j] << (i * 3 + j));
}
}
queue<int> q;
unordered_set<int> s;
q.push(start);
s.insert(start);
while (q.size()) {
int cnt = q.size();
while (cnt--) {
int state = q.front();
q.pop();
if (state == 0) return step;
for (int i = 0; i < 9; ++i) {
int next = state, r = i / 3, c = i % 3;
next ^= (1 << (r * 3 + c));
for (int j = 0; j < 4; ++j) {
int x = r + dirs[j], y = c + dirs[j + 1];
if (x < 0 || x >= M || y < 0 || y >= N) continue;
next ^= (1 << (x * 3 + y));
}
if (s.count(next) == 0) {
q.push(next);
s.insert(next);
}
}
}
++step;
}
return -1;
}
};
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