{ "data": { "question": { "questionId": "3198", "questionFrontendId": "2912", "boundTopicId": null, "title": "Number of Ways to Reach Destination in the Grid", "titleSlug": "number-of-ways-to-reach-destination-in-the-grid", "content": null, "translatedTitle": null, "translatedContent": null, "isPaidOnly": true, "difficulty": "Hard", "likes": 12, "dislikes": 0, "isLiked": null, "similarQuestions": "[]", "exampleTestcases": "3\n2\n2\n[1,1]\n[2,2]\n3\n4\n3\n[1,2]\n[2,3]", "categoryTitle": "Algorithms", "contributors": [], "topicTags": [ { "name": "Math", "slug": "math", "translatedName": null, "__typename": "TopicTagNode" }, { "name": "Dynamic Programming", "slug": "dynamic-programming", "translatedName": null, "__typename": "TopicTagNode" }, { "name": "Combinatorics", "slug": "combinatorics", "translatedName": null, "__typename": "TopicTagNode" } ], "companyTagStats": null, "codeSnippets": null, "stats": "{\"totalAccepted\": \"681\", \"totalSubmission\": \"954\", \"totalAcceptedRaw\": 681, \"totalSubmissionRaw\": 954, \"acRate\": \"71.4%\"}", "hints": [ "We are asked to count the number of sequences of length k + 1 that start from (xs, ys) and end with (xd, yd). i.e., (xs, ys), (x1, y1), ..., (xk - 1, yk - 1), (xd, yd).", "The key point is to see x and y separately.", "Suppose we do i vertical moves and k - i horizontal moves.", "In each vertical move, we change only y. Now let's count the number of sequences of length i + 1 that start with source[2] and end with dest[2]. Let's call this number vertical_count.", "Do the same for horizontal moves and let it be horizontal_count.", "For each i, the number of ways would be vertical_count * horizontal_count * C(n, i) since the order of vertical and horizontal moves could be arbitrary." ], "solution": null, "status": null, "sampleTestCase": "3\n2\n2\n[1,1]\n[2,2]", "metaData": "{\n \"name\": \"numberOfWays\",\n \"params\": [\n {\n \"type\": \"integer\",\n \"name\": \"n\"\n },\n {\n \"type\": \"integer\",\n \"name\": \"m\"\n },\n {\n \"type\": \"integer\",\n \"name\": \"k\"\n },\n {\n \"type\": \"integer[]\",\n \"name\": \"source\"\n },\n {\n \"type\": \"integer[]\",\n \"name\": \"dest\"\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.

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

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

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

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

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

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Python 2.7.12.

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

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

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

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Compiled with gcc 8.2 using the gnu11 standard.

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

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

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

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

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

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C# 10 with .NET 6 runtime

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Node.js 16.13.2.

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

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lodash.js library is included by default.

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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.

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Ruby 3.1

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

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Swift 5.5.2.

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Go 1.21

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

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Python 3.10.

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

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

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Scala 2.13.7.

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Kotlin 1.9.0.

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Rust 1.58.1

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Supports rand v0.6\\u00a0from crates.io

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PHP 8.1.

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With bcmath module

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TypeScript 5.1.6, Node.js 16.13.2.

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

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lodash.js library is included by default.

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Run with Racket 8.3.

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Dart 2.17.3

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Your code will be run directly without compiling

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