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Grokking the Coding Interview Patterns in Python

IPO

Explore how to use heaps to solve the IPO problem where an investor aims to maximize capital by selecting up to k profitable projects. Learn to implement a strategy that meets project capital requirements and dynamically updates available resources to optimize final capital gains.

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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 nn 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≤1 \leq k ≤103\leq 10^3

  • 0≤0 \leq c ≤\leq 10910^9

  • n==n== profits.length

  • n==n== capitals.length

  • 1≤n≤1031 \leq n \leq 10^3

  • 0≤0 \leqprofits[i] ≤104\leq 10^4

  • 0≤0 \leq capitals[i] ≤109\leq 10^9

Examples

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Understand the problem

Let’s take a moment to make sure you’ve correctly understood the problem. The quiz below helps you check if you’re solving the correct problem:

IPO

1.

What is the maximum capital for the following input?

k =2= 2

c =1= 1

capitals =[1,2,3]= [1, 2, 3]

profits =[2,3,5]= [2, 3, 5]

A.

66

B.

55

C.

88

D.

1010

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Figure it out!

We have a game for you to play. Rearrange the logical building blocks to develop a clearer understanding of how to solve this problem.

Sequence - Vertical
Drag and drop the cards to rearrange them in the correct sequence.
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Try it yourself

Implement your solution in the following coding playground.

Python
usercode > main.py
from heapq import *



def maximum_capital(c, k, capitals, profits):



  # Replace this placeholder return statement with your code

  

  return -1
IPO