{
"data": {
"question": {
"questionId": "773",
"questionFrontendId": "558",
"boundTopicId": null,
"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's or False if the node represents a grid of 0'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'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>\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> </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'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> </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 <= x <= 9</code>.</li>\n</ul>\n",
"translatedTitle": null,
"translatedContent": null,
"isPaidOnly": false,
"difficulty": "Medium",
"likes": 126,
"dislikes": 405,
"isLiked": null,
"similarQuestions": "[]",
"exampleTestcases": "[[0,1],[1,1],[1,1],[1,0],[1,0]]\n[[0,1],[1,1],[0,1],[1,1],[1,0],null,null,null,null,[1,0],[1,0],[1,1],[1,1]]\n[[1,0]]\n[[1,0]]",
"categoryTitle": "Algorithms",
"contributors": [],
"topicTags": [
{
"name": "Divide and Conquer",
"slug": "divide-and-conquer",
"translatedName": null,
"__typename": "TopicTagNode"
},
{
"name": "Tree",
"slug": "tree",
"translatedName": null,
"__typename": "TopicTagNode"
}
],
"companyTagStats": null,
"codeSnippets": [
{
"lang": "C++",
"langSlug": "cpp",
"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};",
"__typename": "CodeSnippetNode"
},
{
"lang": "Java",
"langSlug": "java",
"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}",
"__typename": "CodeSnippetNode"
},
{
"lang": "Python",
"langSlug": "python",
"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 ",
"__typename": "CodeSnippetNode"
},
{
"lang": "Python3",
"langSlug": "python3",
"code": "\"\"\"\n# Definition for a QuadTree node.\nclass Node:\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:\n def intersect(self, quadTree1: 'Node', quadTree2: 'Node') -> 'Node':\n ",
"__typename": "CodeSnippetNode"
},
{
"lang": "C#",
"langSlug": "csharp",
"code": "/*\n// Definition for a QuadTree node.\npublic class Node {\n public bool val;\n public bool isLeaf;\n public Node topLeft;\n public Node topRight;\n public Node bottomLeft;\n public Node bottomRight;\n\n public Node(){}\n public 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\npublic class Solution {\n public Node Intersect(Node quadTree1, Node quadTree2) {\n \n }\n}",
"__typename": "CodeSnippetNode"
},
{
"lang": "JavaScript",
"langSlug": "javascript",
"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};",
"__typename": "CodeSnippetNode"
},
{
"lang": "Ruby",
"langSlug": "ruby",
"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\n",
"__typename": "CodeSnippetNode"
},
{
"lang": "Swift",
"langSlug": "swift",
"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}",
"__typename": "CodeSnippetNode"
},
{
"lang": "Go",
"langSlug": "golang",
"code": "/**\n * Definition for a QuadTree node.\n * type Node struct {\n * Val bool\n * IsLeaf bool\n * TopLeft *Node\n * TopRight *Node\n * BottomLeft *Node\n * BottomRight *Node\n * }\n */\n\nfunc intersect(quadTree1 *Node, quadTree2 *Node) *Node {\n \n}",
"__typename": "CodeSnippetNode"
},
{
"lang": "Scala",
"langSlug": "scala",
"code": "/**\n * Definition for a QuadTree node.\n * class Node(var _value: Boolean, var _isLeaf: Boolean) {\n * var value: Int = _value\n * var isLeaf: Boolean = _isLeaf\n * var topLeft: Node = null\n * var topRight: Node = null\n * var bottomLeft: Node = null\n * var bottomRight: Node = null\n * }\n */\n\nobject Solution {\n def intersect(quadTree1: Node, quadTree2: Node): Node = {\n \n }\n}",
"__typename": "CodeSnippetNode"
},
{
"lang": "Kotlin",
"langSlug": "kotlin",
"code": "/**\n * Definition for a QuadTree node.\n * class Node(var `val`: Boolean, var isLeaf: Boolean) {\n * var topLeft: Node? = null\n * var topRight: Node? = null\n * var bottomLeft: Node? = null\n * var bottomRight: Node? = null\n * }\n */\n\nclass Solution {\n fun intersect(quadTree1: Node?, quadTree2: Node?): Node? {\n \n }\n}",
"__typename": "CodeSnippetNode"
},
{
"lang": "PHP",
"langSlug": "php",
"code": "/**\n * Definition for a QuadTree node.\n * class Node {\n * public $val = null;\n * public $isLeaf = null;\n * public $topLeft = null;\n * public $topRight = null;\n * public $bottomLeft = null;\n * public $bottomRight = null;\n * function __construct($val, $isLeaf) {\n * $this->val = $val;\n * $this->isLeaf = $isLeaf;\n * $this->topLeft = null;\n * $this->topRight = null;\n * $this->bottomLeft = null;\n * $this->bottomRight = null;\n * }\n * }\n */\n\nclass Solution {\n /**\n * @param Node $quadTree1\n * @param Node $quadTree2\n * @return Node\n */\n function intersect($quadTree1, $quadTree2) {\n \n }\n}",
"__typename": "CodeSnippetNode"
},
{
"lang": "TypeScript",
"langSlug": "typescript",
"code": "/**\n * Definition for node.\n * class Node {\n * val: boolean\n * isLeaf: boolean\n * topLeft: Node | null\n * topRight: Node | null\n * bottomLeft: Node | null\n * bottomRight: Node | null\n * constructor(val?: boolean, isLeaf?: boolean, topLeft?: Node, topRight?: Node, bottomLeft?: Node, bottomRight?: Node) {\n * this.val = (val===undefined ? false : val)\n * this.isLeaf = (isLeaf===undefined ? false : isLeaf)\n * this.topLeft = (topLeft===undefined ? null : topLeft)\n * this.topRight = (topRight===undefined ? null : topRight)\n * this.bottomLeft = (bottomLeft===undefined ? null : bottomLeft)\n * this.bottomRight = (bottomRight===undefined ? null : bottomRight)\n * }\n * }\n */\n\nfunction intersect(quadTree1: Node | null, quadTree2: Node | null): Node | null {\n\n};",
"__typename": "CodeSnippetNode"
}
],
"stats": "{\"totalAccepted\": \"11K\", \"totalSubmission\": \"23.4K\", \"totalAcceptedRaw\": 11039, \"totalSubmissionRaw\": 23432, \"acRate\": \"47.1%\"}",
"hints": [],
"solution": null,
"status": null,
"sampleTestCase": "[[0,1],[1,1],[1,1],[1,0],[1,0]]\n[[0,1],[1,1],[0,1],[1,1],[1,0],null,null,null,null,[1,0],[1,0],[1,1],[1,1]]",
"metaData": "{\n \"name\": \"intersect\",\n \"params\": [\n {\n \"name\": \"quadTree1\",\n \"type\": \"integer[][]\"\n },\n {\n \"name\": \"quadTree2\",\n \"type\": \"integer[][]\"\n }\n ],\n \"return\": {\n \"type\": \"integer[][]\"\n },\n \"languages\": [\n \"cpp\",\n \"java\",\n \"python\",\n \"csharp\",\n \"javascript\",\n \"python3\",\n \"kotlin\",\n \"ruby\",\n \"scala\",\n \"swift\",\n \"golang\",\n \"php\",\n \"typescript\"\n ],\n \"manual\": true\n}",
"judgerAvailable": true,
"judgeType": "large",
"mysqlSchemas": [],
"enableRunCode": true,
"enableTestMode": false,
"enableDebugger": true,
"envInfo": "{\"cpp\": [\"C++\", \"<p>Compiled with <code> clang 11 </code> using the latest C++ 17 standard.</p>\\r\\n\\r\\n<p>Your code is compiled with level two optimization (<code>-O2</code>). <a href=\\\"https://github.com/google/sanitizers/wiki/AddressSanitizer\\\" target=\\\"_blank\\\">AddressSanitizer</a> is also enabled to help detect out-of-bounds and use-after-free bugs.</p>\\r\\n\\r\\n<p>Most standard library headers are already included automatically for your convenience.</p>\"], \"java\": [\"Java\", \"<p><code> OpenJDK 17 </code>. Java 8 features such as lambda expressions and stream API can be used. </p>\\r\\n\\r\\n<p>Most standard library headers are already included automatically for your convenience.</p>\\r\\n<p>Includes <code>Pair</code> class from https://docs.oracle.com/javase/8/javafx/api/javafx/util/Pair.html.</p>\"], \"python\": [\"Python\", \"<p><code>Python 2.7.12</code>.</p>\\r\\n\\r\\n<p>Most libraries are already imported automatically for your convenience, such as <a href=\\\"https://docs.python.org/2/library/array.html\\\" target=\\\"_blank\\\">array</a>, <a href=\\\"https://docs.python.org/2/library/bisect.html\\\" target=\\\"_blank\\\">bisect</a>, <a href=\\\"https://docs.python.org/2/library/collections.html\\\" target=\\\"_blank\\\">collections</a>. If you need more libraries, you can import it yourself.</p>\\r\\n\\r\\n<p>For Map/TreeMap data structure, you may use <a href=\\\"http://www.grantjenks.com/docs/sortedcontainers/\\\" target=\\\"_blank\\\">sortedcontainers</a> library.</p>\\r\\n\\r\\n<p>Note that Python 2.7 <a href=\\\"https://www.python.org/dev/peps/pep-0373/\\\" target=\\\"_blank\\\">will not be maintained past 2020</a>. For the latest Python, please choose Python3 instead.</p>\"], \"csharp\": [\"C#\", \"<p><a href=\\\"https://docs.microsoft.com/en-us/dotnet/csharp/whats-new/csharp-9\\\" target=\\\"_blank\\\">C# 10 with .NET 6 runtime</a></p>\\r\\n\\r\\n<p>Your code is compiled with debug flag enabled (<code>/debug</code>).</p>\"], \"javascript\": [\"JavaScript\", \"<p><code>Node.js 16.13.2</code>.</p>\\r\\n\\r\\n<p>Your code is run with <code>--harmony</code> flag, enabling <a href=\\\"http://node.green/\\\" target=\\\"_blank\\\">new ES6 features</a>.</p>\\r\\n\\r\\n<p><a href=\\\"https://lodash.com\\\" target=\\\"_blank\\\">lodash.js</a> library is included by default.</p>\\r\\n\\r\\n<p>For Priority Queue / Queue data structures, you may use <a href=\\\"https://github.com/datastructures-js/priority-queue\\\" target=\\\"_blank\\\">datastructures-js/priority-queue</a> and <a href=\\\"https://github.com/datastructures-js/queue\\\" target=\\\"_blank\\\">datastructures-js/queue</a>.</p>\"], \"ruby\": [\"Ruby\", \"<p><code>Ruby 3.1</code></p>\\r\\n\\r\\n<p>Some common data structure implementations are provided in the Algorithms module: https://www.rubydoc.info/github/kanwei/algorithms/Algorithms</p>\"], \"swift\": [\"Swift\", \"<p><code>Swift 5.5.2</code>.</p>\"], \"golang\": [\"Go\", \"<p><code>Go 1.17.6</code>.</p>\\r\\n\\r\\n<p>Support <a href=\\\"https://godoc.org/github.com/emirpasic/gods\\\" target=\\\"_blank\\\">https://godoc.org/github.com/emirpasic/gods</a> library.</p>\"], \"python3\": [\"Python3\", \"<p><code>Python 3.10</code>.</p>\\r\\n\\r\\n<p>Most libraries are already imported automatically for your convenience, such as <a href=\\\"https://docs.python.org/3/library/array.html\\\" target=\\\"_blank\\\">array</a>, <a href=\\\"https://docs.python.org/3/library/bisect.html\\\" target=\\\"_blank\\\">bisect</a>, <a href=\\\"https://docs.python.org/3/library/collections.html\\\" target=\\\"_blank\\\">collections</a>. If you need more libraries, you can import it yourself.</p>\\r\\n\\r\\n<p>For Map/TreeMap data structure, you may use <a href=\\\"http://www.grantjenks.com/docs/sortedcontainers/\\\" target=\\\"_blank\\\">sortedcontainers</a> library.</p>\"], \"scala\": [\"Scala\", \"<p><code>Scala 2.13.7</code>.</p>\"], \"kotlin\": [\"Kotlin\", \"<p><code>Kotlin 1.3.10</code>.</p>\"], \"php\": [\"PHP\", \"<p><code>PHP 8.1</code>.</p>\\r\\n<p>With bcmath module</p>\"], \"typescript\": [\"Typescript\", \"<p><code>TypeScript 4.5.4, Node.js 16.13.2</code>.</p>\\r\\n\\r\\n<p>Your code is run with <code>--harmony</code> flag, enabling <a href=\\\"http://node.green/\\\" target=\\\"_blank\\\">new ES2020 features</a>.</p>\\r\\n\\r\\n<p><a href=\\\"https://lodash.com\\\" target=\\\"_blank\\\">lodash.js</a> library is included by default.</p>\"]}",
"libraryUrl": null,
"adminUrl": null,
"challengeQuestion": null,
"__typename": "QuestionNode"
}
}
}