Given an integer array nums and two integers k and p, return the number of distinct subarrays, which have at most k elements that are divisible by p.
Two arrays nums1 and nums2 are said to be distinct if:
i where nums1[i] != nums2[i].A subarray is defined as a non-empty contiguous sequence of elements in an array.
\n\n\n
Example 1:
\n\n\nInput: nums = [2,3,3,2,2], k = 2, p = 2\nOutput: 11\nExplanation:\nThe elements at indices 0, 3, and 4 are divisible by p = 2.\nThe 11 distinct subarrays which have at most k = 2 elements divisible by 2 are:\n[2], [2,3], [2,3,3], [2,3,3,2], [3], [3,3], [3,3,2], [3,3,2,2], [3,2], [3,2,2], and [2,2].\nNote that the subarrays [2] and [3] occur more than once in nums, but they should each be counted only once.\nThe subarray [2,3,3,2,2] should not be counted because it has 3 elements that are divisible by 2.\n\n\n
Example 2:
\n\n\nInput: nums = [1,2,3,4], k = 4, p = 1\nOutput: 10\nExplanation:\nAll element of nums are divisible by p = 1.\nAlso, every subarray of nums will have at most 4 elements that are divisible by 1.\nSince all subarrays are distinct, the total number of subarrays satisfying all the constraints is 10.\n\n\n
\n
Constraints:
\n\n1 <= nums.length <= 2001 <= nums[i], p <= 2001 <= k <= nums.length\n
Follow up:
\n\nCan you solve this problem in O(n2) time complexity?
\n", "translatedTitle": null, "translatedContent": null, "isPaidOnly": false, "difficulty": "Medium", "likes": 584, "dislikes": 136, "isLiked": null, "similarQuestions": "[{\"title\": \"Subarrays with K Different Integers\", \"titleSlug\": \"subarrays-with-k-different-integers\", \"difficulty\": \"Hard\", \"translatedTitle\": null}, {\"title\": \"Count Number of Nice Subarrays\", \"titleSlug\": \"count-number-of-nice-subarrays\", \"difficulty\": \"Medium\", \"translatedTitle\": null}, {\"title\": \"Subarray With Elements Greater Than Varying Threshold\", \"titleSlug\": \"subarray-with-elements-greater-than-varying-threshold\", \"difficulty\": \"Hard\", \"translatedTitle\": null}]", "exampleTestcases": "[2,3,3,2,2]\n2\n2\n[1,2,3,4]\n4\n1", "categoryTitle": "Algorithms", "contributors": [], "topicTags": [ { "name": "Array", "slug": "array", "translatedName": null, "__typename": "TopicTagNode" }, { "name": "Hash Table", "slug": "hash-table", "translatedName": null, "__typename": "TopicTagNode" }, { "name": "Trie", "slug": "trie", "translatedName": null, "__typename": "TopicTagNode" }, { "name": "Rolling Hash", "slug": "rolling-hash", "translatedName": null, "__typename": "TopicTagNode" }, { "name": "Hash Function", "slug": "hash-function", "translatedName": null, "__typename": "TopicTagNode" }, { "name": "Enumeration", "slug": "enumeration", "translatedName": null, "__typename": "TopicTagNode" } ], "companyTagStats": null, "codeSnippets": [ { "lang": "C++", "langSlug": "cpp", "code": "class Solution {\npublic:\n int countDistinct(vectorCompiled with clang 11 using the latest C++ 20 standard.
Your code is compiled with level two optimization (-O2). AddressSanitizer is also enabled to help detect out-of-bounds and use-after-free bugs.
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.
Most standard library headers are already included automatically for your convenience.
\\r\\nIncludes Pair class from https://docs.oracle.com/javase/8/javafx/api/javafx/util/Pair.html.
Python 2.7.12.
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\\nFor Map/TreeMap data structure, you may use sortedcontainers library.
\\r\\n\\r\\nNote 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.
Your code is compiled with level one optimization (-O1). AddressSanitizer is also enabled to help detect out-of-bounds and use-after-free bugs.
Most standard library headers are already included automatically for your convenience.
\\r\\n\\r\\nFor hash table operations, you may use uthash. \\\"uthash.h\\\" is included by default. Below are some examples:
\\r\\n\\r\\n1. 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\\n2. 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\\n3. 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#\", \"\"], \"javascript\": [\"JavaScript\", \"Node.js 16.13.2.
Your code is run with --harmony flag, enabling new ES6 features.
lodash.js library is included by default.
\\r\\n\\r\\nFor 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
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.
Go 1.21
Support https://godoc.org/github.com/emirpasic/gods@v1.18.1 library.
\"], \"python3\": [\"Python3\", \"Python 3.10.
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\\nFor Map/TreeMap data structure, you may use sortedcontainers library.
\"], \"scala\": [\"Scala\", \"Scala 2.13.7.
Kotlin 1.9.0.
Rust 1.58.1
Supports rand v0.6\\u00a0from crates.io
\"], \"php\": [\"PHP\", \"PHP 8.1.
With bcmath module
\"], \"typescript\": [\"Typescript\", \"TypeScript 5.1.6, Node.js 16.13.2.
Your code is run with --harmony flag, enabling new ES2022 features.
lodash.js library is included by default.
\"], \"racket\": [\"Racket\", \"Run with Racket 8.3.
Dart 2.17.3
\\r\\n\\r\\nYour code will be run directly without compiling
\"]}", "libraryUrl": null, "adminUrl": null, "challengeQuestion": null, "__typename": "QuestionNode" } } }