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            "questionId": "772",
            "questionFrontendId": "427",
            "categoryTitle": "Algorithms",
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            "title": "Construct Quad Tree",
            "titleSlug": "construct-quad-tree",
            "content": "<p>Given a <code>n * n</code> matrix <code>grid</code> of <code>0&#39;s</code> and <code>1&#39;s</code> only. We want to represent the <code>grid</code> with a Quad-Tree.</p>\n\n<p>Return <em>the root of the Quad-Tree</em> representing the <code>grid</code>.</p>\n\n<p>Notice that you can assign the value of a node to <strong>True</strong> or <strong>False</strong> when <code>isLeaf</code> is <strong>False</strong>, and both are <strong>accepted</strong> in the answer.</p>\n\n<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>\n\n<ul>\n\t<li><code>val</code>: True if the node represents a grid of 1&#39;s or False if the node represents a grid of 0&#39;s.</li>\n\t<li><code>isLeaf</code>: True if the node is leaf node on the tree or False if the node has the four children.</li>\n</ul>\n\n<pre>\nclass Node {\n    public boolean val;\n    public boolean isLeaf;\n    public Node topLeft;\n    public Node topRight;\n    public Node bottomLeft;\n    public Node bottomRight;\n}</pre>\n\n<p>We can construct a Quad-Tree from a two-dimensional area using the following steps:</p>\n\n<ol>\n\t<li>If the current grid has the same value (i.e all <code>1&#39;s</code> or all <code>0&#39;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>\n\t<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>\n\t<li>Recurse for each of the children with the proper sub-grid.</li>\n</ol>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/02/11/new_top.png\" style=\"width: 777px; height: 181px;\" />\n<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>\n\n<p><strong>Quad-Tree format:</strong></p>\n\n<p>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>\n\n<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>\n\n<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>\n\n<p>&nbsp;</p>\n<p><strong>Example 1:</strong></p>\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/02/11/grid1.png\" style=\"width: 777px; height: 99px;\" />\n<pre>\n<strong>Input:</strong> grid = [[0,1],[1,0]]\n<strong>Output:</strong> [[0,1],[1,0],[1,1],[1,1],[1,0]]\n<strong>Explanation:</strong> The explanation of this example is shown below:\nNotice that 0 represnts False and 1 represents True in the photo representing the Quad-Tree.\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/02/12/e1tree.png\" style=\"width: 777px; height: 186px;\" />\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/02/12/e2mat.png\" style=\"width: 777px; height: 343px;\" /></p>\n\n<pre>\n<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]]\n<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]]\n<strong>Explanation:</strong> All values in the grid are not the same. We divide the grid into four sub-grids.\nThe topLeft, bottomLeft and bottomRight each has the same value.\nThe topRight have different values so we divide it into 4 sub-grids where each has the same value.\nExplanation is shown in the photo below:\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/02/12/e2tree.png\" style=\"width: 777px; height: 328px;\" />\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>n == grid.length == grid[i].length</code></li>\n\t<li><code>n == 2<sup>x</sup></code> where <code>0 &lt;= x &lt;= 6</code></li>\n</ul>\n",
            "translatedTitle": "建立四叉树",
            "translatedContent": "<p>给你一个 <code>n * n</code> 矩阵 <code>grid</code> ，矩阵由若干 <code>0</code> 和 <code>1</code> 组成。请你用四叉树表示该矩阵 <code>grid</code> 。</p>\n\n<p>你需要返回能表示矩阵的 四叉树 的根结点。</p>\n\n<p>注意，当 <code>isLeaf</code> 为 <strong>False </strong>时，你可以把 <strong>True</strong> 或者 <strong>False</strong> 赋值给节点，两种值都会被判题机制 <strong>接受</strong> 。</p>\n\n<p>四叉树数据结构中，每个内部节点只有四个子节点。此外，每个节点都有两个属性：</p>\n\n<ul>\n\t<li><code>val</code>：储存叶子结点所代表的区域的值。1 对应 <strong>True</strong>，0 对应 <strong>False</strong>；</li>\n\t<li><code>isLeaf</code>: 当这个节点是一个叶子结点时为 <strong>True</strong>，如果它有 4 个子节点则为 <strong>False</strong> 。</li>\n</ul>\n\n<pre>class Node {\n    public boolean val;\n&nbsp; &nbsp; public boolean isLeaf;\n&nbsp; &nbsp; public Node topLeft;\n&nbsp; &nbsp; public Node topRight;\n&nbsp; &nbsp; public Node bottomLeft;\n&nbsp; &nbsp; public Node bottomRight;\n}</pre>\n\n<p>我们可以按以下步骤为二维区域构建四叉树：</p>\n\n<ol>\n\t<li>如果当前网格的值相同（即，全为 <code>0</code> 或者全为 <code>1</code>），将 <code>isLeaf</code> 设为 True ，将 <code>val</code> 设为网格相应的值，并将四个子节点都设为 Null 然后停止。</li>\n\t<li>如果当前网格的值不同，将 <code>isLeaf</code> 设为 False， 将 <code>val</code> 设为任意值，然后如下图所示，将当前网格划分为四个子网格。</li>\n\t<li>使用适当的子网格递归每个子节点。</li>\n</ol>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/02/11/new_top.png\" style=\"height: 181px; width: 777px;\"></p>\n\n<p>如果你想了解更多关于四叉树的内容，可以参考 <a href=\"https://en.wikipedia.org/wiki/Quadtree\">wiki</a> 。</p>\n\n<p><strong>四叉树格式：</strong></p>\n\n<p>输出为使用层序遍历后四叉树的序列化形式，其中 <code>null</code> 表示路径终止符，其下面不存在节点。</p>\n\n<p>它与二叉树的序列化非常相似。唯一的区别是节点以列表形式表示 <code>[isLeaf, val]</code> 。</p>\n\n<p>如果 <code>isLeaf</code> 或者 <code>val</code> 的值为 True ，则表示它在列表&nbsp;<code>[isLeaf, val]</code> 中的值为 <strong>1</strong> ；如果 <code>isLeaf</code> 或者 <code>val</code> 的值为 False ，则表示值为 <strong>0 </strong>。</p>\n\n<p>&nbsp;</p>\n\n<p><strong>示例 1：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/02/11/grid1.png\" style=\"height: 99px; width: 777px;\"></p>\n\n<pre><strong>输入：</strong>grid = [[0,1],[1,0]]\n<strong>输出：</strong>[[0,1],[1,0],[1,1],[1,1],[1,0]]\n<strong>解释：</strong>此示例的解释如下：\n请注意，在下面四叉树的图示中，0 表示 false，1 表示 True 。\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/02/12/e1tree.png\" style=\"height: 186px; width: 777px;\">\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/02/12/e2mat.png\" style=\"height: 343px; width: 777px;\"></p>\n\n<pre><strong>输入：</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]]\n<strong>输出：</strong>[[0,1],[1,1],[0,1],[1,1],[1,0],null,null,null,null,[1,0],[1,0],[1,1],[1,1]]\n<strong>解释：</strong>网格中的所有值都不相同。我们将网格划分为四个子网格。\ntopLeft，bottomLeft 和 bottomRight 均具有相同的值。\ntopRight 具有不同的值，因此我们将其再分为 4 个子网格，这样每个子网格都具有相同的值。\n解释如下图所示：\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/02/12/e2tree.png\" style=\"height: 328px; width: 777px;\">\n</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<pre><strong>输入：</strong>grid = [[1,1],[1,1]]\n<strong>输出：</strong>[[1,1]]\n</pre>\n\n<p><strong>示例 4：</strong></p>\n\n<pre><strong>输入：</strong>grid = [[0]]\n<strong>输出：</strong>[[1,0]]\n</pre>\n\n<p><strong>示例 5：</strong></p>\n\n<pre><strong>输入：</strong>grid = [[1,1,0,0],[1,1,0,0],[0,0,1,1],[0,0,1,1]]\n<strong>输出：</strong>[[0,1],[1,1],[1,0],[1,0],[1,1]]\n</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</strong></p>\n\n<ol>\n\t<li><code>n == grid.length == grid[i].length</code></li>\n\t<li><code>n == 2^x</code> 其中 <code>0 &lt;= x &lt;= 6</code></li>\n</ol>\n",
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                    "code": "/*\n// Definition for a QuadTree node.\nclass Node {\npublic:\n    bool val;\n    bool isLeaf;\n    Node* topLeft;\n    Node* topRight;\n    Node* bottomLeft;\n    Node* bottomRight;\n    \n    Node() {\n        val = false;\n        isLeaf = false;\n        topLeft = NULL;\n        topRight = NULL;\n        bottomLeft = NULL;\n        bottomRight = NULL;\n    }\n    \n    Node(bool _val, bool _isLeaf) {\n        val = _val;\n        isLeaf = _isLeaf;\n        topLeft = NULL;\n        topRight = NULL;\n        bottomLeft = NULL;\n        bottomRight = NULL;\n    }\n    \n    Node(bool _val, bool _isLeaf, Node* _topLeft, Node* _topRight, Node* _bottomLeft, Node* _bottomRight) {\n        val = _val;\n        isLeaf = _isLeaf;\n        topLeft = _topLeft;\n        topRight = _topRight;\n        bottomLeft = _bottomLeft;\n        bottomRight = _bottomRight;\n    }\n};\n*/\n\nclass Solution {\npublic:\n    Node* construct(vector<vector<int>>& grid) {\n        \n    }\n};",
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                    "code": "# Definition for a QuadTree node.\n# class Node\n#     attr_accessor :val, :isLeaf, :topLeft, :topRight, :bottomLeft, :bottomRight\n#     def initialize(val=false, isLeaf=false, topLeft=nil, topRight=nil, bottomLeft=nil, bottomRight=nil)\n#         @val = val\n#         @isLeaf = isLeaf\n#         @topLeft = topLeft\n#         @topRight = topRight\n#         @bottomLeft = bottomLeft\n#         @bottomRight = bottomRight\n#     end\n# end\n\n# @param {Integer[][]} grid\n# @return {Node}\ndef construct(grid)\n\t\nend",
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