{ "data": { "question": { "questionId": "2839", "questionFrontendId": "2736", "categoryTitle": "Algorithms", "boundTopicId": 2303156, "title": "Maximum Sum Queries", "titleSlug": "maximum-sum-queries", "content": "

You are given two 0-indexed integer arrays nums1 and nums2, each of length n, and a 1-indexed 2D array queries where queries[i] = [xi, yi].

\n\n

For the ith query, find the maximum value of nums1[j] + nums2[j] among all indices j (0 <= j < n), where nums1[j] >= xi and nums2[j] >= yi, or -1 if there is no j satisfying the constraints.

\n\n

Return an array answer where answer[i] is the answer to the ith query.

\n\n

 

\n

Example 1:

\n\n
\nInput: nums1 = [4,3,1,2], nums2 = [2,4,9,5], queries = [[4,1],[1,3],[2,5]]\nOutput: [6,10,7]\nExplanation: \nFor the 1st query xi = 4 and yi = 1, we can select index j = 0 since nums1[j] >= 4 and nums2[j] >= 1. The sum nums1[j] + nums2[j] is 6, and we can show that 6 is the maximum we can obtain.\n\nFor the 2nd query xi = 1 and yi = 3, we can select index j = 2 since nums1[j] >= 1 and nums2[j] >= 3. The sum nums1[j] + nums2[j] is 10, and we can show that 10 is the maximum we can obtain. \n\nFor the 3rd query xi = 2 and yi = 5, we can select index j = 3 since nums1[j] >= 2 and nums2[j] >= 5. The sum nums1[j] + nums2[j] is 7, and we can show that 7 is the maximum we can obtain.\n\nTherefore, we return [6,10,7].\n
\n\n

Example 2:

\n\n
\nInput: nums1 = [3,2,5], nums2 = [2,3,4], queries = [[4,4],[3,2],[1,1]]\nOutput: [9,9,9]\nExplanation: For this example, we can use index j = 2 for all the queries since it satisfies the constraints for each query.\n
\n\n

Example 3:

\n\n
\nInput: nums1 = [2,1], nums2 = [2,3], queries = [[3,3]]\nOutput: [-1]\nExplanation: There is one query in this example with xi = 3 and yi = 3. For every index, j, either nums1[j] < xi or nums2[j] < yi. Hence, there is no solution. \n
\n\n

 

\n

Constraints:

\n\n\n", "translatedTitle": "最大和查询", "translatedContent": "

给你两个长度为 n 、下标从 0 开始的整数数组 nums1nums2 ,另给你一个下标从 1 开始的二维数组 queries ,其中 queries[i] = [xi, yi]

\n\n

对于第 i 个查询,在所有满足 nums1[j] >= xinums2[j] >= yi 的下标 j (0 <= j < n) 中,找出 nums1[j] + nums2[j]最大值 ,如果不存在满足条件的 j 则返回 -1

\n\n

返回数组 answer其中 answer[i] 是第 i 个查询的答案。

\n\n

 

\n\n

示例 1:

\n\n
输入:nums1 = [4,3,1,2], nums2 = [2,4,9,5], queries = [[4,1],[1,3],[2,5]]\n输出:[6,10,7]\n解释:\n对于第 1 个查询:xi = 4 且 yi = 1 ,可以选择下标 j = 0 ,此时 nums1[j] >= 4 且 nums2[j] >= 1nums1[j] + nums2[j] 等于 6 ,可以证明 6 是可以获得的最大值。\n对于第 2 个查询:xi = 1 且 yi = 3 ,可以选择下标 j = 2 ,此时 nums1[j] >= 1 且 nums2[j] >= 3nums1[j] + nums2[j] 等于 10 ,可以证明 10 是可以获得的最大值。\n对于第 3 个查询:xi = 2 且 yi = 5 ,可以选择下标 j = 3 ,此时 nums1[j] >= 2 且 nums2[j] >= 5nums1[j] + nums2[j] 等于 7 ,可以证明 7 是可以获得的最大值。\n因此,我们返回 [6,10,7] 。\n
\n\n

示例 2:

\n\n
输入:nums1 = [3,2,5], nums2 = [2,3,4], queries = [[4,4],[3,2],[1,1]]\n输出:[9,9,9]\n解释:对于这个示例,我们可以选择下标 j = 2 ,该下标可以满足每个查询的限制。\n
\n\n

示例 3:

\n\n
输入:nums1 = [2,1], nums2 = [2,3], queries = [[3,3]]\n输出:[-1]\n解释:示例中的查询 xi = 3 且 yi = 3 。对于每个下标 j ,都只满足 nums1[j] < xi 或者 nums2[j] < yi 。因此,不存在答案。 \n
\n\n

 

\n\n

提示:

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"translatedName": "线段树", "__typename": "TopicTagNode" }, { "name": "Array", "slug": "array", "translatedName": "数组", "__typename": "TopicTagNode" }, { "name": "Binary Search", "slug": "binary-search", "translatedName": "二分查找", "__typename": "TopicTagNode" }, { "name": "Sorting", "slug": "sorting", "translatedName": "排序", "__typename": "TopicTagNode" }, { "name": "Monotonic Stack", "slug": "monotonic-stack", "translatedName": "单调栈", "__typename": "TopicTagNode" } ], "companyTagStats": null, "codeSnippets": [ { "lang": "C++", "langSlug": "cpp", "code": "class Solution {\npublic:\n vector maximumSumQueries(vector& nums1, vector& nums2, vector>& queries) {\n \n }\n};", "__typename": "CodeSnippetNode" }, { "lang": "Java", "langSlug": "java", "code": "class Solution {\n public int[] maximumSumQueries(int[] nums1, int[] nums2, int[][] queries) {\n\n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Python", "langSlug": "python", "code": "class Solution(object):\n def maximumSumQueries(self, nums1, nums2, queries):\n \"\"\"\n :type nums1: List[int]\n :type nums2: List[int]\n :type queries: List[List[int]]\n :rtype: List[int]\n \"\"\"", "__typename": "CodeSnippetNode" }, { "lang": "Python3", "langSlug": "python3", "code": "class Solution:\n def maximumSumQueries(self, nums1: List[int], nums2: List[int], queries: List[List[int]]) -> List[int]:", "__typename": "CodeSnippetNode" }, { "lang": "C", "langSlug": "c", "code": "/**\n * Note: The returned array must be malloced, assume caller calls free().\n */\nint* maximumSumQueries(int* nums1, int nums1Size, int* nums2, int nums2Size, int** queries, int queriesSize, int* queriesColSize, int* returnSize){\n\n}", "__typename": "CodeSnippetNode" }, { "lang": "C#", "langSlug": "csharp", "code": "public class Solution {\n public int[] MaximumSumQueries(int[] nums1, int[] nums2, int[][] queries) {\n\n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "JavaScript", "langSlug": "javascript", "code": "/**\n * @param {number[]} nums1\n * @param {number[]} nums2\n * @param {number[][]} queries\n * @return {number[]}\n */\nvar maximumSumQueries = function(nums1, nums2, queries) {\n\n};", "__typename": "CodeSnippetNode" }, { "lang": "TypeScript", "langSlug": "typescript", "code": "function maximumSumQueries(nums1: number[], nums2: number[], queries: number[][]): number[] {\n\n};", "__typename": "CodeSnippetNode" }, { "lang": "PHP", "langSlug": "php", "code": "class Solution {\n\n /**\n * @param Integer[] $nums1\n * @param Integer[] $nums2\n * @param Integer[][] $queries\n * @return Integer[]\n */\n function maximumSumQueries($nums1, $nums2, $queries) {\n\n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Swift", "langSlug": "swift", "code": "class Solution {\n func maximumSumQueries(_ nums1: [Int], _ nums2: [Int], _ queries: [[Int]]) -> [Int] {\n\n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Kotlin", "langSlug": "kotlin", "code": "class Solution {\n fun maximumSumQueries(nums1: IntArray, nums2: IntArray, queries: Array): IntArray {\n\n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Dart", "langSlug": "dart", "code": "class Solution {\n List maximumSumQueries(List nums1, List nums2, List> queries) {\n\n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Go", "langSlug": "golang", "code": "func maximumSumQueries(nums1 []int, nums2 []int, queries [][]int) []int {\n\n}", "__typename": "CodeSnippetNode" }, { "lang": "Ruby", "langSlug": "ruby", "code": "# @param {Integer[]} nums1\n# @param {Integer[]} nums2\n# @param {Integer[][]} queries\n# @return {Integer[]}\ndef maximum_sum_queries(nums1, nums2, queries)\n\nend", "__typename": "CodeSnippetNode" }, { "lang": "Scala", "langSlug": "scala", "code": "object Solution {\n def maximumSumQueries(nums1: Array[Int], nums2: Array[Int], queries: Array[Array[Int]]): Array[Int] = {\n\n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Rust", "langSlug": "rust", "code": "impl Solution {\n pub fn maximum_sum_queries(nums1: Vec, nums2: Vec, queries: Vec>) -> Vec {\n\n }\n}", "__typename": "CodeSnippetNode" }, { "lang": "Racket", "langSlug": "racket", "code": "(define/contract (maximum-sum-queries nums1 nums2 queries)\n (-> (listof exact-integer?) (listof exact-integer?) (listof (listof exact-integer?)) (listof exact-integer?))\n\n )", "__typename": "CodeSnippetNode" }, { "lang": "Erlang", "langSlug": "erlang", "code": "-spec maximum_sum_queries(Nums1 :: [integer()], Nums2 :: [integer()], Queries :: [[integer()]]) -> [integer()].\nmaximum_sum_queries(Nums1, Nums2, Queries) ->\n .", "__typename": "CodeSnippetNode" }, { "lang": "Elixir", "langSlug": "elixir", "code": "defmodule Solution do\n @spec maximum_sum_queries(nums1 :: [integer], nums2 :: [integer], queries :: [[integer]]) :: [integer]\n def maximum_sum_queries(nums1, nums2, queries) do\n\n end\nend", "__typename": "CodeSnippetNode" } ], "stats": "{\"totalAccepted\": \"12.1K\", \"totalSubmission\": \"23.1K\", \"totalAcceptedRaw\": 12113, \"totalSubmissionRaw\": 23150, \"acRate\": \"52.3%\"}", "hints": [ "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.", "Before answering a query (min_x, min_y), add all (x, y) pairs with x >= min_x to some data structure.", "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.", "To find the insertion position use binary search (built-in in many languages).", "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." ], "solution": null, "status": null, "sampleTestCase": "[4,3,1,2]\n[2,4,9,5]\n[[4,1],[1,3],[2,5]]", "metaData": "{\n \"name\": \"maximumSumQueries\",\n \"params\": [\n {\n \"name\": \"nums1\",\n \"type\": \"integer[]\"\n },\n {\n \"type\": \"integer[]\",\n \"name\": \"nums2\"\n },\n {\n \"type\": \"integer[][]\",\n \"name\": \"queries\"\n }\n ],\n \"return\": {\n \"type\": \"integer[]\"\n }\n}", "judgerAvailable": true, "judgeType": "large", "mysqlSchemas": [], "enableRunCode": true, "envInfo": "{\"cpp\":[\"C++\",\"

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