{ "data": { "question": { "questionId": "2635", "questionFrontendId": "2543", "boundTopicId": null, "title": "Check if Point Is Reachable", "titleSlug": "check-if-point-is-reachable", "content": "

There exists an infinitely large grid. You are currently at point (1, 1), and you need to reach the point (targetX, targetY) using a finite number of steps.

\n\n

In one step, you can move from point (x, y) to any one of the following points:

\n\n\n\n

Given two integers targetX and targetY representing the X-coordinate and Y-coordinate of your final position, return true if you can reach the point from (1, 1) using some number of steps, and false otherwise.

\n\n

 

\n

Example 1:

\n\n
\nInput: targetX = 6, targetY = 9\nOutput: false\nExplanation: It is impossible to reach (6,9) from (1,1) using any sequence of moves, so false is returned.\n
\n\n

Example 2:

\n\n
\nInput: targetX = 4, targetY = 7\nOutput: true\nExplanation: You can follow the path (1,1) -> (1,2) -> (1,4) -> (1,8) -> (1,7) -> (2,7) -> (4,7).\n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": null, "translatedContent": null, "isPaidOnly": false, "difficulty": "Hard", "likes": 234, "dislikes": 47, "isLiked": null, "similarQuestions": "[{\"title\": \"Reaching Points\", \"titleSlug\": \"reaching-points\", \"difficulty\": \"Hard\", \"translatedTitle\": null}]", "exampleTestcases": "6\n9\n4\n7", "categoryTitle": "Algorithms", "contributors": [], "topicTags": [ { "name": "Math", "slug": "math", "translatedName": null, "__typename": "TopicTagNode" }, { "name": "Number Theory", "slug": "number-theory", "translatedName": null, "__typename": "TopicTagNode" } ], "companyTagStats": null, "codeSnippets": [ { "lang": "C++", "langSlug": "cpp", "code": "class Solution {\npublic:\n bool isReachable(int targetX, int targetY) {\n \n }\n};", "__typename": "CodeSnippetNode" }, { "lang": "Java", "langSlug": "java", "code": "class Solution {\n public boolean isReachable(int targetX, int targetY) {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Python", "langSlug": "python", "code": "class Solution(object):\n def isReachable(self, targetX, targetY):\n \"\"\"\n :type targetX: int\n :type targetY: int\n :rtype: bool\n \"\"\"\n ", "__typename": "CodeSnippetNode" }, { "lang": "Python3", "langSlug": "python3", "code": "class Solution:\n def isReachable(self, targetX: int, targetY: int) -> bool:\n ", "__typename": "CodeSnippetNode" }, { "lang": "C", "langSlug": "c", "code": "bool isReachable(int targetX, int targetY) {\n \n}", "__typename": "CodeSnippetNode" }, { "lang": "C#", "langSlug": "csharp", "code": "public class Solution {\n public bool IsReachable(int targetX, int targetY) {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "JavaScript", "langSlug": "javascript", "code": "/**\n * @param {number} targetX\n * @param {number} targetY\n * @return {boolean}\n */\nvar isReachable = function(targetX, targetY) {\n \n};", "__typename": "CodeSnippetNode" }, { "lang": "TypeScript", "langSlug": "typescript", "code": "function isReachable(targetX: number, targetY: number): boolean {\n \n};", "__typename": "CodeSnippetNode" }, { "lang": "PHP", "langSlug": "php", "code": "class Solution {\n\n /**\n * @param Integer $targetX\n * @param Integer $targetY\n * @return Boolean\n */\n function isReachable($targetX, $targetY) {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Swift", "langSlug": "swift", "code": "class Solution {\n func isReachable(_ targetX: Int, _ targetY: Int) -> Bool {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Kotlin", "langSlug": "kotlin", "code": "class Solution {\n fun isReachable(targetX: Int, targetY: Int): Boolean {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Dart", "langSlug": "dart", "code": "class Solution {\n bool isReachable(int targetX, int targetY) {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Go", "langSlug": "golang", "code": "func isReachable(targetX int, targetY int) bool {\n \n}", "__typename": "CodeSnippetNode" }, { "lang": "Ruby", "langSlug": "ruby", "code": "# @param {Integer} target_x\n# @param {Integer} target_y\n# @return {Boolean}\ndef is_reachable(target_x, target_y)\n \nend", "__typename": "CodeSnippetNode" }, { "lang": "Scala", "langSlug": "scala", "code": "object Solution {\n def isReachable(targetX: Int, targetY: Int): Boolean = {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Rust", "langSlug": "rust", "code": "impl Solution {\n pub fn is_reachable(target_x: i32, target_y: i32) -> bool {\n \n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Racket", "langSlug": "racket", "code": "(define/contract (is-reachable targetX targetY)\n (-> exact-integer? exact-integer? boolean?)\n )", "__typename": "CodeSnippetNode" }, { "lang": "Erlang", "langSlug": "erlang", "code": "-spec is_reachable(TargetX :: integer(), TargetY :: integer()) -> boolean().\nis_reachable(TargetX, TargetY) ->\n .", "__typename": "CodeSnippetNode" }, { "lang": "Elixir", "langSlug": "elixir", "code": "defmodule Solution do\n @spec is_reachable(target_x :: integer, target_y :: integer) :: boolean\n def is_reachable(target_x, target_y) do\n \n end\nend", "__typename": "CodeSnippetNode" } ], "stats": "{\"totalAccepted\": \"6.7K\", \"totalSubmission\": \"16.1K\", \"totalAcceptedRaw\": 6688, \"totalSubmissionRaw\": 16056, \"acRate\": \"41.7%\"}", "hints": [ "Let’s go in reverse order, from (targetX, targetY) to (1, 1). So, now we can move from (x, y) to (x+y, y), (x, y+x), (x/2, y) if x is even, and (x, y/2) if y is even.", "When is it optimal to use the third and fourth operations?", "Think how GCD of (x, y) is affected if we apply the first two operations.", "How can we check if we can reach (1, 1) using the GCD value calculate above?" ], "solution": null, "status": null, "sampleTestCase": "6\n9", "metaData": "{\n \"name\": \"isReachable\",\n \"params\": [\n {\n \"name\": \"targetX\",\n \"type\": \"integer\"\n },\n {\n \"type\": \"integer\",\n \"name\": \"targetY\"\n }\n ],\n \"return\": {\n \"type\": \"boolean\"\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" } } }