mirror of
https://gitee.com/coder-xiaomo/leetcode-problemset
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207 lines
22 KiB
JSON
207 lines
22 KiB
JSON
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"title": "Maximum Sum Queries",
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"content": "<p>You are given two <strong>0-indexed</strong> integer arrays <code>nums1</code> and <code>nums2</code>, each of length <code>n</code>, and a <strong>1-indexed 2D array</strong> <code>queries</code> where <code>queries[i] = [x<sub>i</sub>, y<sub>i</sub>]</code>.</p>\n\n<p>For the <code>i<sup>th</sup></code> query, find the <strong>maximum value</strong> of <code>nums1[j] + nums2[j]</code> among all indices <code>j</code> <code>(0 <= j < n)</code>, where <code>nums1[j] >= x<sub>i</sub></code> and <code>nums2[j] >= y<sub>i</sub></code>, or <strong>-1</strong> if there is no <code>j</code> satisfying the constraints.</p>\n\n<p>Return <em>an array </em><code>answer</code><em> where </em><code>answer[i]</code><em> is the answer to the </em><code>i<sup>th</sup></code><em> query.</em></p>\n\n<p> </p>\n<p><strong class=\"example\">Example 1:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums1 = [4,3,1,2], nums2 = [2,4,9,5], queries = [[4,1],[1,3],[2,5]]\n<strong>Output:</strong> [6,10,7]\n<strong>Explanation:</strong> \nFor the 1st query <code node=\"[object Object]\">x<sub>i</sub> = 4</code> and <code node=\"[object Object]\">y<sub>i</sub> = 1</code>, we can select index <code node=\"[object Object]\">j = 0</code> since <code node=\"[object Object]\">nums1[j] >= 4</code> and <code node=\"[object Object]\">nums2[j] >= 1</code>. The sum <code node=\"[object Object]\">nums1[j] + nums2[j]</code> is 6, and we can show that 6 is the maximum we can obtain.\n\nFor the 2nd query <code node=\"[object Object]\">x<sub>i</sub> = 1</code> and <code node=\"[object Object]\">y<sub>i</sub> = 3</code>, we can select index <code node=\"[object Object]\">j = 2</code> since <code node=\"[object Object]\">nums1[j] >= 1</code> and <code node=\"[object Object]\">nums2[j] >= 3</code>. The sum <code node=\"[object Object]\">nums1[j] + nums2[j]</code> is 10, and we can show that 10 is the maximum we can obtain. \n\nFor the 3rd query <code node=\"[object Object]\">x<sub>i</sub> = 2</code> and <code node=\"[object Object]\">y<sub>i</sub> = 5</code>, we can select index <code node=\"[object Object]\">j = 3</code> since <code node=\"[object Object]\">nums1[j] >= 2</code> and <code node=\"[object Object]\">nums2[j] >= 5</code>. The sum <code node=\"[object Object]\">nums1[j] + nums2[j]</code> is 7, and we can show that 7 is the maximum we can obtain.\n\nTherefore, we return <code node=\"[object Object]\">[6,10,7]</code>.\n</pre>\n\n<p><strong class=\"example\">Example 2:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums1 = [3,2,5], nums2 = [2,3,4], queries = [[4,4],[3,2],[1,1]]\n<strong>Output:</strong> [9,9,9]\n<strong>Explanation:</strong> For this example, we can use index <code node=\"[object Object]\">j = 2</code> for all the queries since it satisfies the constraints for each query.\n</pre>\n\n<p><strong class=\"example\">Example 3:</strong></p>\n\n<pre>\n<strong>Input:</strong> nums1 = [2,1], nums2 = [2,3], queries = [[3,3]]\n<strong>Output:</strong> [-1]\n<strong>Explanation:</strong> There is one query in this example with <code node=\"[object Object]\">x<sub>i</sub></code> = 3 and <code node=\"[object Object]\">y<sub>i</sub></code> = 3. For every index, j, either nums1[j] < <code node=\"[object Object]\">x<sub>i</sub></code> or nums2[j] < <code node=\"[object Object]\">y<sub>i</sub></code>. Hence, there is no solution. \n</pre>\n\n<p> </p>\n<p><strong>Constraints:</strong></p>\n\n<ul>\n\t<li><code>nums1.length == nums2.length</code> </li>\n\t<li><code>n == nums1.length </code></li>\n\t<li><code>1 <= n <= 10<sup>5</sup></code></li>\n\t<li><code>1 <= nums1[i], nums2[i] <= 10<sup>9</sup> </code></li>\n\t<li><code>1 <= queries.length <= 10<sup>5</sup></code></li>\n\t<li><code>queries[i].length == 2</code></li>\n\t<li><code>x<sub>i</sub> == queries[i][1]</code></li>\n\t<li><code>y<sub>i</sub> == queries[i][2]</code></li>\n\t<li><code>1 <= x<sub>i</sub>, y<sub>i</sub> <= 10<sup>9</sup></code></li>\n</ul>\n",
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"Sort (x, y) tuples and queries by x-coordinate descending. Don’t forget to index queries before sorting so that you can answer them in the correct order.",
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"Before answering a query (min_x, min_y), add all (x, y) pairs with x >= min_x to some data structure.",
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"Use a monotone descending map to store (y, x + y) pairs. A monotone map has ascending keys and descending values. When inserting a pair (y, x + y), remove all pairs (y', x' + y') with y' < y and x' + y' <= x + y.",
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"When querying for max (x + y) over y >= y', use binary search to find the first pair (y, x + y) with y >= y'. It will have the maximum value of x + y because the map has monotone descending values."
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Adding an item to a hash.</b>\\r\\n<pre>\\r\\nstruct hash_entry {\\r\\n int id; /* we'll use this field as the key */\\r\\n char name[10];\\r\\n UT_hash_handle hh; /* makes this structure hashable */\\r\\n};\\r\\n\\r\\nstruct hash_entry *users = NULL;\\r\\n\\r\\nvoid add_user(struct hash_entry *s) {\\r\\n HASH_ADD_INT(users, id, s);\\r\\n}\\r\\n</pre>\\r\\n</p>\\r\\n\\r\\n<p><b>2. Looking up an item in a hash:</b>\\r\\n<pre>\\r\\nstruct hash_entry *find_user(int user_id) {\\r\\n struct hash_entry *s;\\r\\n HASH_FIND_INT(users, &user_id, s);\\r\\n return s;\\r\\n}\\r\\n</pre>\\r\\n</p>\\r\\n\\r\\n<p><b>3. Deleting an item in a hash:</b>\\r\\n<pre>\\r\\nvoid delete_user(struct hash_entry *user) {\\r\\n HASH_DEL(users, user); \\r\\n}\\r\\n</pre>\\r\\n</p>\"], \"csharp\": [\"C#\", \"<p><a href=\\\"https://learn.microsoft.com/en-us/dotnet/csharp/whats-new/csharp-10\\\" target=\\\"_blank\\\">C# 10 with .NET 6 runtime</a></p>\"], \"javascript\": [\"JavaScript\", \"<p><code>Node.js 16.13.2</code>.</p>\\r\\n\\r\\n<p>Your code is run with <code>--harmony</code> flag, enabling <a href=\\\"http://node.green/\\\" target=\\\"_blank\\\">new ES6 features</a>.</p>\\r\\n\\r\\n<p><a href=\\\"https://lodash.com\\\" target=\\\"_blank\\\">lodash.js</a> library is included by default.</p>\\r\\n\\r\\n<p>For Priority Queue / Queue data structures, you may use 5.3.0 version of <a href=\\\"https://github.com/datastructures-js/priority-queue/tree/fb4fdb984834421279aeb081df7af624d17c2a03\\\" target=\\\"_blank\\\">datastructures-js/priority-queue</a> and 4.2.1 version of <a href=\\\"https://github.com/datastructures-js/queue/tree/e63563025a5a805aa16928cb53bcd517bfea9230\\\" target=\\\"_blank\\\">datastructures-js/queue</a>.</p>\"], \"ruby\": [\"Ruby\", \"<p><code>Ruby 3.1</code></p>\\r\\n\\r\\n<p>Some common data structure implementations are provided in the Algorithms module: https://www.rubydoc.info/github/kanwei/algorithms/Algorithms</p>\"], \"swift\": [\"Swift\", \"<p><code>Swift 5.5.2</code>.</p>\"], \"golang\": [\"Go\", \"<p><code>Go 1.21</code></p>\\r\\n<p>Support <a href=\\\"https://github.com/emirpasic/gods/tree/v1.18.1\\\" target=\\\"_blank\\\">https://godoc.org/github.com/emirpasic/gods@v1.18.1</a> library.</p>\"], \"python3\": [\"Python3\", \"<p><code>Python 3.10</code>.</p>\\r\\n\\r\\n<p>Most libraries are already imported automatically for your convenience, such as <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>. If you need more libraries, you can import it yourself.</p>\\r\\n\\r\\n<p>For Map/TreeMap data structure, you may use <a href=\\\"http://www.grantjenks.com/docs/sortedcontainers/\\\" target=\\\"_blank\\\">sortedcontainers</a> library.</p>\"], \"scala\": [\"Scala\", \"<p><code>Scala 2.13.7</code>.</p>\"], \"kotlin\": [\"Kotlin\", \"<p><code>Kotlin 1.9.0</code>.</p>\"], \"rust\": [\"Rust\", \"<p><code>Rust 1.58.1</code></p>\\r\\n\\r\\n<p>Supports <a href=\\\"https://crates.io/crates/rand\\\" target=\\\"_blank\\\">rand </a> v0.6\\u00a0from crates.io</p>\"], \"php\": [\"PHP\", \"<p><code>PHP 8.1</code>.</p>\\r\\n<p>With bcmath module</p>\"], \"typescript\": [\"Typescript\", \"<p><code>TypeScript 5.1.6, Node.js 16.13.2</code>.</p>\\r\\n\\r\\n<p>Your code is run with <code>--harmony</code> flag, enabling <a href=\\\"http://node.green/\\\" target=\\\"_blank\\\">new ES2022 features</a>.</p>\\r\\n\\r\\n<p><a href=\\\"https://lodash.com\\\" target=\\\"_blank\\\">lodash.js</a> library is included by default.</p>\"], \"racket\": [\"Racket\", \"<p>Run with <code>Racket 8.3</code>.</p>\"], \"erlang\": [\"Erlang\", \"Erlang/OTP 25.0\"], \"elixir\": [\"Elixir\", \"Elixir 1.13.4 with Erlang/OTP 25.0\"], \"dart\": [\"Dart\", \"<p>Dart 2.17.3</p>\\r\\n\\r\\n<p>Your code will be run directly without compiling</p>\"]}",
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