Solution: IPO

Explore how to maximize an investor's capital by selecting up to k projects using a two-heap approach. Understand how min-heaps prioritize projects by capital requirements and max-heaps help choose the most profitable projects. This lesson guides you through an efficient solution to optimize investment decisions with constrained resources and limited project selections.

We'll cover the following...

Statement
Solution
- Naive approach
- Optimized approach using heaps

Statement

An investor is looking to maximize their capital by undertaking a set of profitable projects. Due to limited time and resources, they can complete at most k distinct projects.

There are $n$ available projects. Each project i has:

A profit of profits[i] earned upon completion.
A minimum capital requirement of capital[i] needed to start the project.

The investor starts with an initial capital of c. After completing a project, its profit is immediately added to the investor's current capital.

The goal is to choose up to k different projects in a way that maximizes the investor’s final capital. Return the maximum capital achievable after completing these projects.

It is guaranteed that the answer fits within a 32-bit signed integer.

Constraints:

$1 \leq$ k $\leq 10^3$
$0 \leq$ c $\leq$ $10^9$
$n==$ profits.length
$n==$ capitals.length
$1 \leq n$ ...