mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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181 lines
18 KiB
JSON
181 lines
18 KiB
JSON
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"questionId": "3411",
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"title": "Find Products of Elements of Big Array",
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"titleSlug": "find-products-of-elements-of-big-array",
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"content": "<p>A <strong>powerful array</strong> for an integer <code>x</code> is the shortest sorted array of powers of two that sum up to <code>x</code>. For example, the powerful array for 11 is <code>[1, 2, 8]</code>.</p>\n\n<p>The array <code>big_nums</code> is created by concatenating the <strong>powerful</strong> arrays for every positive integer <code>i</code> in ascending order: 1, 2, 3, and so forth. Thus, <code>big_nums</code> starts as <code>[<u>1</u>, <u>2</u>, <u>1, 2</u>, <u>4</u>, <u>1, 4</u>, <u>2, 4</u>, <u>1, 2, 4</u>, <u>8</u>, ...]</code>.</p>\n\n<p>You are given a 2D integer matrix <code>queries</code>, where for <code>queries[i] = [from<sub>i</sub>, to<sub>i</sub>, mod<sub>i</sub>]</code> you should calculate <code>(big_nums[from<sub>i</sub>] * big_nums[from<sub>i</sub> + 1] * ... * big_nums[to<sub>i</sub>]) % mod<sub>i</sub></code><!-- notionvc: a71131cc-7b52-4786-9a4b-660d6d864f89 -->.</p>\n\n<p>Return an integer array <code>answer</code> such that <code>answer[i]</code> is the answer to the <code>i<sup>th</sup></code> query.</p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">queries = [[1,3,7]]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">[4]</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>There is one query.</p>\n\n<p><code>big_nums[1..3] = [2,1,2]</code>. The product of them is 4. The remainder of 4 under 7 is 4.</p>\n</div>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<div class=\"example-block\">\n<p><strong>Input:</strong> <span class=\"example-io\">queries = [[2,5,3],[7,7,4]]</span></p>\n\n<p><strong>Output:</strong> <span class=\"example-io\">[2,2]</span></p>\n\n<p><strong>Explanation:</strong></p>\n\n<p>There are two queries.</p>\n\n<p>First query: <code>big_nums[2..5] = [1,2,4,1]</code>. The product of them is 8. The remainder of 8 under 3 is 2.</p>\n\n<p>Second query: <code>big_nums[7] = 2</code>. The remainder of 2 under 4 is 2.</p>\n</div>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>1 <= queries.length <= 500</code></li>\n\t<li><code>queries[i].length == 3</code></li>\n\t<li><code>0 <= queries[i][0] <= queries[i][1] <= 10<sup>15</sup></code></li>\n\t<li><code>1 <= queries[i][2] <= 10<sup>5</sup></code></li>\n</ul>\n",
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"difficulty": "Hard",
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"categoryTitle": "Algorithms",
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"name": "Array",
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"name": "Binary Search",
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"code": "impl Solution {\n pub fn find_products_of_elements(queries: Vec<Vec<i64>>) -> Vec<i32> {\n \n }\n}",
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"Find a way to calculate <code>f(n, i)</code> which is the total number of numbers in <code>[1, n]</code> when the <code>i<sup>th</sup></code> bit is set in <code>O(log(n))</code> time.",
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"Use binary search to find the last number for each query (and there might be one “incomplete” number for the query).",
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"Use a similar way to find the product (we only need to save the sum of exponents of power of <code>2</code>)."
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