Maximum Total Value - Video Solutions
Leetcode 3971 | weekly contest 507 | Maximum Total Value | Binary Search
Maximum Total Value - Video Solution
Watch 4 video solutions for Maximum Total Value, a hard level problem involving Array, Math, Binary Search. This walkthrough by Code With Vick has 608 views views. Want to try solving it yourself? Practice on FleetCode or read the detailed text solution.
Problem Statement
You are given two integer arrays value and decay, and an integer m.
value[i]represents the initial value at indexi.decay[i]represents how much the value decreases after each selection of indexi.
You may select any index multiple times. The total number of selections across all indices must not exceed m.
If you select index i for the tth time, where t is 1-indexed, the value gained is value[i] - decay[i] * (t - 1).
Return the maximum total value you can obtain. Since the answer may be large, return it modulo 109 + 7.
Example 1:
Input: value = [6,5,4], decay = [2,1,1], m = 4
Output: 19
Explanation:
One optimal sequence of selections is as follows:
- By selecting index 0, the value gained is 6.
- By selecting index 1, the value gained is 5.
- By selecting index 2, the value gained is 4.
- By selecting index 0 again, the value gained is
6 - 2 = 4.
The total value is 6 + 5 + 4 + 4 = 19. No other sequence of at most 4 selections gives a higher total value.
Example 2:
Input: value = [7,2,2], decay = [3,2,1], m = 2
Output: 11
Explanation:
One optimal sequence of selections is as follows:
- By selecting index 0, the value gained is 7.
- By selecting index 0 again, the value gained is
7 - 3 = 4.
The total value is 7 + 4 = 11.
Example 3:
Input: value = [4,3], decay = [5,4], m = 5
Output: 7
Explanation:
One optimal sequence of selections is as follows:
- By selecting index 0, the value gained is 4.
- By selecting index 1, the value gained is 3.
The total value is 4 + 3 = 7.
Constraints:
1 <= value.length == decay.length <= 1051 <= value[i], decay[i] <= 109āāāāāāā1 <= m <= 109
Approach Overview
Problem Overview: The exact algorithm and optimal strategy for Maximum Total Value depend entirely on the precise problem statement, including constraints, input format, and what "value" represents. Multiple LeetCode-style problems share this title pattern but require very different techniques such as dynamic programming, greedy selection, or heap-based optimization.
Without the original prompt, generating a concrete algorithm risks presenting an incorrect solution. For example, a "maximum total value" objective might involve selecting non-overlapping intervals (typically solved with dynamic programming and binary search), choosing k items under constraints (often solved using greedy strategies and sorting), or maximizing weighted profit across events (frequently solved with DP + prefix decisions or priority queues). Each variation leads to different complexity guarantees and implementation details.
Provide the full problem description including constraints, input structure, and example cases. With that information, the correct solution approach, complexity analysis, and optimized implementations can be produced.
Complexity Analysis
| Approach | Time | Space | When to Use |
|---|---|---|---|
| Brute Force Enumeration | Varies (often O(2^n) or O(n^2)) | O(1) to O(n) | Small constraints where all combinations can be checked |
| Greedy with Sorting | O(n log n) | O(1) to O(n) | Problems where locally optimal picks lead to global maximum |
| Dynamic Programming | O(n^2) or O(n log n) | O(n) | Overlapping subproblems such as weighted selections or interval choices |
| Heap / Priority Queue Optimization | O(n log n) | O(n) | When repeatedly selecting the best available value dynamically |