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        "question": {
            "questionId": "773",
            "questionFrontendId": "558",
            "categoryTitle": "Algorithms",
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            "title": "Logical OR of Two Binary Grids Represented as Quad-Trees",
            "titleSlug": "logical-or-of-two-binary-grids-represented-as-quad-trees",
            "content": "<p>A Binary Matrix is a matrix in which all the elements are either <strong>0</strong> or <strong>1</strong>.</p>\n\n<p>Given <code>quadTree1</code> and <code>quadTree2</code>. <code>quadTree1</code> represents a <code>n * n</code> binary matrix and <code>quadTree2</code> represents another <code>n * n</code> binary matrix.</p>\n\n<p>Return <em>a Quad-Tree</em> representing the <code>n * n</code> binary matrix which is the result of <strong>logical bitwise OR</strong> of the two binary matrixes represented by <code>quadTree1</code> and <code>quadTree2</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 input/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/qt1.png\" style=\"width: 550px; height: 196px;\" /> <img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/02/11/qt2.png\" style=\"width: 550px; height: 278px;\" />\n<pre>\n<strong>Input:</strong> quadTree1 = [[0,1],[1,1],[1,1],[1,0],[1,0]]\n, quadTree2 = [[0,1],[1,1],[0,1],[1,1],[1,0],null,null,null,null,[1,0],[1,0],[1,1],[1,1]]\n<strong>Output:</strong> [[0,0],[1,1],[1,1],[1,1],[1,0]]\n<strong>Explanation:</strong> quadTree1 and quadTree2 are shown above. You can see the binary matrix which is represented by each Quad-Tree.\nIf we apply logical bitwise OR on the two binary matrices we get the binary matrix below which is represented by the result Quad-Tree.\nNotice that the binary matrices shown are only for illustration, you don&#39;t have to construct the binary matrix to get the result tree.\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/02/11/qtr.png\" style=\"width: 777px; height: 222px;\" />\n</pre>\n\n<p><strong>Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> quadTree1 = [[1,0]], quadTree2 = [[1,0]]\n<strong>Output:</strong> [[1,0]]\n<strong>Explanation:</strong> Each tree represents a binary matrix of size 1*1. Each matrix contains only zero.\nThe resulting matrix is of size 1*1 with also zero.\n</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>quadTree1</code> and <code>quadTree2</code> are both <strong>valid</strong> Quad-Trees each representing a <code>n * n</code> grid.</li>\n\t<li><code>n == 2<sup>x</sup></code> where <code>0 &lt;= x &lt;= 9</code>.</li>\n</ul>\n",
            "translatedTitle": "四叉树交集",
            "translatedContent": "<p>二进制矩阵中的所有元素不是 <strong>0</strong> 就是 <strong>1 </strong>。</p>\n\n<p>给你两个四叉树，<code>quadTree1</code> 和 <code>quadTree2</code>。其中 <code>quadTree1</code> 表示一个 <code>n * n</code> 二进制矩阵，而 <code>quadTree2</code> 表示另一个 <code>n * n</code> 二进制矩阵。</p>\n\n<p>请你返回一个表示 <code>n * n</code> 二进制矩阵的四叉树，它是 <code>quadTree1</code> 和 <code>quadTree2</code> 所表示的两个二进制矩阵进行 <strong>按位逻辑或运算</strong> 的结果。</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>\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>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 <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> </p>\n\n<p><strong>示例 1：</strong></p>\n\n<p><img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/02/11/qt1.png\" style=\"height: 196px; width: 550px;\" /> <img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/02/11/qt2.png\" style=\"height: 278px; width: 550px;\" /></p>\n\n<pre>\n<strong>输入：</strong>quadTree1 = [[0,1],[1,1],[1,1],[1,0],[1,0]]\n, quadTree2 = [[0,1],[1,1],[0,1],[1,1],[1,0],null,null,null,null,[1,0],[1,0],[1,1],[1,1]]\n<strong>输出：</strong>[[0,0],[1,1],[1,1],[1,1],[1,0]]\n<strong>解释：</strong>quadTree1 和 quadTree2 如上所示。由四叉树所表示的二进制矩阵也已经给出。\n如果我们对这两个矩阵进行按位逻辑或运算，则可以得到下面的二进制矩阵，由一个作为结果的四叉树表示。\n注意，我们展示的二进制矩阵仅仅是为了更好地说明题意，你无需构造二进制矩阵来获得结果四叉树。\n<img alt=\"\" src=\"https://assets.leetcode.com/uploads/2020/02/11/qtr.png\" style=\"height: 222px; width: 777px;\" />\n</pre>\n\n<p><strong>示例 2：</strong></p>\n\n<pre>\n<strong>输入：</strong>quadTree1 = [[1,0]]\n, quadTree2 = [[1,0]]\n<strong>输出：</strong>[[1,0]]\n<strong>解释：</strong>两个数所表示的矩阵大小都为 1*1，值全为 0 \n结果矩阵大小为 1*1，值全为 0 。\n</pre>\n\n<p><strong>示例 3：</strong></p>\n\n<pre>\n<strong>输入：</strong>quadTree1 = [[0,0],[1,0],[1,0],[1,1],[1,1]]\n, quadTree2 = [[0,0],[1,1],[1,1],[1,0],[1,1]]\n<strong>输出：</strong>[[1,1]]\n</pre>\n\n<p><strong>示例 4：</strong></p>\n\n<pre>\n<strong>输入：</strong>quadTree1 = [[0,0],[1,1],[1,0],[1,1],[1,1]]\n, quadTree2 = [[0,0],[1,1],[0,1],[1,1],[1,1],null,null,null,null,[1,1],[1,0],[1,0],[1,1]]\n<strong>输出：</strong>[[0,0],[1,1],[0,1],[1,1],[1,1],null,null,null,null,[1,1],[1,0],[1,0],[1,1]]\n</pre>\n\n<p><strong>示例 5：</strong></p>\n\n<pre>\n<strong>输入：</strong>quadTree1 = [[0,1],[1,0],[0,1],[1,1],[1,0],null,null,null,null,[1,0],[1,0],[1,1],[1,1]]\n, quadTree2 = [[0,1],[0,1],[1,0],[1,1],[1,0],[1,0],[1,0],[1,1],[1,1]]\n<strong>输出：</strong>[[0,0],[0,1],[0,1],[1,1],[1,0],[1,0],[1,0],[1,1],[1,1],[1,0],[1,0],[1,1],[1,1]]\n</pre>\n\n<p> </p>\n\n<p><strong>提示：</strong></p>\n\n<ul>\n\t<li><code>quadTree1</code> 和 <code>quadTree2</code> 都是符合题目要求的四叉树，每个都代表一个 <code>n * n</code> 的矩阵。</li>\n\t<li><code>n == 2^x</code> ，其中 <code>0 <= x <= 9</code>.</li>\n</ul>\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* intersect(Node* quadTree1, Node* quadTree2) {\n        \n    }\n};",
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                    "code": "/*\n// Definition for a QuadTree node.\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\n    public Node() {}\n\n    public Node(boolean _val,boolean _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 {\n    public Node intersect(Node quadTree1, Node quadTree2) {\n        \n    }\n}",
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                    "code": "\"\"\"\n# Definition for a QuadTree node.\nclass Node(object):\n    def __init__(self, val, isLeaf, topLeft, topRight, bottomLeft, bottomRight):\n        self.val = val\n        self.isLeaf = isLeaf\n        self.topLeft = topLeft\n        self.topRight = topRight\n        self.bottomLeft = bottomLeft\n        self.bottomRight = bottomRight\n\"\"\"\n\nclass Solution(object):\n    def intersect(self, quadTree1, quadTree2):\n        \"\"\"\n        :type quadTree1: Node\n        :type quadTree2: Node\n        :rtype: Node\n        \"\"\"\n        ",
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                    "code": "/**\n * // Definition for a QuadTree node.\n * function Node(val,isLeaf,topLeft,topRight,bottomLeft,bottomRight) {\n *    this.val = val;\n *    this.isLeaf = isLeaf;\n *    this.topLeft = topLeft;\n *    this.topRight = topRight;\n *    this.bottomLeft = bottomLeft;\n *    this.bottomRight = bottomRight;\n * };\n */\n\n/**\n * @param {Node} quadTree1\n * @param {Node} quadTree2\n * @return {Node}\n */\nvar intersect = function(quadTree1, quadTree2) {\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 {Node} quadTree1\n# @param {Node} quadTree2\n# @return {Node}\ndef intersect(quadTree1, quadTree2)\n\t\nend",
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                    "code": "/**\n * Definition for a Node.\n * public class Node {\n *     public var val: Bool\n *     public var isLeaf: Bool\n *     public var topLeft: Node?\n *     public var topRight: Node?\n *     public var bottomLeft: Node?\n *     public var bottomRight: Node?\n *     public init(_ val: Bool, _ isLeaf: Bool) {\n *         self.val = val\n *         self.isLeaf = isLeaf\n *         self.topLeft = nil\n *         self.topRight = nil\n *         self.bottomLeft = nil\n *         self.bottomRight = nil\n *     }\n * }\n */\n\nclass Solution {\n    func intersect(_ quadTree1: Node?, _ quadTree2: Node?) -> Node? {\n        \n    }\n}",
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