Problem

At Nimbus Compute, you need to allocate a limited resource budget across a set of projects. Each project consumes a certain number of resource units and produces a value. Write a function that returns the maximum total value achievable without exceeding the budget.

This is a classic 0/1 resource allocation problem: each project can be selected at most once.

Formal Specification

• Input:
  • costs: a list of integers where costs[i] is the resource cost of project i
  • values: a list of integers where values[i] is the value gained from project i
  • capacity: an integer representing the total available resource units
• Output:
  • An integer: the maximum total value obtainable without exceeding capacity

Examples

Example 1

Input: costs = [2, 3, 4, 5], values = [3, 4, 5, 8], capacity = 5
Output: 8

Selecting only the project with cost 5 gives value 8, which is better than choosing costs 2 + 3 for value 7.

Example 2

Input: costs = [1, 2, 3], values = [6, 10, 12], capacity = 5
Output: 22

Choose projects with costs 2 and 3 for a total value of 10 + 12 = 22.

Constraints

• 1 <= len(costs) == len(values) <= 200
• 0 <= capacity <= 10^4
• 1 <= costs[i] <= 10^4
• 0 <= values[i] <= 10^4