{ "data": { "question": { "questionId": "4063", "questionFrontendId": "3729", "categoryTitle": "Algorithms", "boundTopicId": 3814996, "title": "Count Distinct Subarrays Divisible by K in Sorted Array", "titleSlug": "count-distinct-subarrays-divisible-by-k-in-sorted-array", "content": "
You are given an integer array nums sorted in non-descending order and a positive integer k.
A subarray of nums is good if the sum of its elements is divisible by k.
Return an integer denoting the number of distinct good subarrays of nums.
Subarrays are distinct if their sequences of values are. For example, there are 3 distinct subarrays in [1, 1, 1], namely [1], [1, 1], and [1, 1, 1].
\n
Example 1:
\n\nInput: nums = [1,2,3], k = 3
\n\nOutput: 3
\n\nExplanation:
\n\nThe good subarrays are [1, 2], [3], and [1, 2, 3]. For example, [1, 2, 3] is good because the sum of its elements is 1 + 2 + 3 = 6, and 6 % k = 6 % 3 = 0.
Example 2:
\n\nInput: nums = [2,2,2,2,2,2], k = 6
\n\nOutput: 2
\n\nExplanation:
\n\nThe good subarrays are [2, 2, 2] and [2, 2, 2, 2, 2, 2]. For example, [2, 2, 2] is good because the sum of its elements is 2 + 2 + 2 = 6, and 6 % k = 6 % 6 = 0.
Note that [2, 2, 2] is counted only once.
\n
Constraints:
\n\n1 <= nums.length <= 1051 <= nums[i] <= 109nums is sorted in non-descending order.1 <= k <= 109给你一个按 非降序 排列的整数数组 nums 和一个正整数 k。
如果 nums 的某个 子数组 的元素和可以被 k 整除,则称其为 良好 子数组。
返回一个整数,表示 nums 中 不同 的 良好 子数组的数量。
子数组 是数组中连续且 非空 的一段元素序列。
\n\n当两个子数组的数值序列不同,它们就被视为 不同 的子数组。例如,在 [1, 1, 1] 中,有 3 个 不同 的子数组,分别是 [1]、[1, 1] 和 [1, 1, 1]。
\n\n
示例 1:
\n\n输入: nums = [1,2,3], k = 3
\n\n输出: 3
\n\n解释:
\n\n良好子数组为 [1, 2]、[3] 和 [1, 2, 3]。例如,[1, 2, 3] 是良好的,因为其元素和为 1 + 2 + 3 = 6,且 6 % k = 6 % 3 = 0。
示例 2:
\n\n输入: nums = [2,2,2,2,2,2], k = 6
\n\n输出: 2
\n\n解释:
\n\n良好子数组为 [2, 2, 2] 和 [2, 2, 2, 2, 2, 2]。例如,[2, 2, 2] 是良好的,因为其元素和为 2 + 2 + 2 = 6,且 6 % k = 6 % 6 = 0。
注意,[2, 2, 2] 只计数一次。
\n\n
提示:
\n\n1 <= nums.length <= 1051 <= nums[i] <= 109nums 为非降序排列。1 <= k <= 109(i, j), so the value sequence is identified by that boundary and how many elements you take from each edge.",
"Count single-value sequences per run by testing (L*val) % k == 0."
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