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50 lines
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50 lines
2.1 KiB
HTML
<p>Given an integer array <code>nums</code> and two integers <code>k</code> and <code>p</code>, return <em>the number of <strong>distinct subarrays,</strong> which have <strong>at most</strong></em> <code>k</code> <em>elements </em>that are <em>divisible by</em> <code>p</code>.</p>
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<p>Two arrays <code>nums1</code> and <code>nums2</code> are said to be <strong>distinct</strong> if:</p>
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<ul>
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<li>They are of <strong>different</strong> lengths, or</li>
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<li>There exists <strong>at least</strong> one index <code>i</code> where <code>nums1[i] != nums2[i]</code>.</li>
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</ul>
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<p>A <strong>subarray</strong> is defined as a <strong>non-empty</strong> contiguous sequence of elements in an array.</p>
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<p> </p>
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<p><strong class="example">Example 1:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [<u><strong>2</strong></u>,3,3,<u><strong>2</strong></u>,<u><strong>2</strong></u>], k = 2, p = 2
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<strong>Output:</strong> 11
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<strong>Explanation:</strong>
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The elements at indices 0, 3, and 4 are divisible by p = 2.
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The 11 distinct subarrays which have at most k = 2 elements divisible by 2 are:
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[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].
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Note that the subarrays [2] and [3] occur more than once in nums, but they should each be counted only once.
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The subarray [2,3,3,2,2] should not be counted because it has 3 elements that are divisible by 2.
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</pre>
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<p><strong class="example">Example 2:</strong></p>
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<pre>
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<strong>Input:</strong> nums = [1,2,3,4], k = 4, p = 1
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<strong>Output:</strong> 10
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<strong>Explanation:</strong>
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All element of nums are divisible by p = 1.
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Also, every subarray of nums will have at most 4 elements that are divisible by 1.
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Since all subarrays are distinct, the total number of subarrays satisfying all the constraints is 10.
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</pre>
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<p> </p>
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<p><strong>Constraints:</strong></p>
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<ul>
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<li><code>1 <= nums.length <= 200</code></li>
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<li><code>1 <= nums[i], p <= 200</code></li>
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<li><code>1 <= k <= nums.length</code></li>
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</ul>
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<p> </p>
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<p><strong>Follow up:</strong></p>
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<p>Can you solve this problem in O(n<sup>2</sup>) time complexity?</p>
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