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    LeetCode link: 3478. Choose K Elements With Maximum Sum, difficulty: Medium.

    You are given two integer arrays, nums1 and nums2, both of length n, along with a positive integer k.

    For each index i from 0 to n - 1, perform the following:

    • Find all indices j where nums1[j] is less than nums1[i].
    • Choose at most k values of nums2[j] at these indices to maximize the total sum.

    Return an array answer of size n, where answer[i] represents the result for the corresponding index i.

    Example 1:

    Input: nums1 = [4,2,1,5,3], nums2 = [10,20,30,40,50], k = 2

    Output: [80,30,0,80,50]

    Explanation:

    • For i = 0: Select the 2 largest values from nums2 at indices [1, 2, 4] where nums1[j] < nums1[0], resulting in 50 + 30 = 80.
    • For i = 1: Select the 2 largest values from nums2 at index [2] where nums1[j] < nums1[1], resulting in 30.
    • For i = 2: No indices satisfy nums1[j] < nums1[2], resulting in 0.
    • For i = 3: Select the 2 largest values from nums2 at indices [0, 1, 2, 4] where nums1[j] < nums1[3], resulting in 50 + 30 = 80.
    • For i = 4: Select the 2 largest values from nums2 at indices [1, 2] where nums1[j] < nums1[4], resulting in 30 + 20 = 50.

    Example 2:

    Input: nums1 = [2,2,2,2], nums2 = [3,1,2,3], k = 1

    Output: [0,0,0,0]

    Explanation:

    Since all elements in nums1 are equal, no indices satisfy the condition nums1[j] < nums1[i] for any i, resulting in 0 for all positions.

    Constraints:

    • n == nums1.length == nums2.length
    • 1 <= n <= 10^5
    • 1 <= nums1[i], nums2[i] <= 10^6
    • 1 <= k <= n
    Hint 1

    Sort nums1 and its corresponding nums2 values together based on nums1.

    Hint 2

    Use a max heap to track the top k values of nums2 as you process each element in the sorted order.

    Intuition
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    • Seeing this, everyone will definitely think of sorting nums1 from small to large, so that the front is less than or equal to the back, but the indexes will be messy when sorting. If there is no good way to solve this problem, the whole question cannot be solved. Please think about it first.

      Click to view the answer

      Bring the index when sorting, that is, the object to be sorted is an array of tuples of (num, index). This technique must be mastered, as it will be used in many questions.

      After solving the above problems, the indexes are all there, let's continue reading:

    • Requirement 2: Choose at most k values of nums2[j] at these indices to maximize the total sum.

      After seeing this, have you thought of any good method?

      Click to view the answer

      Heap sort, maintain a large root heap of size k. This is also a knowledge point that is often tested, must be mastered.

      Seeing this, please implement the code according to the above prompts.

    • Finally, it is found that the repeated num that appear continuously should be specially processed, that is, the values ​​in answer corresponding to the same num should be the same. There are many ways to deal with it. What is the simplest way to deal with it?

      Click to view the answer

      Use a Map, key is num, and the same key directly uses the value corresponding to key.

    Complexity

    Time complexity

    O(N * logN)

    Space complexity

    O(N)

    Python # 

    class Solution:
    def findMaxSum(self, nums1: List[int], nums2: List[int], k: int) -> List[int]:
        num_index_list = [(num, index) for index, num in enumerate(nums1)] # key 1
        num_index_list.sort()

        answer = [None] * len(nums1)
        k_max_nums = []
        sum_ = 0
        num_to_sum = defaultdict(int) # key 2

        for i, num_index in enumerate(num_index_list):
            num, index = num_index

            if num in num_to_sum:
                answer[index] = num_to_sum[num]
            else:
                answer[index] = sum_
                num_to_sum[num] = sum_

            heapq.heappush(k_max_nums, nums2[index])
            sum_ += nums2[index]

            if len(k_max_nums) > k:
                num = heapq.heappop(k_max_nums) # key 3
                sum_ -= num

        return answer

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