Maximize funds with capital-gated projects

Q: Maximize funds with capital-gated projects

This question evaluates algorithm design and resource-constrained optimization skills, including greedy selection strategies and the use of efficient data structures for scalable selection and profit maximization.

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Question

You start with initial funds W and may undertake at most K projects. Each project i has a required capital C[i] and yields profit P[i]; you can only start project i if your current funds are at least C[i], and upon completion your funds increase by P[i]. Choose up to K projects to maximize your final funds. Design an efficient algorithm, specify the data structures, analyze time and space complexity, and justify correctness. Discuss how your solution scales when N is as large as 2e5.

Maximize funds with capital-gated projects

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