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| 1 | +<h2><a href="https://leetcode.com/problems/construct-quad-tree/">427. Construct Quad Tree</a></h2><h3>Medium</h3><hr><div><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> |
| 2 | + |
| 3 | +<p>Return <em>the root of the Quad-Tree representing </em><code>grid</code>.</p> |
| 4 | + |
| 5 | +<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> |
| 6 | + |
| 7 | +<ul> |
| 8 | + <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> |
| 9 | + <li><code>isLeaf</code>: True if the node is a leaf node on the tree or False if the node has four children.</li> |
| 10 | +</ul> |
| 11 | + |
| 12 | +<pre>class Node { |
| 13 | + public boolean val; |
| 14 | + public boolean isLeaf; |
| 15 | + public Node topLeft; |
| 16 | + public Node topRight; |
| 17 | + public Node bottomLeft; |
| 18 | + public Node bottomRight; |
| 19 | +}</pre> |
| 20 | + |
| 21 | +<p>We can construct a Quad-Tree from a two-dimensional area using the following steps:</p> |
| 22 | + |
| 23 | +<ol> |
| 24 | + <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> |
| 25 | + <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> |
| 26 | + <li>Recurse for each of the children with the proper sub-grid.</li> |
| 27 | +</ol> |
| 28 | +<img alt="" src="https://assets.leetcode.com/uploads/2020/02/11/new_top.png" style="width: 777px; height: 181px;"> |
| 29 | +<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> |
| 30 | + |
| 31 | +<p><strong>Quad-Tree format:</strong></p> |
| 32 | + |
| 33 | +<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> |
| 34 | + |
| 35 | +<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> |
| 36 | + |
| 37 | +<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> |
| 38 | + |
| 39 | +<p> </p> |
| 40 | +<p><strong class="example">Example 1:</strong></p> |
| 41 | +<img alt="" src="https://assets.leetcode.com/uploads/2020/02/11/grid1.png" style="width: 777px; height: 99px;"> |
| 42 | +<pre><strong>Input:</strong> grid = [[0,1],[1,0]] |
| 43 | +<strong>Output:</strong> [[0,1],[1,0],[1,1],[1,1],[1,0]] |
| 44 | +<strong>Explanation:</strong> The explanation of this example is shown below: |
| 45 | +Notice that 0 represnts False and 1 represents True in the photo representing the Quad-Tree. |
| 46 | +<img alt="" src="https://assets.leetcode.com/uploads/2020/02/12/e1tree.png" style="width: 777px; height: 186px;"> |
| 47 | +</pre> |
| 48 | + |
| 49 | +<p><strong class="example">Example 2:</strong></p> |
| 50 | + |
| 51 | +<p><img alt="" src="https://assets.leetcode.com/uploads/2020/02/12/e2mat.png" style="width: 777px; height: 343px;"></p> |
| 52 | + |
| 53 | +<pre><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]] |
| 54 | +<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]] |
| 55 | +<strong>Explanation:</strong> All values in the grid are not the same. We divide the grid into four sub-grids. |
| 56 | +The topLeft, bottomLeft and bottomRight each has the same value. |
| 57 | +The topRight have different values so we divide it into 4 sub-grids where each has the same value. |
| 58 | +Explanation is shown in the photo below: |
| 59 | +<img alt="" src="https://assets.leetcode.com/uploads/2020/02/12/e2tree.png" style="width: 777px; height: 328px;"> |
| 60 | +</pre> |
| 61 | + |
| 62 | +<p> </p> |
| 63 | +<p><strong>Constraints:</strong></p> |
| 64 | + |
| 65 | +<ul> |
| 66 | + <li><code>n == grid.length == grid[i].length</code></li> |
| 67 | + <li><code>n == 2<sup>x</sup></code> where <code>0 <= x <= 6</code></li> |
| 68 | +</ul> |
| 69 | +</div> |
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