leetcode-problemset/leetcode/originData/count-of-interesting-subarrays.json

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            "title": "Count of Interesting Subarrays",
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            "content": "<p>You are given a <strong>0-indexed</strong> integer array <code>nums</code>, an integer <code>modulo</code>, and an integer <code>k</code>.</p>\n\n<p>Your task is to find the count of subarrays that are <strong>interesting</strong>.</p>\n\n<p>A <strong>subarray</strong> <code>nums[l..r]</code> is <strong>interesting</strong> if the following condition holds:</p>\n\n<ul>\n\t<li>Let <code>cnt</code> be the number of indices <code>i</code> in the range <code>[l, r]</code> such that <code>nums[i] % modulo == k</code>. Then, <code>cnt % modulo == k</code>.</li>\n</ul>\n\n<p>Return <em>an integer denoting the count of interesting subarrays. </em></p>\n\n<p><span><strong>Note:</strong> A subarray is <em>a contiguous non-empty sequence of elements within an array</em>.</span></p>\n\n<p>&nbsp;</p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [3,2,4], modulo = 2, k = 1\n<strong>Output:</strong> 3\n<strong>Explanation:</strong> In this example the interesting subarrays are: \nThe subarray nums[0..0] which is [3]. \n- There is only one index, i = 0, in the range [0, 0] that satisfies nums[i] % modulo == k. \n- Hence, cnt = 1 and cnt % modulo == k.  \nThe subarray nums[0..1] which is [3,2].\n- There is only one index, i = 0, in the range [0, 1] that satisfies nums[i] % modulo == k.  \n- Hence, cnt = 1 and cnt % modulo == k.\nThe subarray nums[0..2] which is [3,2,4]. \n- There is only one index, i = 0, in the range [0, 2] that satisfies nums[i] % modulo == k. \n- Hence, cnt = 1 and cnt % modulo == k. \nIt can be shown that there are no other interesting subarrays. So, the answer is 3.</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums = [3,1,9,6], modulo = 3, k = 0\n<strong>Output:</strong> 2\n<strong>Explanation: </strong>In this example the interesting subarrays are: \nThe subarray nums[0..3] which is [3,1,9,6]. \n- There are three indices, i = 0, 2, 3, in the range [0, 3] that satisfy nums[i] % modulo == k. \n- Hence, cnt = 3 and cnt % modulo == k. \nThe subarray nums[1..1] which is [1]. \n- There is no index, i, in the range [1, 1] that satisfies nums[i] % modulo == k. \n- Hence, cnt = 0 and cnt % modulo == k. \nIt can be shown that there are no other interesting subarrays. So, the answer is 2.</pre>\n\n<p>&nbsp;</p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 &lt;= nums.length &lt;= 10<sup>5 </sup></code></li>\n\t<li><code>1 &lt;= nums[i] &lt;= 10<sup>9</sup></code></li>\n\t<li><code>1 &lt;= modulo &lt;= 10<sup>9</sup></code></li>\n\t<li><code>0 &lt;= k &lt; modulo</code></li>\n</ul>\n",
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                    "lang": "C++",
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                    "code": "class Solution {\npublic:\n    long long countInterestingSubarrays(vector<int>& nums, int modulo, int k) {\n        \n    }\n};",
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                    "code": "class Solution {\n    public long countInterestingSubarrays(List<Integer> nums, int modulo, int k) {\n        \n    }\n}",
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                    "lang": "Python",
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                    "code": "class Solution(object):\n    def countInterestingSubarrays(self, nums, modulo, k):\n        \"\"\"\n        :type nums: List[int]\n        :type modulo: int\n        :type k: int\n        :rtype: int\n        \"\"\"\n        ",
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                    "code": "public class Solution {\n    public long CountInterestingSubarrays(IList<int> nums, int modulo, int k) {\n        \n    }\n}",
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                    "code": "/**\n * @param {number[]} nums\n * @param {number} modulo\n * @param {number} k\n * @return {number}\n */\nvar countInterestingSubarrays = function(nums, modulo, k) {\n    \n};",
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                    "code": "class Solution {\n\n    /**\n     * @param Integer[] $nums\n     * @param Integer $modulo\n     * @param Integer $k\n     * @return Integer\n     */\n    function countInterestingSubarrays($nums, $modulo, $k) {\n        \n    }\n}",
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                    "code": "class Solution {\n    func countInterestingSubarrays(_ nums: [Int], _ modulo: Int, _ k: Int) -> Int {\n        \n    }\n}",
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                    "code": "class Solution {\n    fun countInterestingSubarrays(nums: List<Int>, modulo: Int, k: Int): Long {\n        \n    }\n}",
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                    "lang": "Go",
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                    "code": "func countInterestingSubarrays(nums []int, modulo int, k int) int64 {\n    \n}",
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                    "lang": "Ruby",
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                    "code": "# @param {Integer[]} nums\n# @param {Integer} modulo\n# @param {Integer} k\n# @return {Integer}\ndef count_interesting_subarrays(nums, modulo, k)\n    \nend",
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                    "code": "object Solution {\n    def countInterestingSubarrays(nums: List[Int], modulo: Int, k: Int): Long = {\n        \n    }\n}",
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                    "lang": "Rust",
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                    "code": "impl Solution {\n    pub fn count_interesting_subarrays(nums: Vec<i32>, modulo: i32, k: i32) -> i64 {\n        \n    }\n}",
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                    "code": "(define/contract (count-interesting-subarrays nums modulo k)\n  (-> (listof exact-integer?) exact-integer? exact-integer? exact-integer?)\n\n  )",
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                    "lang": "Erlang",
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                    "code": "-spec count_interesting_subarrays(Nums :: [integer()], Modulo :: integer(), K :: integer()) -> integer().\ncount_interesting_subarrays(Nums, Modulo, K) ->\n  .",
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                    "code": "defmodule Solution do\n  @spec count_interesting_subarrays(nums :: [integer], modulo :: integer, k :: integer) :: integer\n  def count_interesting_subarrays(nums, modulo, k) do\n\n  end\nend",
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            "hints": [
                "The problem can be solved using prefix sums.",
                "Let <code>count[i]</code> be the number of indices where <code>nums[i] % modulo == k</code> among the first <code>i</code> indices.",
                "<code>count[0] = 0</code> and <code>count[i] = count[i - 1] + (nums[i - 1] % modulo == k ? 1 : 0)</code> for <code>i = 1, 2, ..., n</code>.",
                "Now we want to calculate for each <code>i = 1, 2, ..., n</code>, how many indices <code>j < i</code> such that <code>(count[i] - count[j]) % modulo == k</code>.",
                "Rewriting <code>(count[i] - count[j]) % modulo == k</code> becomes <code>count[j] = (count[i] + modulo - k) % modulo</code>.",
                "Using a map data structure, for each <code>i = 0, 1, 2, ..., n</code>, we just sum up all <code>map[(count[i] + modulo - k) % modulo]</code> before increasing <code>map[count[i] % modulo]</code>, and the total sum is the final answer."
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