{ "data": { "question": { "questionId": "1000045", "questionFrontendId": "面试题 17.23", "categoryTitle": "LCCI", "boundTopicId": 100609, "title": "Max Black Square LCCI", "titleSlug": "max-black-square-lcci", "content": "

Imagine you have a square matrix, where each cell (pixel) is either black or white Design an algorithm to find the maximum subsquare such that all four borders are filled with black pixels.

\r\n\r\n

Return an array [r, c, size], where rc are the row number and the column number of the subsquare's upper left corner respectively, and size is the side length of the subsquare. If there are more than one answers, return the one that has smallest r. If there are more than one answers that have the same r, return the one that has smallest c. If there's no answer, return an empty array.

\r\n\r\n

Example 1:

\r\n\r\n
\r\nInput:\r\n[\r\n   [1,0,1],\r\n   [0,0,1],\r\n   [0,0,1]\r\n]\r\nOutput: [1,0,2]\r\nExplanation: 0 represents black, and 1 represents white, bold elements in the input is the answer.\r\n
\r\n\r\n

Example 2:

\r\n\r\n
\r\nInput:\r\n[\r\n   [0,1,1],\r\n   [1,0,1],\r\n   [1,1,0]\r\n]\r\nOutput: [0,0,1]\r\n
\r\n\r\n

Note:

\r\n\r\n\r\n", "translatedTitle": "最大黑方阵", "translatedContent": "

给定一个方阵,其中每个单元(像素)非黑即白。设计一个算法,找出 4 条边皆为黑色像素的最大子方阵。

\n\n

返回一个数组 [r, c, size] ,其中 rc 分别代表子方阵左上角的行号和列号,size 是子方阵的边长。若有多个满足条件的子方阵,返回 r 最小的,若 r 相同,返回 c 最小的子方阵。若无满足条件的子方阵,返回空数组。

\n\n

示例 1:

\n\n
输入:\n[\n   [1,0,1],\n   [0,0,1],\n   [0,0,1]\n]\n输出: [1,0,2]\n解释: 输入中 0 代表黑色,1 代表白色,标粗的元素即为满足条件的最大子方阵\n
\n\n

示例 2:

\n\n
输入:\n[\n   [0,1,1],\n   [1,0,1],\n   [1,1,0]\n]\n输出: [0,0,1]\n
\n\n

提示:

\n\n\n", "isPaidOnly": false, "difficulty": "Medium", "likes": 35, "dislikes": 0, "isLiked": null, "similarQuestions": "[]", "contributors": [], "langToValidPlayground": "{\"cpp\": false, \"java\": true, \"python\": true, \"python3\": false, \"mysql\": false, \"mssql\": false, \"oraclesql\": false, \"c\": false, \"csharp\": false, \"javascript\": false, \"ruby\": false, \"bash\": false, \"swift\": false, \"golang\": false, \"scala\": false, \"html\": false, \"pythonml\": false, \"kotlin\": false, \"rust\": false, \"php\": false, \"typescript\": false, \"racket\": false, \"erlang\": false, \"elixir\": false}", "topicTags": [ { "name": "Array", "slug": "array", "translatedName": "数组", "__typename": "TopicTagNode" }, { "name": "Dynamic Programming", "slug": "dynamic-programming", "translatedName": "动态规划", "__typename": "TopicTagNode" }, { "name": "Matrix", "slug": "matrix", "translatedName": "矩阵", "__typename": "TopicTagNode" } ], "companyTagStats": null, "codeSnippets": [ { "lang": "C++", "langSlug": "cpp", "code": "class Solution {\npublic:\n vector findSquare(vector>& matrix) {\n\n }\n};", "__typename": "CodeSnippetNode" }, { "lang": "Java", "langSlug": "java", "code": "class Solution {\n public int[] findSquare(int[][] matrix) {\n\n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Python", "langSlug": "python", "code": "class Solution(object):\n def findSquare(self, matrix):\n \"\"\"\n :type matrix: List[List[int]]\n :rtype: List[int]\n \"\"\"", "__typename": "CodeSnippetNode" }, { "lang": "Python3", "langSlug": "python3", "code": "class Solution:\n def findSquare(self, matrix: List[List[int]]) -> List[int]:", "__typename": "CodeSnippetNode" }, { "lang": "C", "langSlug": "c", "code": "\n\n/**\n * Note: The returned array must be malloced, assume caller calls free().\n */\nint* findSquare(int** matrix, int matrixSize, int* matrixColSize, int* returnSize){\n\n}\n", "__typename": "CodeSnippetNode" }, { "lang": "C#", "langSlug": "csharp", "code": "public class Solution {\n public int[] FindSquare(int[][] matrix) {\n\n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "JavaScript", "langSlug": "javascript", "code": "/**\n * @param {number[][]} matrix\n * @return {number[]}\n */\nvar findSquare = function(matrix) {\n\n};", "__typename": "CodeSnippetNode" }, { "lang": "Ruby", "langSlug": "ruby", "code": "# @param {Integer[][]} matrix\n# @return {Integer[]}\ndef find_square(matrix)\n\nend", "__typename": "CodeSnippetNode" }, { "lang": "Swift", "langSlug": "swift", "code": "class Solution {\n func findSquare(_ matrix: [[Int]]) -> [Int] {\n\n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Go", "langSlug": "golang", "code": "func findSquare(matrix [][]int) []int {\n\n}", "__typename": "CodeSnippetNode" }, { "lang": "Scala", "langSlug": "scala", "code": "object Solution {\n def findSquare(matrix: Array[Array[Int]]): Array[Int] = {\n\n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Kotlin", "langSlug": "kotlin", "code": "class Solution {\n fun findSquare(matrix: Array): IntArray {\n\n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Rust", "langSlug": "rust", "code": "impl Solution {\n pub fn find_square(matrix: Vec>) -> Vec {\n\n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "PHP", "langSlug": "php", "code": "class Solution {\n\n /**\n * @param Integer[][] $matrix\n * @return Integer[]\n */\n function findSquare($matrix) {\n\n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "TypeScript", "langSlug": "typescript", "code": "function findSquare(matrix: number[][]): number[] {\n\n};", "__typename": "CodeSnippetNode" }, { "lang": "Racket", "langSlug": "racket", "code": "(define/contract (find-square matrix)\n (-> (listof (listof exact-integer?)) (listof exact-integer?))\n\n )", "__typename": "CodeSnippetNode" }, { "lang": "Erlang", "langSlug": "erlang", "code": "-spec find_square(Matrix :: [[integer()]]) -> [integer()].\nfind_square(Matrix) ->\n .", "__typename": "CodeSnippetNode" }, { "lang": "Elixir", "langSlug": "elixir", "code": "defmodule Solution do\n @spec find_square(matrix :: [[integer]]) :: [integer]\n def find_square(matrix) do\n\n end\nend", "__typename": "CodeSnippetNode" } ], "stats": "{\"totalAccepted\": \"5.6K\", \"totalSubmission\": \"14.9K\", \"totalAcceptedRaw\": 5608, \"totalSubmissionRaw\": 14922, \"acRate\": \"37.6%\"}", "hints": [ "从蛮力解法开始。你能先试试最大的正方形吗?", "最大的正方形是N×N。所以你先试一下该正方形,如果可行,那么你便知道已经找到了最佳正方形。否则,可以尝试下一个最小的正方形。", "描述蛮力解法的时间复杂度。", "你能通过预处理来优化这个解决方案吗?", "你应该能在O(N\b^3)时间内完成,其中N是正方形一边的长度。", "当你检查一个特定的正方形是否有效时(所有边框为黑色),需要检查在一个坐标的上面(或下面)和这个坐标的左边(或右边)有多少个黑色像素。你能预先计算出给定单元格上面和左边的黑色像素的数量吗?" ], "solution": null, "status": null, "sampleTestCase": "[[1,0,1],[0,0,1],[0,0,1]]", "metaData": "{\r\n \"name\": \"findSquare\",\r\n \"params\": [\r\n {\r\n \"name\": \"matrix\",\r\n \"type\": \"integer[][]\"\r\n }\r\n ],\r\n \"return\": {\r\n \"type\": \"integer[]\"\r\n }\r\n}", "judgerAvailable": true, "judgeType": "large", "mysqlSchemas": [], "enableRunCode": true, "envInfo": "{\"cpp\":[\"C++\",\"

\\u7248\\u672c\\uff1aclang 11<\\/code> \\u91c7\\u7528\\u6700\\u65b0C++ 17\\u6807\\u51c6\\u3002<\\/p>\\r\\n\\r\\n

\\u7f16\\u8bd1\\u65f6\\uff0c\\u5c06\\u4f1a\\u91c7\\u7528-O2<\\/code>\\u7ea7\\u4f18\\u5316\\u3002AddressSanitizer<\\/a> \\u4e5f\\u88ab\\u5f00\\u542f\\u6765\\u68c0\\u6d4bout-of-bounds<\\/code>\\u548cuse-after-free<\\/code>\\u9519\\u8bef\\u3002<\\/p>\\r\\n\\r\\n

\\u4e3a\\u4e86\\u4f7f\\u7528\\u65b9\\u4fbf\\uff0c\\u5927\\u90e8\\u5206\\u6807\\u51c6\\u5e93\\u7684\\u5934\\u6587\\u4ef6\\u5df2\\u7ecf\\u88ab\\u81ea\\u52a8\\u5bfc\\u5165\\u3002<\\/p>\"],\"java\":[\"Java\",\"

\\u7248\\u672c\\uff1aOpenJDK 17<\\/code>\\u3002\\u53ef\\u4ee5\\u4f7f\\u7528Java 8\\u7684\\u7279\\u6027\\u4f8b\\u5982\\uff0clambda expressions \\u548c stream API\\u3002<\\/p>\\r\\n\\r\\n

\\u4e3a\\u4e86\\u65b9\\u4fbf\\u8d77\\u89c1\\uff0c\\u5927\\u90e8\\u5206\\u6807\\u51c6\\u5e93\\u7684\\u5934\\u6587\\u4ef6\\u5df2\\u88ab\\u5bfc\\u5165\\u3002<\\/p>\\r\\n\\r\\n

\\u5305\\u542b Pair \\u7c7b: https:\\/\\/docs.oracle.com\\/javase\\/8\\/javafx\\/api\\/javafx\\/util\\/Pair.html <\\/p>\"],\"python\":[\"Python\",\"

\\u7248\\u672c\\uff1a Python 2.7.12<\\/code><\\/p>\\r\\n\\r\\n

\\u4e3a\\u4e86\\u65b9\\u4fbf\\u8d77\\u89c1\\uff0c\\u5927\\u90e8\\u5206\\u5e38\\u7528\\u5e93\\u5df2\\u7ecf\\u88ab\\u81ea\\u52a8 \\u5bfc\\u5165\\uff0c\\u5982\\uff1aarray<\\/a>, bisect<\\/a>, collections<\\/a>\\u3002\\u5982\\u679c\\u60a8\\u9700\\u8981\\u4f7f\\u7528\\u5176\\u4ed6\\u5e93\\u51fd\\u6570\\uff0c\\u8bf7\\u81ea\\u884c\\u5bfc\\u5165\\u3002<\\/p>\\r\\n\\r\\n

\\u6ce8\\u610f Python 2.7 \\u5c06\\u57282020\\u5e74\\u540e\\u4e0d\\u518d\\u7ef4\\u62a4<\\/a>\\u3002 \\u5982\\u60f3\\u4f7f\\u7528\\u6700\\u65b0\\u7248\\u7684Python\\uff0c\\u8bf7\\u9009\\u62e9Python 3\\u3002<\\/p>\"],\"c\":[\"C\",\"

\\u7248\\u672c\\uff1aGCC 8.2<\\/code>\\uff0c\\u91c7\\u7528GNU99\\u6807\\u51c6\\u3002<\\/p>\\r\\n\\r\\n

\\u7f16\\u8bd1\\u65f6\\uff0c\\u5c06\\u4f1a\\u91c7\\u7528-O1<\\/code>\\u7ea7\\u4f18\\u5316\\u3002 AddressSanitizer<\\/a>\\u4e5f\\u88ab\\u5f00\\u542f\\u6765\\u68c0\\u6d4bout-of-bounds<\\/code>\\u548cuse-after-free<\\/code>\\u9519\\u8bef\\u3002<\\/p>\\r\\n\\r\\n

\\u4e3a\\u4e86\\u4f7f\\u7528\\u65b9\\u4fbf\\uff0c\\u5927\\u90e8\\u5206\\u6807\\u51c6\\u5e93\\u7684\\u5934\\u6587\\u4ef6\\u5df2\\u7ecf\\u88ab\\u81ea\\u52a8\\u5bfc\\u5165\\u3002<\\/p>\\r\\n\\r\\n

\\u5982\\u60f3\\u4f7f\\u7528\\u54c8\\u5e0c\\u8868\\u8fd0\\u7b97, \\u60a8\\u53ef\\u4ee5\\u4f7f\\u7528 uthash<\\/a>\\u3002 \\\"uthash.h\\\"\\u5df2\\u7ecf\\u9ed8\\u8ba4\\u88ab\\u5bfc\\u5165\\u3002\\u8bf7\\u770b\\u5982\\u4e0b\\u793a\\u4f8b:<\\/p>\\r\\n\\r\\n

1. \\u5f80\\u54c8\\u5e0c\\u8868\\u4e2d\\u6dfb\\u52a0\\u4e00\\u4e2a\\u5bf9\\u8c61\\uff1a<\\/b>\\r\\n

\\r\\nstruct hash_entry {\\r\\n    int id;            \\/* we'll use this field as the key *\\/\\r\\n    char name[10];\\r\\n    UT_hash_handle hh; \\/* makes this structure hashable *\\/\\r\\n};\\r\\n\\r\\nstruct hash_entry *users = NULL;\\r\\n\\r\\nvoid add_user(struct hash_entry *s) {\\r\\n    HASH_ADD_INT(users, id, s);\\r\\n}\\r\\n<\\/pre>\\r\\n<\\/p>\\r\\n\\r\\n

2. \\u5728\\u54c8\\u5e0c\\u8868\\u4e2d\\u67e5\\u627e\\u4e00\\u4e2a\\u5bf9\\u8c61\\uff1a<\\/b>\\r\\n

\\r\\nstruct hash_entry *find_user(int user_id) {\\r\\n    struct hash_entry *s;\\r\\n    HASH_FIND_INT(users, &user_id, s);\\r\\n    return s;\\r\\n}\\r\\n<\\/pre>\\r\\n<\\/p>\\r\\n\\r\\n

3. \\u4ece\\u54c8\\u5e0c\\u8868\\u4e2d\\u5220\\u9664\\u4e00\\u4e2a\\u5bf9\\u8c61\\uff1a<\\/b>\\r\\n

\\r\\nvoid delete_user(struct hash_entry *user) {\\r\\n    HASH_DEL(users, user);  \\r\\n}\\r\\n<\\/pre>\\r\\n<\\/p>\"],\"csharp\":[\"C#\",\"

C# 10<\\/a> \\u8fd0\\u884c\\u5728 .NET 6 \\u4e0a<\\/p>\\r\\n\\r\\n

\\u60a8\\u7684\\u4ee3\\u7801\\u5728\\u7f16\\u8bd1\\u65f6\\u9ed8\\u8ba4\\u5f00\\u542f\\u4e86debug\\u6807\\u8bb0(\\/debug:pdbonly<\\/code>)\\u3002<\\/p>\"],\"javascript\":[\"JavaScript\",\"

\\u7248\\u672c\\uff1aNode.js 16.13.2<\\/code><\\/p>\\r\\n\\r\\n

\\u60a8\\u7684\\u4ee3\\u7801\\u5728\\u6267\\u884c\\u65f6\\u5c06\\u5e26\\u4e0a --harmony<\\/code> \\u6807\\u8bb0\\u6765\\u5f00\\u542f \\u65b0\\u7248ES6\\u7279\\u6027<\\/a>\\u3002<\\/p>\\r\\n\\r\\n

lodash.js<\\/a> \\u5e93\\u5df2\\u7ecf\\u9ed8\\u8ba4\\u88ab\\u5305\\u542b\\u3002<\\/p>\\r\\n\\r\\n

\\u5982\\u9700\\u4f7f\\u7528\\u961f\\u5217\\/\\u4f18\\u5148\\u961f\\u5217\\uff0c\\u60a8\\u53ef\\u4f7f\\u7528 datastructures-js\\/priority-queue<\\/a> \\u548c datastructures-js\\/queue<\\/a>\\u3002<\\/p>\"],\"ruby\":[\"Ruby\",\"

\\u4f7f\\u7528Ruby 3.1<\\/code>\\u6267\\u884c<\\/p>\\r\\n\\r\\n

\\u4e00\\u4e9b\\u5e38\\u7528\\u7684\\u6570\\u636e\\u7ed3\\u6784\\u5df2\\u5728 Algorithms \\u6a21\\u5757\\u4e2d\\u63d0\\u4f9b\\uff1ahttps:\\/\\/www.rubydoc.info\\/github\\/kanwei\\/algorithms\\/Algorithms<\\/p>\"],\"swift\":[\"Swift\",\"

\\u7248\\u672c\\uff1aSwift 5.5.2<\\/code><\\/p>\\r\\n\\r\\n

\\u6211\\u4eec\\u901a\\u5e38\\u4fdd\\u8bc1\\u66f4\\u65b0\\u5230 Apple\\u653e\\u51fa\\u7684\\u6700\\u65b0\\u7248Swift<\\/a>\\u3002\\u5982\\u679c\\u60a8\\u53d1\\u73b0Swift\\u4e0d\\u662f\\u6700\\u65b0\\u7248\\u7684\\uff0c\\u8bf7\\u8054\\u7cfb\\u6211\\u4eec\\uff01\\u6211\\u4eec\\u5c06\\u5c3d\\u5feb\\u66f4\\u65b0\\u3002<\\/p>\"],\"golang\":[\"Go\",\"

\\u7248\\u672c\\uff1aGo 1.17<\\/code><\\/p>\\r\\n\\r\\n

\\u652f\\u6301 https:\\/\\/godoc.org\\/github.com\\/emirpasic\\/gods<\\/a> \\u7b2c\\u4e09\\u65b9\\u5e93\\u3002<\\/p>\"],\"python3\":[\"Python3\",\"

\\u7248\\u672c\\uff1aPython 3.10<\\/code><\\/p>\\r\\n\\r\\n

\\u4e3a\\u4e86\\u65b9\\u4fbf\\u8d77\\u89c1\\uff0c\\u5927\\u90e8\\u5206\\u5e38\\u7528\\u5e93\\u5df2\\u7ecf\\u88ab\\u81ea\\u52a8 \\u5bfc\\u5165\\uff0c\\u5982array<\\/a>, bisect<\\/a>, collections<\\/a>\\u3002 \\u5982\\u679c\\u60a8\\u9700\\u8981\\u4f7f\\u7528\\u5176\\u4ed6\\u5e93\\u51fd\\u6570\\uff0c\\u8bf7\\u81ea\\u884c\\u5bfc\\u5165\\u3002<\\/p>\\r\\n\\r\\n

\\u5982\\u9700\\u4f7f\\u7528 Map\\/TreeMap \\u6570\\u636e\\u7ed3\\u6784\\uff0c\\u60a8\\u53ef\\u4f7f\\u7528 sortedcontainers<\\/a> \\u5e93\\u3002<\\/p>\"],\"scala\":[\"Scala\",\"

\\u7248\\u672c\\uff1aScala 2.13<\\/code><\\/p>\"],\"kotlin\":[\"Kotlin\",\"

\\u7248\\u672c\\uff1aKotlin 1.3.10<\\/code><\\/p>\"],\"rust\":[\"Rust\",\"

\\u7248\\u672c\\uff1arust 1.58.1<\\/code><\\/p>\\r\\n\\r\\n

\\u652f\\u6301 crates.io \\u7684 rand<\\/a><\\/p>\"],\"php\":[\"PHP\",\"

PHP 8.1<\\/code>.<\\/p>\\r\\n\\r\\n

With bcmath module.<\\/p>\"],\"typescript\":[\"TypeScript\",\"

TypeScript 4.5.4<\\/p>\\r\\n\\r\\n

Compile Options: --alwaysStrict --strictBindCallApply --strictFunctionTypes --target ES2020<\\/p>\"],\"racket\":[\"Racket\",\"

Racket CS<\\/a> v8.3<\\/p>\\r\\n\\r\\n

\\u4f7f\\u7528 #lang racket<\\/p>\\r\\n\\r\\n

\\u5df2\\u9884\\u5148 (require data\\/gvector data\\/queue data\\/order data\\/heap). \\u82e5\\u9700\\u4f7f\\u7528\\u5176\\u5b83\\u6570\\u636e\\u7ed3\\u6784\\uff0c\\u53ef\\u81ea\\u884c require\\u3002<\\/p>\"],\"erlang\":[\"Erlang\",\"Erlang\\/OTP 24.2\"],\"elixir\":[\"Elixir\",\"Elixir 1.13.0 with Erlang\\/OTP 24.2\"]}", "book": { "id": "2", "bookName": "《程序员面试金典(第 6 版)》", "pressName": "图灵公司", "source": "《程序员面试金典(第 6 版)》独家授权", "shortDescription": "英文版:Cracking the Coding Interview,源自硅谷程序员的面试红宝书", "fullDescription": "本书是原谷歌资深面试官的经验之作,帮助了许多想要加入脸书、苹果、谷歌等 IT 名企的求职者拿到 Dream offer。本专题的 100+ 编程面试题是在原书基础上精心挑选出来的,帮助你轻松应战 IT 名企技术面试。", "bookImgUrl": "https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2019/09/30/book_2.jpg", "pressImgUrl": "https://assets.leetcode-cn.com/aliyun-lc-upload/uploads/2020/02/11/logo20190828-02.png", "productUrl": "", "__typename": "CategoryInfoNode" }, "isSubscribed": false, "isDailyQuestion": false, "dailyRecordStatus": null, "editorType": "CKEDITOR", "ugcQuestionId": null, "style": "LEETCODE", "exampleTestcases": "", "__typename": "QuestionNode" } } }