<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:
    typedef std::pair<int, int> point; 
    
    bool valid(point p, int rows, int cols) {
        if(p.first<0 || p.first>=rows || p.second<0 || p.second>=cols)
            return false;
        return true; 
    }

    vector<int> findDiagonalOrder(vector<vector<int>>& mat) {

        int rows=mat.size();
        int cols=mat[0].size(); 
        
        vector<vector<point>> hlist; 
        
        for(int i=0; i<rows; i++) {
            vector<point> dlist;
            int k=i;
            int j=0;  
            while(j<=i) {
                point p({k,j});
                if (valid(p, rows, cols)) {
                    dlist.push_back(p);
                } else {
                    break;
                }
                k--;
                j++;
            }      
            hlist.push_back(dlist); 
        }

        for(int i=1; i<cols; i++) {
            vector<point> dlist;
            int k=i;
            int j=rows-1;  
            while(k<cols) {
                point p({j,k});
                if (valid(p, rows, cols)) {
                    dlist.push_back(p);
                } else {
                    break;
                }
                k++;
                j--;
            }      
            hlist.push_back(dlist); 
        }



        vector<int> out; 
        for(int i=0; i<hlist.size(); i++) {
            bool is_odd=i%2; 
            if(!is_odd) {
                for(int j=0; j<hlist[i].size(); j++) {
                    point x=hlist[i][j];
                    out.push_back(mat[x.first][x.second]);
                }
            } else {
                for(int j=hlist[i].size()-1; j>=0; j--) {
                    point x=hlist[i][j];
                    out.push_back(mat[x.first][x.second]);
                }
            }
        }
        return out;
    }
};
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