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

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        "question": {
            "questionId": "2915",
            "questionFrontendId": "2845",
            "categoryTitle": "Algorithms",
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            "title": "Count of Interesting Subarrays",
            "titleSlug": "count-of-interesting-subarrays",
            "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",
            "translatedTitle": "统计趣味子数组的数目",
            "translatedContent": "<p>给你一个下标从 <strong>0</strong> 开始的整数数组 <code>nums</code> ，以及整数 <code>modulo</code> 和整数 <code>k</code> 。</p>\n\n<p>请你找出并统计数组中 <strong>趣味子数组</strong> 的数目。</p>\n\n<p>如果 <strong>子数组</strong> <code>nums[l..r]</code> 满足下述条件，则称其为 <strong>趣味子数组</strong> ：</p>\n\n<ul>\n\t<li>在范围 <code>[l, r]</code> 内，设 <code>cnt</code> 为满足 <code>nums[i] % modulo == k</code> 的索引 <code>i</code> 的数量。并且 <code>cnt % modulo == k</code> 。</li>\n</ul>\n\n<p>以整数形式表示并返回趣味子数组的数目。<em> </em></p>\n\n<p><span><strong>注意：</strong>子数组是数组中的一个连续非空的元素序列。</span></p>\n\n<p>&nbsp;</p>\n\n<p><strong class=\"example\">示例 1：</strong></p>\n\n<pre>\n<strong>输入：</strong>nums = [3,2,4], modulo = 2, k = 1\n<strong>输出：</strong>3\n<strong>解释：</strong>在这个示例中，趣味子数组分别是： \n子数组 nums[0..0] ，也就是 [3] 。 \n- 在范围 [0, 0] 内，只存在 1 个下标 i = 0 满足 nums[i] % modulo == k 。\n- 因此 cnt = 1 ，且 cnt % modulo == k 。\n子数组 nums[0..1] ，也就是 [3,2] 。\n- 在范围 [0, 1] 内，只存在 1 个下标 i = 0 满足 nums[i] % modulo == k 。\n- 因此 cnt = 1 ，且 cnt % modulo == k 。\n子数组 nums[0..2] ，也就是 [3,2,4] 。\n- 在范围 [0, 2] 内，只存在 1 个下标 i = 0 满足 nums[i] % modulo == k 。\n- 因此 cnt = 1 ，且 cnt % modulo == k 。\n可以证明不存在其他趣味子数组。因此，答案为 3 。</pre>\n\n<p><strong class=\"example\">示例 2：</strong></p>\n\n<pre>\n<strong>输入：</strong>nums = [3,1,9,6], modulo = 3, k = 0\n<strong>输出：</strong>2\n<strong>解释：</strong>在这个示例中，趣味子数组分别是： \n子数组 nums[0..3] ，也就是 [3,1,9,6] 。\n- 在范围 [0, 3] 内，只存在 3 个下标 i = 0, 2, 3 满足 nums[i] % modulo == k 。\n- 因此 cnt = 3 ，且 cnt % modulo == k 。\n子数组 nums[1..1] ，也就是 [1] 。\n- 在范围 [1, 1] 内，不存在下标满足 nums[i] % modulo == k 。\n- 因此 cnt = 0 ，且 cnt % modulo == k 。\n可以证明不存在其他趣味子数组，因此答案为 2 。</pre>\n\n<p>&nbsp;</p>\n\n<p><strong>提示：</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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                "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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href=\\\"https:\\/\\/github.com\\/emirpasic\\/gods\\/tree\\/v1.18.1\\\" target=\\\"_blank\\\">https:\\/\\/godoc.org\\/github.com\\/emirpasic\\/gods@v1.18.1<\\/a> \\u7b2c\\u4e09\\u65b9\\u5e93\\u3002<\\/p>\"],\"python3\":[\"Python3\",\"<p>\\u7248\\u672c\\uff1a<code>Python 3.10<\\/code><\\/p>\\r\\n\\r\\n<p>\\u4e3a\\u4e86\\u65b9\\u4fbf\\u8d77\\u89c1\\uff0c\\u5927\\u90e8\\u5206\\u5e38\\u7528\\u5e93\\u5df2\\u7ecf\\u88ab\\u81ea\\u52a8 \\u5bfc\\u5165\\uff0c\\u5982<a href=\\\"https:\\/\\/docs.python.org\\/3\\/library\\/array.html\\\" target=\\\"_blank\\\">array<\\/a>, <a href=\\\"https:\\/\\/docs.python.org\\/3\\/library\\/bisect.html\\\" target=\\\"_blank\\\">bisect<\\/a>, <a href=\\\"https:\\/\\/docs.python.org\\/3\\/library\\/collections.html\\\" target=\\\"_blank\\\">collections<\\/a>\\u3002 \\u5982\\u679c\\u60a8\\u9700\\u8981\\u4f7f\\u7528\\u5176\\u4ed6\\u5e93\\u51fd\\u6570\\uff0c\\u8bf7\\u81ea\\u884c\\u5bfc\\u5165\\u3002<\\/p>\\r\\n\\r\\n<p>\\u5982\\u9700\\u4f7f\\u7528 Map\\/TreeMap 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