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72 lines
4.2 KiB
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72 lines
4.2 KiB
HTML
<p>Given a <code>n * n</code> matrix <code>grid</code> of <code>0's</code> and <code>1's</code> only. We want to represent <code>grid</code> with a Quad-Tree.</p>
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<p>Return <em>the root of the Quad-Tree representing </em><code>grid</code>.</p>
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<p>A Quad-Tree is a tree data structure in which each internal node has exactly four children. Besides, each node has two attributes:</p>
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<ul>
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<li><code>val</code>: True if the node represents a grid of 1's or False if the node represents a grid of 0's. Notice that you can assign the <code>val</code> to True or False when <code>isLeaf</code> is False, and both are accepted in the answer.</li>
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<li><code>isLeaf</code>: True if the node is a leaf node on the tree or False if the node has four children.</li>
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</ul>
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<pre>
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class Node {
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public boolean val;
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public boolean isLeaf;
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public Node topLeft;
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public Node topRight;
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public Node bottomLeft;
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public Node bottomRight;
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}</pre>
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<p>We can construct a Quad-Tree from a two-dimensional area using the following steps:</p>
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<ol>
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<li>If the current grid has the same value (i.e all <code>1's</code> or all <code>0's</code>) set <code>isLeaf</code> True and set <code>val</code> to the value of the grid and set the four children to Null and stop.</li>
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<li>If the current grid has different values, set <code>isLeaf</code> to False and set <code>val</code> to any value and divide the current grid into four sub-grids as shown in the photo.</li>
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<li>Recurse for each of the children with the proper sub-grid.</li>
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</ol>
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<img alt="" src="https://assets.leetcode.com/uploads/2020/02/11/new_top.png" style="width: 777px; height: 181px;" />
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<p>If you want to know more about the Quad-Tree, you can refer to the <a href="https://en.wikipedia.org/wiki/Quadtree">wiki</a>.</p>
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<p><strong>Quad-Tree format:</strong></p>
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<p>You don't need to read this section for solving the problem. This is only if you want to understand the output format here. The output represents the serialized format of a Quad-Tree using level order traversal, where <code>null</code> signifies a path terminator where no node exists below.</p>
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<p>It is very similar to the serialization of the binary tree. The only difference is that the node is represented as a list <code>[isLeaf, val]</code>.</p>
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<p>If the value of <code>isLeaf</code> or <code>val</code> is True we represent it as <strong>1</strong> in the list <code>[isLeaf, val]</code> and if the value of <code>isLeaf</code> or <code>val</code> is False we represent it as <strong>0</strong>.</p>
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<p> </p>
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<p><strong class="example">Example 1:</strong></p>
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<img alt="" src="https://assets.leetcode.com/uploads/2020/02/11/grid1.png" style="width: 777px; height: 99px;" />
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<pre>
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<strong>Input:</strong> grid = [[0,1],[1,0]]
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<strong>Output:</strong> [[0,1],[1,0],[1,1],[1,1],[1,0]]
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<strong>Explanation:</strong> The explanation of this example is shown below:
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Notice that 0 represents False and 1 represents True in the photo representing the Quad-Tree.
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<img alt="" src="https://assets.leetcode.com/uploads/2020/02/12/e1tree.png" style="width: 777px; height: 186px;" />
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</pre>
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<p><strong class="example">Example 2:</strong></p>
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<p><img alt="" src="https://assets.leetcode.com/uploads/2020/02/12/e2mat.png" style="width: 777px; height: 343px;" /></p>
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<pre>
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<strong>Input:</strong> grid = [[1,1,1,1,0,0,0,0],[1,1,1,1,0,0,0,0],[1,1,1,1,1,1,1,1],[1,1,1,1,1,1,1,1],[1,1,1,1,0,0,0,0],[1,1,1,1,0,0,0,0],[1,1,1,1,0,0,0,0],[1,1,1,1,0,0,0,0]]
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<strong>Output:</strong> [[0,1],[1,1],[0,1],[1,1],[1,0],null,null,null,null,[1,0],[1,0],[1,1],[1,1]]
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<strong>Explanation:</strong> All values in the grid are not the same. We divide the grid into four sub-grids.
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The topLeft, bottomLeft and bottomRight each has the same value.
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The topRight have different values so we divide it into 4 sub-grids where each has the same value.
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Explanation is shown in the photo below:
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<img alt="" src="https://assets.leetcode.com/uploads/2020/02/12/e2tree.png" style="width: 777px; height: 328px;" />
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</pre>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>n == grid.length == grid[i].length</code></li>
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<li><code>n == 2<sup>x</sup></code> where <code>0 <= x <= 6</code></li>
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</ul>
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