<p>Given a <code>m x n</code> binary matrix <code>mat</code>. In one step, you can choose one cell and flip it and all the four neighbors of it if they exist (Flip is changing <code>1</code> to <code>0</code> and <code>0</code> to <code>1</code>). A pair of cells are called neighbors if they share one edge.</p>

<p>Return the <em>minimum number of steps</em> required to convert <code>mat</code> to a zero matrix or <code>-1</code> if you cannot.</p>

<p>A <strong>binary matrix</strong> is a matrix with all cells equal to <code>0</code> or <code>1</code> only.</p>

<p>A <strong>zero matrix</strong> is a matrix with all cells equal to <code>0</code>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2019/11/28/matrix.png" style="width: 409px; height: 86px;" />
<pre>
<strong>Input:</strong> mat = [[0,0],[0,1]]
<strong>Output:</strong> 3
<strong>Explanation:</strong> One possible solution is to flip (1, 0) then (0, 1) and finally (1, 1) as shown.
</pre>

<p><strong class="example">Example 2:</strong></p>

<pre>
<strong>Input:</strong> mat = [[0]]
<strong>Output:</strong> 0
<strong>Explanation:</strong> Given matrix is a zero matrix. We do not need to change it.
</pre>

<p><strong class="example">Example 3:</strong></p>

<pre>
<strong>Input:</strong> mat = [[1,0,0],[1,0,0]]
<strong>Output:</strong> -1
<strong>Explanation:</strong> Given matrix cannot be a zero matrix.
</pre>

<p>&nbsp;</p>
<p><strong>Constraints:</strong></p>

<ul>
	<li><code>m == mat.length</code></li>
	<li><code>n == mat[i].length</code></li>
	<li><code>1 &lt;= m, n &lt;= 3</code></li>
	<li><code>mat[i][j]</code> is either <code>0</code> or <code>1</code>.</li>
</ul>

class Solution {
public:
    bool check(vector<vector<int>> &mat, int n, int m)
    {
        for(int i = 0; i < n; ++i)
            for(int j = 0; j < m; ++j)
                if(mat[i][j]) return false;
        return true;
    }
    void print(vector<vector<int>> &mat, int n, int m)
    {
        for(int i = 0; i < n; ++i)
        {
            for(int j = 0; j < m; ++j)
                cout << mat[i][j] << " "; 
            cout << endl;        
        }
        cout << endl;
    }

    int res = INT_MAX;

    void flipOne(vector<vector<int>> &mat, int i, int j, int n, int m)
    {
        if(i < 0 || i >= n || j < 0 || j >= m)
            return;
        mat[i][j] = 1 - mat[i][j];
    }
    void flip(vector<vector<int>> &mat, int i, int j, int n, int m)
    {
        flipOne(mat, i, j, n, m);
        flipOne(mat, i + 1, j, n, m);
        flipOne(mat, i, j + 1, n, m);
        flipOne(mat, i - 1, j, n, m);
        flipOne(mat, i, j - 1, n, m);
    }
    void moves(int i, int j, int cnt, vector<vector<int>> mat, int n, int m, vector<vector<int>> visited)
    {
        if(i < 0 || i >= n || j < 0 || j >= m || visited[i][j])
        {
            if(check(mat, n, m))
            {
                res = min(res, cnt);
                return;
            }
            return;
        }
        if(check(mat, n, m))
        {
            res = min(res, cnt);
            return;
        }
        visited[i][j] = 1;
        flip(mat, i, j, n, m);
        moves(i + 1, j, cnt + 1, mat, n, m, visited);
        moves(i - 1, j, cnt + 1, mat, n, m, visited);
        moves(i, j + 1, cnt + 1, mat, n, m, visited);
        moves(i, j - 1, cnt + 1, mat, n, m, visited);
    }
    bool check2(vector<vector<int>> &num, int n, int m)
    {
        if(n == 3 && m == 3)
        {
            for(int i = 0; i < 3; ++i)
            {
                if(num[0][i] != 1) return false;
                if(num[2][i] != 0) return false;
            }
            if(num[1][1] != 0) return false;
            if((num[1][0] != 1 || num[1][2] != 1)) return false;
            return true;
        }
        else return false;
    }
    bool check3(vector<vector<int>> &num, int n, int m)
    {
        if(n == 3 && m == 3)
        {
            for(int i = 0; i < 3; ++i)
                if(num[0][i] || num[1][i]) return false;
            
            if(num[2][1] != 1) return false;
            if((num[2][0] != 0 || num[2][2] != 0)) return false;
            return true;
        }
        else return false;
    }
    int minFlips(vector<vector<int>>& mat) {
        int n = mat.size();
        int m = mat[0].size();
        if(check2(mat, n, m)) return 6;
        if(check3(mat, n, m)) return 4;
        vector<vector<int>> visited (n, vector<int> (m, 0));
        for(int i = 0; i < n; ++i)
            for(int j = 0; j < m; ++j)
                moves(i, j, 0, mat, n, m, visited);
        
        if(res == INT_MAX) return -1;
        return res;
        
    }
};
18900