Minimum Cost to Acquire Required Items - Solution & Explanation

Problem Overview: You must acquire a required number of items while minimizing the total cost. The challenge comes from multiple purchase options or pricing rules, where certain combinations or purchase sizes change the effective cost. The goal is to determine the cheapest strategy that still satisfies the required quantity.

Approach 1: Brute Force Enumeration (O(k) time, O(1) space)

The most direct way is to enumerate all reasonable purchase combinations and compute the total cost for each. For example, if there are bundle sizes or alternative purchase rules, iterate through how many times you apply each option and calculate the remaining items that must be bought individually. Each configuration produces a total cost, and you keep track of the minimum. This approach works because the number of realistic combinations is small and bounded. The downside is unnecessary repeated calculations when many combinations lead to the same effective purchase pattern.

This method is useful for validating logic during development or when constraints are tiny. It also helps reveal patterns that lead to a more optimized solution. The time complexity is O(k), where k represents the number of candidate purchase strategies you test, and space complexity remains O(1) since only a few counters and cost variables are stored.

Approach 2: Greedy Case Analysis (O(1) time, O(1) space)

A more efficient method relies on observing how the pricing rules interact. Instead of testing every possibility, analyze the structure of the pricing and derive a small number of meaningful cases. For example, compare the cost of buying items individually versus buying them in discounted groups. If a bundle provides a cheaper per‑item rate, maximize its usage; otherwise prefer individual purchases. In some scenarios you evaluate a few boundary cases such as "all bundles", "all individual", or "bundles plus remainder".

This turns the problem into a small mathematical comparison. You compute the total cost for each candidate case and return the minimum. Since the number of cases is constant, the algorithm runs in O(1) time and O(1) space. This pattern frequently appears in problems combining greedy decision making with small math calculations, where a local price advantage determines the optimal strategy.

Recommended for interviews: Greedy case analysis. Interviewers expect you to reason about the pricing structure and reduce the solution to a few deterministic scenarios instead of brute forcing every combination. Showing the brute force idea demonstrates understanding, but identifying the mathematical cases proves you can simplify the search space and derive an optimal O(1) solution.