{ "data": { "question": { "questionId": "1622", "questionFrontendId": "1499", "boundTopicId": null, "title": "Max Value of Equation", "titleSlug": "max-value-of-equation", "content": "

You are given an array points containing the coordinates of points on a 2D plane, sorted by the x-values, where points[i] = [xi, yi] such that xi < xj for all 1 <= i < j <= points.length. You are also given an integer k.

\n\n

Return the maximum value of the equation yi + yj + |xi - xj| where |xi - xj| <= k and 1 <= i < j <= points.length.

\n\n

It is guaranteed that there exists at least one pair of points that satisfy the constraint |xi - xj| <= k.

\n\n

 

\n

Example 1:

\n\n
\nInput: points = [[1,3],[2,0],[5,10],[6,-10]], k = 1\nOutput: 4\nExplanation: The first two points satisfy the condition |xi - xj| <= 1 and if we calculate the equation we get 3 + 0 + |1 - 2| = 4. Third and fourth points also satisfy the condition and give a value of 10 + -10 + |5 - 6| = 1.\nNo other pairs satisfy the condition, so we return the max of 4 and 1.\n
\n\n

Example 2:

\n\n
\nInput: points = [[0,0],[3,0],[9,2]], k = 3\nOutput: 3\nExplanation: Only the first two points have an absolute difference of 3 or less in the x-values, and give the value of 0 + 0 + |0 - 3| = 3.\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": null, "translatedContent": null, "isPaidOnly": false, "difficulty": "Hard", "likes": 1275, "dislikes": 53, "isLiked": null, "similarQuestions": "[{\"title\": \"Count Pairs in Two Arrays\", \"titleSlug\": \"count-pairs-in-two-arrays\", \"difficulty\": \"Medium\", \"translatedTitle\": null}]", "exampleTestcases": "[[1,3],[2,0],[5,10],[6,-10]]\n1\n[[0,0],[3,0],[9,2]]\n3", "categoryTitle": "Algorithms", "contributors": [], "topicTags": [ { "name": "Array", "slug": "array", "translatedName": null, "__typename": "TopicTagNode" }, { "name": "Queue", "slug": "queue", "translatedName": null, "__typename": "TopicTagNode" }, { "name": "Sliding Window", "slug": "sliding-window", "translatedName": null, "__typename": "TopicTagNode" }, { "name": "Heap (Priority Queue)", "slug": "heap-priority-queue", "translatedName": null, "__typename": "TopicTagNode" }, { "name": "Monotonic Queue", "slug": "monotonic-queue", "translatedName": null, "__typename": "TopicTagNode" } ], "companyTagStats": null, "codeSnippets": [ { "lang": "C++", "langSlug": "cpp", "code": "class Solution {\npublic:\n int findMaxValueOfEquation(vector>& points, int k) {\n \n }\n};", "__typename": "CodeSnippetNode" }, { "lang": "Java", "langSlug": "java", "code": "class Solution {\n public int findMaxValueOfEquation(int[][] points, int k) {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Python", "langSlug": "python", "code": "class Solution(object):\n def findMaxValueOfEquation(self, points, k):\n \"\"\"\n :type points: List[List[int]]\n :type k: int\n :rtype: int\n \"\"\"\n ", "__typename": "CodeSnippetNode" }, { "lang": "Python3", "langSlug": "python3", "code": "class Solution:\n def findMaxValueOfEquation(self, points: List[List[int]], k: int) -> int:\n ", "__typename": "CodeSnippetNode" }, { "lang": "C", "langSlug": "c", "code": "int findMaxValueOfEquation(int** points, int pointsSize, int* pointsColSize, int k) {\n \n}", "__typename": "CodeSnippetNode" }, { "lang": "C#", "langSlug": "csharp", "code": "public class Solution {\n public int FindMaxValueOfEquation(int[][] points, int k) {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "JavaScript", "langSlug": "javascript", "code": "/**\n * @param {number[][]} points\n * @param {number} k\n * @return {number}\n */\nvar findMaxValueOfEquation = function(points, k) {\n \n};", "__typename": "CodeSnippetNode" }, { "lang": "TypeScript", "langSlug": "typescript", "code": "function findMaxValueOfEquation(points: number[][], k: number): number {\n \n};", "__typename": "CodeSnippetNode" }, { "lang": "PHP", "langSlug": "php", "code": "class Solution {\n\n /**\n * @param Integer[][] $points\n * @param Integer $k\n * @return Integer\n */\n function findMaxValueOfEquation($points, $k) {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Swift", "langSlug": "swift", "code": "class Solution {\n func findMaxValueOfEquation(_ points: [[Int]], _ k: Int) -> Int {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Kotlin", "langSlug": "kotlin", "code": "class Solution {\n fun findMaxValueOfEquation(points: Array, k: Int): Int {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Dart", "langSlug": "dart", "code": "class Solution {\n int findMaxValueOfEquation(List> points, int k) {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Go", "langSlug": "golang", "code": "func findMaxValueOfEquation(points [][]int, k int) int {\n \n}", "__typename": "CodeSnippetNode" }, { "lang": "Ruby", "langSlug": "ruby", "code": "# @param {Integer[][]} points\n# @param {Integer} k\n# @return {Integer}\ndef find_max_value_of_equation(points, k)\n \nend", "__typename": "CodeSnippetNode" }, { "lang": "Scala", "langSlug": "scala", "code": "object Solution {\n def findMaxValueOfEquation(points: Array[Array[Int]], k: Int): Int = {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Rust", "langSlug": "rust", "code": "impl Solution {\n pub fn find_max_value_of_equation(points: Vec>, k: i32) -> i32 {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Racket", "langSlug": "racket", "code": "(define/contract (find-max-value-of-equation points k)\n (-> (listof (listof exact-integer?)) exact-integer? exact-integer?)\n )", "__typename": "CodeSnippetNode" }, { "lang": "Erlang", "langSlug": "erlang", "code": "-spec find_max_value_of_equation(Points :: [[integer()]], K :: integer()) -> integer().\nfind_max_value_of_equation(Points, K) ->\n .", "__typename": "CodeSnippetNode" }, { "lang": "Elixir", "langSlug": "elixir", "code": "defmodule Solution do\n @spec find_max_value_of_equation(points :: [[integer]], k :: integer) :: integer\n def find_max_value_of_equation(points, k) do\n \n end\nend", "__typename": "CodeSnippetNode" } ], "stats": "{\"totalAccepted\": \"40.6K\", \"totalSubmission\": \"91.1K\", \"totalAcceptedRaw\": 40570, \"totalSubmissionRaw\": 91069, \"acRate\": \"44.5%\"}", "hints": [ "Use a priority queue to store for each point i, the tuple [yi-xi, xi]", "Loop through the array and pop elements from the heap if the condition xj - xi > k, where j is the current index and i is the point on top the queue.", "After popping elements from the queue. If the queue is not empty, calculate the equation with the current point and the point on top of the queue and maximize the answer." ], "solution": null, "status": null, "sampleTestCase": "[[1,3],[2,0],[5,10],[6,-10]]\n1", "metaData": "{\n \"name\": \"findMaxValueOfEquation\",\n \"params\": [\n {\n \"name\": \"points\",\n \"type\": \"integer[][]\"\n },\n {\n \"type\": \"integer\",\n \"name\": \"k\"\n }\n ],\n \"return\": {\n \"type\": \"integer\"\n }\n}", "judgerAvailable": true, "judgeType": "large", "mysqlSchemas": [], "enableRunCode": true, "enableTestMode": false, "enableDebugger": true, "envInfo": "{\"cpp\": [\"C++\", \"

Compiled with clang 11 using the latest C++ 20 standard.

\\r\\n\\r\\n

Your code is compiled with level two optimization (-O2). AddressSanitizer is also enabled to help detect out-of-bounds and use-after-free bugs.

\\r\\n\\r\\n

Most standard library headers are already included automatically for your convenience.

\"], \"java\": [\"Java\", \"

OpenJDK 17. Java 8 features such as lambda expressions and stream API can be used.

\\r\\n\\r\\n

Most standard library headers are already included automatically for your convenience.

\\r\\n

Includes Pair class from https://docs.oracle.com/javase/8/javafx/api/javafx/util/Pair.html.

\"], \"python\": [\"Python\", \"

Python 2.7.12.

\\r\\n\\r\\n

Most libraries are already imported automatically for your convenience, such as array, bisect, collections. If you need more libraries, you can import it yourself.

\\r\\n\\r\\n

For Map/TreeMap data structure, you may use sortedcontainers library.

\\r\\n\\r\\n

Note that Python 2.7 will not be maintained past 2020. For the latest Python, please choose Python3 instead.

\"], \"c\": [\"C\", \"

Compiled with gcc 8.2 using the gnu11 standard.

\\r\\n\\r\\n

Your code is compiled with level one optimization (-O1). AddressSanitizer is also enabled to help detect out-of-bounds and use-after-free bugs.

\\r\\n\\r\\n

Most standard library headers are already included automatically for your convenience.

\\r\\n\\r\\n

For hash table operations, you may use uthash. \\\"uthash.h\\\" is included by default. Below are some examples:

\\r\\n\\r\\n

1. Adding an item to a hash.\\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
\\r\\n

\\r\\n\\r\\n

2. Looking up an item in a hash:\\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
\\r\\n

\\r\\n\\r\\n

3. Deleting an item in a hash:\\r\\n

\\r\\nvoid delete_user(struct hash_entry *user) {\\r\\n    HASH_DEL(users, user);  \\r\\n}\\r\\n
\\r\\n

\"], \"csharp\": [\"C#\", \"

C# 10 with .NET 6 runtime

\"], \"javascript\": [\"JavaScript\", \"

Node.js 16.13.2.

\\r\\n\\r\\n

Your code is run with --harmony flag, enabling new ES6 features.

\\r\\n\\r\\n

lodash.js library is included by default.

\\r\\n\\r\\n

For Priority Queue / Queue data structures, you may use 5.3.0 version of datastructures-js/priority-queue and 4.2.1 version of datastructures-js/queue.

\"], \"ruby\": [\"Ruby\", \"

Ruby 3.1

\\r\\n\\r\\n

Some common data structure implementations are provided in the Algorithms module: https://www.rubydoc.info/github/kanwei/algorithms/Algorithms

\"], \"swift\": [\"Swift\", \"

Swift 5.5.2.

\"], \"golang\": [\"Go\", \"

Go 1.21

\\r\\n

Support https://godoc.org/github.com/emirpasic/gods@v1.18.1 library.

\"], \"python3\": [\"Python3\", \"

Python 3.10.

\\r\\n\\r\\n

Most libraries are already imported automatically for your convenience, such as array, bisect, collections. If you need more libraries, you can import it yourself.

\\r\\n\\r\\n

For Map/TreeMap data structure, you may use sortedcontainers library.

\"], \"scala\": [\"Scala\", \"

Scala 2.13.7.

\"], \"kotlin\": [\"Kotlin\", \"

Kotlin 1.9.0.

\"], \"rust\": [\"Rust\", \"

Rust 1.58.1

\\r\\n\\r\\n

Supports rand v0.6\\u00a0from crates.io

\"], \"php\": [\"PHP\", \"

PHP 8.1.

\\r\\n

With bcmath module

\"], \"typescript\": [\"Typescript\", \"

TypeScript 5.1.6, Node.js 16.13.2.

\\r\\n\\r\\n

Your code is run with --harmony flag, enabling new ES2022 features.

\\r\\n\\r\\n

lodash.js library is included by default.

\"], \"racket\": [\"Racket\", \"

Run with Racket 8.3.

\"], \"erlang\": [\"Erlang\", \"Erlang/OTP 25.0\"], \"elixir\": [\"Elixir\", \"Elixir 1.13.4 with Erlang/OTP 25.0\"], \"dart\": [\"Dart\", \"

Dart 2.17.3

\\r\\n\\r\\n

Your code will be run directly without compiling

\"]}", "libraryUrl": null, "adminUrl": null, "challengeQuestion": null, "__typename": "QuestionNode" } } }