IPO

Explore strategies to maximize an investor's final capital by selecting up to k profitable projects under capital constraints. Learn how to apply heaps to efficiently solve this optimization problem, understand problem requirements, and implement solutions in a hands-on coding environment.

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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 $n$ 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
$1 \leq n \leq 10^3$
$0 \leq$ profits[i] $\leq 10^4$
$0 \leq$ capitals[i] $\leq 10^9$

Examples

JavaScript

usercode > Solution.js

import { MinHeap, MaxHeap } from "./Heap.js";

/* The following definition is for MinHeap.

  You can use the same methods for MaxHeap.
  class MinHeap {

    size();          // return number of elements
    peek();          // return top element without removing
    push(val);       // insert element
    pop();           // remove and return top element
  }
*/

function maximumCapital(c, k, capitals, profits){

    // Replace this placeholder return statement with your code

    return -1
}

export{maximumCapital};

IPO

IPO

Statement

Examples

Understand the problem

Figure it out!

Try it yourself