Maximum Sum Obtained of Any Permutation

arraygreedysorting

Problem Statement

We have an array of integers, nums , and an array of requests where requests[i] = [start _i , end _i ] . The i ^th request asks for the sum of nums[start _i ] + nums[start _i + 1] + ... + nums[end _i - 1] + nums[end _i ] . Both start _i and end _i are 0-indexed .

Return the maximum total sum of all requests among all permutations of nums .

Since the answer may be too large, return it modulo 10 ^9 + 7 .

Examples

Example 1

Input: nums = [1,2,3,4,5], requests = [[1,3],[0,1]]
Output: 19
One permutation of nums is [2,1,3,4,5] with the following result: 
requests[0] -> nums[1] + nums[2] + nums[3] = 1 + 3 + 4 = 8
requests[1] -> nums[0] + nums[1] = 2 + 1 = 3
Total sum: 8 + 3 = 11.
A permutation with a higher total sum is [3,5,4,2,1] with the following result:
requests[0] -> nums[1] + nums[2] + nums[3] = 5 + 4 + 2 = 11
requests[1] -> nums[0] + nums[1] = 3 + 5 = 8
Total sum: 11 + 8 = 19, which is the best that you can do.

Example 2

Input: nums = [1,2,3,4,5,6], requests = [[0,1]]
Output: 11
A permutation with the max total sum is [6,5,4,3,2,1] with request sums [11].

Example 3

Input: nums = [1,2,3,4,5,10], requests = [[0,2],[1,3],[1,1]]
Output: 47
A permutation with the max total sum is [4,10,5,3,2,1] with request sums [19,18,10].

Constraints

n == nums.length

1 <= n <= 10 ^5

0 <= nums[i] <= 10 ^5

1 <= requests.length <= 10 ^5

requests[i].length == 2

0 <= start _i <= end _i < n

🤔

Medium

Difficulty

Topic Info

ModuleDSA

CategoryArray

Sub-topicGreedy