Is Maximum Total Sum with Threshold Constraints easy or hard?

Maximum Total Sum with Threshold Constraints is typically rated Medium. The implementation is short, but recognizing the greedy rule—sorting thresholds and decreasing the allowed value step by step—is the key insight that makes the problem straightforward.

Maximum Total Sum with Threshold Constraints Python/Java solution

Most implementations sort the threshold array and iterate from the largest value downward. For each step, assign min(threshold, previous_value - 1) and add it to the running total. The same greedy logic works in Python, Java, C++, Go, TypeScript, and Rust with O(n log n) complexity.

How to solve Maximum Total Sum with Threshold Constraints in O(n)?

An exact O(n) solution generally isn't possible because the greedy strategy requires ordering thresholds by size. Sorting dominates the runtime at O(n log n). After sorting, the assignment step itself is O(n) using a simple greedy rule that reduces the previous value by one each iteration.

What is the best approach for Maximum Total Sum with Threshold Constraints?

The best approach is Greedy with Sorting. Sort the thresholds in descending order and assign values greedily so each assignment is at most the threshold and strictly smaller than the previous assignment. This guarantees the maximum possible total while satisfying the constraints. The time complexity is O(n log n) due to sorting.

Is Maximum Total Sum with Threshold Constraints asked at Google/Amazon/Meta?

Greedy allocation problems with sorting constraints appear frequently in interviews at companies like Amazon, Google, and Meta. Variants often involve assigning values under upper bounds, scheduling tasks with decreasing limits, or maximizing sums under ordering constraints.

What data structure is used in Maximum Total Sum with Threshold Constraints?

The primary structures are arrays and sorting. A max heap (priority queue) can also be used to repeatedly extract the largest threshold while maintaining the greedy constraint. Both approaches rely on processing elements in descending order of their limits.

What is the time complexity of Maximum Total Sum with Threshold Constraints?

The optimal greedy solution runs in O(n log n) time because the thresholds must be sorted first. After sorting, a single linear pass assigns the values and computes the total sum in O(n). The extra space usage is O(1) if sorting is done in place.

3763. Maximum Total Sum with Threshold Constraints - Practice Online

You are given two integer arrays nums and threshold, both of length n.

Starting at step = 1, you perform the following repeatedly:

Choose an unused index i such that threshold[i] <= step.
- If no such index exists, the process ends.
Add nums[i] to your running total.
Mark index i as used and increment step by 1.

Return the maximum total sum you can obtain by choosing indices optimally.

Example 1:

Input: nums = [1,10,4,2,1,6], threshold = [5,1,5,5,2,2]

Output: 17

Explanation:

At step = 1, choose i = 1 since threshold[1] <= step. The total sum becomes 10. Mark index 1.
At step = 2, choose i = 4 since threshold[4] <= step. The total sum becomes 11. Mark index 4.
At step = 3, choose i = 5 since threshold[5] <= step. The total sum becomes 17. Mark index 5.
At step = 4, we cannot choose indices 0, 2, or 3 because their thresholds are > 4, so we end the process.

Example 2:

Input: nums = [4,1,5,2,3], threshold = [3,3,2,3,3]

Output: 0

Explanation:

At step = 1 there is no index i with threshold[i] <= 1, so the process ends immediately. Thus, the total sum is 0.

Example 3:

Input: nums = [2,6,10,13], threshold = [2,1,1,1]

Output: 31

Explanation:

At step = 1, choose i = 3 since threshold[3] <= step. The total sum becomes 13. Mark index 3.
At step = 2, choose i = 2 since threshold[2] <= step. The total sum becomes 23. Mark index 2.
At step = 3, choose i = 1 since threshold[1] <= step. The total sum becomes 29. Mark index 1.
At step = 4, choose i = 0 since threshold[0] <= step. The total sum becomes 31. Mark index 0.
After step = 4 all indices have been chosen, so the process ends.

Constraints:

n == nums.length == threshold.length
1 <= n <= 10⁵
1 <= nums[i] <= 10⁹
1 <= threshold[i] <= n