Solution: IPO

Explore how to maximize investment capital by selecting up to k profitable projects using a two-heap approach. Learn to implement an optimized solution with min and max heaps, analyze time and space complexity, and apply these strategies to solve similar dynamic data problems effectively.

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
$1 \leq n$ ...