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1589. Maximum Sum Obtained of Any Permutation

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Description

We have an array of integers, nums, and an array of requests where requests[i] = [starti, endi]. The ith request asks for the sum of nums[starti] + nums[starti + 1] + ... + nums[endi - 1] + nums[endi]. Both starti and endi 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 109 + 7.

 

Example 1:

Input: nums = [1,2,3,4,5], requests = [[1,3],[0,1]]
Output: 19
Explanation: 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
Explanation: 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
Explanation: 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 <= 105
• 0 <= nums[i] <= 105
• 1 <= requests.length <= 105
• requests[i].length == 2
• 0 <= starti <= endi < n

Solutions

Python3

class Solution:
    def maxSumRangeQuery(self, nums: List[int], requests: List[List[int]]) -> int:
        n = 100010
        delta = [0] * n
        for start, end in requests:
            delta[start] += 1
            delta[end + 1] -= 1
        for i in range(1, n):
            delta[i] += delta[i - 1]
        nums.sort()
        delta.sort()
        i, j, res = n - 1, len(nums) - 1, 0
        while i > 0 and delta[i] > 0:
            res += delta[i] * nums[j]
            i -= 1
            j -= 1
        return res % 1000000007

Java

class Solution {
    public int maxSumRangeQuery(int[] nums, int[][] requests) {
        int n = 100010;
        int[] delta = new int[n];
        for (int[] request : requests) {
            ++delta[request[0]];
            --delta[request[1] + 1];
        }
        for (int i = 1; i < n; ++i) {
            delta[i] += delta[i - 1];
        }
        Arrays.sort(nums);
        Arrays.sort(delta);
        long res = 0;
        for (int i = n - 1, j = nums.length - 1; i >= 0 && delta[i] > 0; --i, --j) {
            res += (long) delta[i] * nums[j];
        }
        return (int) (res % 1000000007);
    }
}

C++

class Solution {
public:
    int maxSumRangeQuery(vector<int>& nums, vector<vector<int>>& requests) {
        int n = 100010;
        vector<int> delta(n);
        for (auto request : requests) {
            ++delta[request[0]];
            --delta[request[1] + 1];
        }
        for (int i = 1; i < n; ++i) {
            delta[i] += delta[i - 1];
        }
        sort(nums.begin(), nums.end());
        sort(delta.begin(), delta.end());
        long long res = 0;
        for (int i = n - 1, j = nums.size() - 1; i >= 0 && delta[i] > 0; --i, --j) {
            res += (long long)delta[i] * nums[j];
        }
        return (int)(res % 1000000007);
    }
};

Go

func maxSumRangeQuery(nums []int, requests [][]int) int {
	n := 100010
	delta := make([]int, n)
	for _, request := range requests {
		delta[request[0]]++
		delta[request[1]+1]--
	}
	for i := 1; i < n; i++ {
		delta[i] += delta[i-1]
	}
	sort.Ints(nums)
	sort.Ints(delta)
	i, j, res := n-1, len(nums)-1, 0
	for i >= 0 && delta[i] > 0 {
		res += delta[i] * nums[j]
		i--
		j--
	}
	return res % 1000000007
}

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