{ "data": { "question": { "questionId": "4010", "questionFrontendId": "3695", "categoryTitle": "Algorithms", "boundTopicId": 3793173, "title": "Maximize Alternating Sum Using Swaps", "titleSlug": "maximize-alternating-sum-using-swaps", "content": "
You are given an integer array nums.
You want to maximize the alternating sum of nums, which is defined as the value obtained by adding elements at even indices and subtracting elements at odd indices. That is, nums[0] - nums[1] + nums[2] - nums[3]...
You are also given a 2D integer array swaps where swaps[i] = [pi, qi]. For each pair [pi, qi] in swaps, you are allowed to swap the elements at indices pi and qi. These swaps can be performed any number of times and in any order.
Return the maximum possible alternating sum of nums.
\n
Example 1:
\n\nInput: nums = [1,2,3], swaps = [[0,2],[1,2]]
\n\nOutput: 4
\n\nExplanation:
\n\nThe maximum alternating sum is achieved when nums is [2, 1, 3] or [3, 1, 2]. As an example, you can obtain nums = [2, 1, 3] as follows.
nums[0] and nums[2]. nums is now [3, 2, 1].nums[1] and nums[2]. nums is now [3, 1, 2].nums[0] and nums[2]. nums is now [2, 1, 3].Example 2:
\n\nInput: nums = [1,2,3], swaps = [[1,2]]
\n\nOutput: 2
\n\nExplanation:
\n\nThe maximum alternating sum is achieved by not performing any swaps.
\nExample 3:
\n\nInput: nums = [1,1000000000,1,1000000000,1,1000000000], swaps = []
\n\nOutput: -2999999997
\n\nExplanation:
\n\nSince we cannot perform any swaps, the maximum alternating sum is achieved by not performing any swaps.
\n\n
Constraints:
\n\n2 <= nums.length <= 1051 <= nums[i] <= 1090 <= swaps.length <= 105swaps[i] = [pi, qi]0 <= pi < qi <= nums.length - 1[pi, qi] != [pj, qj]给你一个整数数组 nums。
你希望最大化 nums 的 交替和:将偶数下标的元素 相加 并 减去 奇数索引的元素获得的值。即 nums[0] - nums[1] + nums[2] - nums[3]...
同时给你一个二维整数数组 swaps,其中 swaps[i] = [pi, qi]。对于 swaps 中的每对 [pi, qi],你可以交换索引 pi 和 qi 处的元素。这些交换可以进行任意次数和任意顺序。
返回 nums 可能的最大 交替和。
\n\n
示例 1:
\n\n输入:nums = [1,2,3], swaps = [[0,2],[1,2]]
\n\n输出:4
\n\n解释:
\n\n当 nums 为 [2, 1, 3] 或 [3, 1, 2] 时,可以实现最大交替和。例如,你可以通过以下方式得到 nums = [2, 1, 3]。
nums[0] 和 nums[2]。此时 nums 为 [3, 2, 1]。nums[1] 和 nums[2]。此时 nums 为 [3, 1, 2]。nums[0] 和 nums[2]。此时 nums 为 [2, 1, 3]。示例 2:
\n\n输入:nums = [1,2,3], swaps = [[1,2]]
\n\n输出:2
\n\n解释:
\n\n不进行任何交换即可实现最大交替和。
\n示例 3:
\n\n输入:nums = [1,1000000000,1,1000000000,1,1000000000], swaps = []
\n\n输出:-2999999997
\n\n解释:
\n\n由于我们不能进行任何交换,因此不进行任何交换即可实现最大交替和。
\n\n\n
提示:
\n\n2 <= nums.length <= 1051 <= nums[i] <= 1090 <= swaps.length <= 105swaps[i] = [pi, qi]0 <= pi < qi <= nums.length - 1[pi, qi] != [pj, qj]E be the count of even indices inside that component. In each component, place the largest E values on the component's even indices.",
"The component's contribution to the alternating sum is 2 * sumTopE - sumAll, where sumTopE is the sum of the largest E values and sumAll is the sum of all values in the component."
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