IPO

class Solution {
public:
    int maximizeCapital(int rounds, int initialCapital, vector<int>& gains, vector<int>& costs) {
        int projectCount = gains.size();
        vector<pair<int, int>> projectList;
        for (int i = 0; i < projectCount; i++) {
            projectList.emplace_back(costs[i], gains[i]);
        }
        sort(projectList.begin(), projectList.end());
        priority_queue<int> maxHeap;
        int index = 0;
        for (int i = 0; i < rounds; i++) {
            while (index < projectCount && projectList[index].first <= initialCapital) {
                maxHeap.push(projectList[index++].second);
            }
            if (maxHeap.empty()) {
                break;
            }
            initialCapital += maxHeap.top();
            maxHeap.pop();
        }
        return initialCapital;
    }
};

Solution Summary

The given C++ code outlines an approach to maximize capital through a number of investment rounds with available projects, each requiring a specific cost and offering a potential gain. The method defined in the code, maximizeCapital, determines how to choose projects to achieve this goal.

• Begin by capturing the total number of projects and create a list pairing each project's cost with its potential gain.
• Sort the list of projects based on their costs to prioritize lower cost projects first. This sorting is essential for efficiently finding the projects you can afford in each round.
• Use a maximum heap (priority queue) to keep track of the projects' gains you can afford. This allows you to always access the project with the highest potential gain.
• Iterate over each investment round:
  • During each round, add all projects you can afford (given your current capital) to the maximum heap.
  • If the maximum heap isn't empty, it means there are profitable projects you can undertake. Add the top project's gain from the heap to your capital, and remove this project from the heap.
  • If the heap is empty before using all your rounds, break out of the loop as no further projects can be undertaken.
• After completing all possible investment rounds, or running out of achievable projects, the value of initialCapital will be your maximized capital.

Utilize this structured approach to make strategic investments based on available capital and project gains, optimizing your returns across multiple investment rounds. This strategy maximizes the use of available resources by prioritizing projects that can be afforded and offer the highest returns, efficiently leveraging sorting and a maximum heap for optimal performance.

class Solution {
    class Venture implements Comparable<Venture> {
        int cost, gain;

        public Venture(int cost, int gain) {
            this.cost = cost;
            this.gain = gain;
        }

        public int compareTo(Venture other) {
            return cost - other.cost;
        }
    }

    public int findOptimalCapital(int iterations, int initialWealth, int[] gains, int[] costs) {
        int count = gains.length;
        Venture[] ventures = new Venture[count];
        for (int i = 0; i < count; i++) {
            ventures[i] = new Venture(costs[i], gains[i]);
        }
        Arrays.sort(ventures);
        PriorityQueue<Integer> profitsQueue = new PriorityQueue<Integer>(count, Collections.reverseOrder());
        int index = 0;
        for (int i = 0; i < iterations; i++) {
            while (index < count && ventures[index].cost <= initialWealth) {
                profitsQueue.add(ventures[index++].gain);
            }
            if (profitsQueue.isEmpty()) {
                break;
            }
            initialWealth += profitsQueue.poll();
        }
        return initialWealth;
    }
}

In the given Java code example, the Solution class is implemented to solve the problem of maximizing the capital from an initial amount through a series of investments represented by gains and costs over a fixed number of iterations. The code processes this through the following key steps:

• Define an inner class Venture which represents an investment opportunity. It includes properties for cost and gain and implements the Comparable interface to enable sorting based on cost.

• The findOptimalCapital method takes four parameters: the number of investment iterations (iterations), an initialWealth, arrays of gains, and costs. This method aims to compute the maximum possible capital after all iterations.

• The Ventures are instantiated and stored in an array. The array is then sorted by cost to prioritize cheaper investments.

• A PriorityQueue is employed (specifically, in descending order) to manage and prioritize higher gains.

• The method iterates up to the given number of iterations, in each iteration, adding eligible investments (those that can be afforded given the current wealth) to the PriorityQueue. The highest gain investment is then selected from this queue, and the profit is added to the capital.

• The process repeats until all iterations are complete or no eligible investments are left to consider.

• Finally, the method returns the accumulated initialWealth which now reflects the optimized capital after considering all possible investments.

This solution effectively uses sorting and a max-heap (via PriorityQueue) to ensure that each investment chosen is the most profitable one that can be afforded in each iteration, thus aiming to maximize the return on investment.

class InvestmentStrategy:
    def maximizeCapital(self, numberOfRounds: int, startingCapital: int, profitList: List[int], requiredCapital: List[int]) -> int:
        projectCount = len(profitList)
        projectDetails = list(zip(requiredCapital, profitList))
        projectDetails.sort()
        availableProjects = []
        nextProject = 0
        for _ in range(numberOfRounds):
            while nextProject < projectCount and projectDetails[nextProject][0] <= startingCapital:
                heappush(availableProjects, -projectDetails[nextProject][1])
                nextProject += 1
            if not availableProjects:
                break
            startingCapital += -heappop(availableProjects)
        return startingCapital

The solution involves implementing an investment strategy to maximize capital over a specified number of rounds, given a list of potential projects each with their own capital requirements and profit potential. This Python3 script utilizes a greedy algorithm and a min-heap to prioritize projects based on their profit after ensuring capital requirements are met.

Here's a breakdown of how the code works:

• The InvestmentStrategy class defines a method called maximizeCapital which takes the following parameters:

  • numberOfRounds: The number of investment rounds to be executed.
  • startingCapital: The initial amount of capital available.
  • profitList: A list of potential profits from various projects.
  • requiredCapital: A list of capital required for each corresponding project in profitList.

• The list of projects is combined into pairs of (required capital, profit) and sorted based on the required capital to prioritize projects with lower initial capital needs.

• Keep track of projects available for investment using a min-heap availableProjects, which allows for efficient extraction of the project with the highest profit that can currently be afforded.

• For up to numberOfRounds, the code evaluates which projects can be taken on with the current capital, pushing them into the heap if applicable. Once the limit is reached or if no additional projects meet the capital requirement, the loop breaks.

• For each project executed, the profit is extracted from the heap (the max profit available) and added to startingCapital.

• Finally, the total accumulated capital after processing all feasible rounds is returned.

This approach ensures that at each round, the project with the best return relative to the available capital is chosen, thus aiming to maximize returns over the specified number of investment rounds.