<p>You start at the cell <code>(rStart, cStart)</code> of an <code>rows x cols</code> grid facing east. The northwest corner is at the first row and column in the grid, and the southeast corner is at the last row and column.</p>

<p>You will walk in a clockwise spiral shape to visit every position in this grid. Whenever you move outside the grid&#39;s boundary, we continue our walk outside the grid (but may return to the grid boundary later.). Eventually, we reach all <code>rows * cols</code> spaces of the grid.</p>

<p>Return <em>an array of coordinates representing the positions of the grid in the order you visited them</em>.</p>

<p>&nbsp;</p>
<p><strong class="example">Example 1:</strong></p>
<img alt="" src="https://s3-lc-upload.s3.amazonaws.com/uploads/2018/08/24/example_1.png" style="width: 174px; height: 99px;" />
<pre>
<strong>Input:</strong> rows = 1, cols = 4, rStart = 0, cStart = 0
<strong>Output:</strong> [[0,0],[0,1],[0,2],[0,3]]
</pre>

<p><strong class="example">Example 2:</strong></p>
<img alt="" src="https://s3-lc-upload.s3.amazonaws.com/uploads/2018/08/24/example_2.png" style="width: 202px; height: 142px;" />
<pre>
<strong>Input:</strong> rows = 5, cols = 6, rStart = 1, cStart = 4
<strong>Output:</strong> [[1,4],[1,5],[2,5],[2,4],[2,3],[1,3],[0,3],[0,4],[0,5],[3,5],[3,4],[3,3],[3,2],[2,2],[1,2],[0,2],[4,5],[4,4],[4,3],[4,2],[4,1],[3,1],[2,1],[1,1],[0,1],[4,0],[3,0],[2,0],[1,0],[0,0]]
</pre>

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

<ul>
	<li><code>1 &lt;= rows, cols &lt;= 100</code></li>
	<li><code>0 &lt;= rStart &lt; rows</code></li>
	<li><code>0 &lt;= cStart &lt; cols</code></li>
</ul>

class Solution {
public:
    vector<vector<int>> spiralMatrixIII(int rows, int cols, int rStart, int cStart) {
        int y = rStart, x = cStart, step = 1;
        vector<vector<int>> out;
        auto is_done = [&]() {
            if (out.size() == rows * cols) return true;
            return false;
        };
        auto write = [&]() {
            if (!is_done() && y > -1 && y < rows && x > -1 && x < cols) {
                out.push_back({y, x});
            }
        };
        write();
        while (!is_done()) {
            // left -> right
            for (int i = 0; i < step; ++i) {   // 
                ++x;
                write();
            }

            // top -> down
            for (int i = 0; i < step; ++i) {   // 1,1 
                ++y;
                write();
            }
            ++step;

            // right -> left
            for (int i = 0; i < step; ++i) {
                --x;
                write();
            }
            // bottom -> up
            for (int i = 0; i < step; ++i) {
                --y;
                write();
            }
            ++step;
        }
        return out;
    }
};

/*

00  01  02  03  04  05
10  11  12  13  14  15
20  21  22  23  24  25
30  31  32  33  34  35
40  41  42  43  44  45

step 1, 2

step: 1

while (check())

left -> right 
top -> down
++step

right->left
bottom->up
++step

*/
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