<p>Given an <code>m x n</code> matrix <code>mat</code>, return <em>an array of all the elements of the array in a diagonal order</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://assets.leetcode.com/uploads/2021/04/10/diag1-grid.jpg" style="width: 334px; height: 334px;" />
<pre>
<strong>Input:</strong> mat = [[1,2,3],[4,5,6],[7,8,9]]
<strong>Output:</strong> [1,2,4,7,5,3,6,8,9]
</pre>

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

<pre>
<strong>Input:</strong> mat = [[1,2],[3,4]]
<strong>Output:</strong> [1,2,3,4]
</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;= 10<sup>4</sup></code></li>
	<li><code>1 &lt;= m * n &lt;= 10<sup>4</sup></code></li>
	<li><code>-10<sup>5</sup> &lt;= mat[i][j] &lt;= 10<sup>5</sup></code></li>
</ul>

class Solution {
public:
    inline bool valid(int i, int j) {
        return i >= 0 && i < r && j >= 0 && j < c;
    }    
    vector<int> findDiagonalOrder(vector<vector<int>>& mat) {
        queue<pair<int, int>> q;
        r = mat.size();
        if (r == 0) {
            return {};
        }
        c = mat[0].size();
        q.emplace(0, 0);
        vector<int> res;
        const static vector<pair<int, int>> moves = {{-1, 1},{1, -1}};
        const static vector<pair<int, int>> next = {{1, 0},{0, 1}};

        while (!q.empty()) {
            auto p = q.front();
            q.pop();
            int idx = (p.first + p.second) % 2;
            if (!valid(p.first, p.second)) {
                q.emplace(p.first + moves[idx].first, p.second + moves[idx].second);
                continue;
            }
            res.emplace_back(mat[p.first][p.second]);
            if (p.first == r - 1 && p.second == c - 1) {
                break;
            }
            auto i = p.first + moves[idx].first, j = p.second + moves[idx].second;
            if (!valid(i, j)) {
                i += next[idx].first; j += next[idx].second;                
            } 
            q.emplace(i, j);
        }
        return res;
    }
private:
    int r, c;
};
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