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Java-based LeetCode algorithm problem solutions, regularly updated
502\. IPO
Hard
Suppose LeetCode will start its **IPO** soon. In order to sell a good price of its shares to Venture Capital, LeetCode would like to work on some projects to increase its capital before the **IPO**. Since it has limited resources, it can only finish at most `k` distinct projects before the **IPO**. Help LeetCode design the best way to maximize its total capital after finishing at most `k` distinct projects.
You are given `n` projects where the ith project has a pure profit `profits[i]` and a minimum capital of `capital[i]` is needed to start it.
Initially, you have `w` capital. When you finish a project, you will obtain its pure profit and the profit will be added to your total capital.
Pick a list of **at most** `k` distinct projects from given projects to **maximize your final capital**, and return _the final maximized capital_.
The answer is guaranteed to fit in a 32-bit signed integer.
**Example 1:**
**Input:** k = 2, w = 0, profits = [1,2,3], capital = [0,1,1]
**Output:** 4
**Explanation:**
Since your initial capital is 0, you can only start the project indexed 0.
After finishing it you will obtain profit 1 and your capital becomes 1.
With capital 1, you can either start the project indexed 1 or the project indexed 2.
Since you can choose at most 2 projects, you need to finish the project indexed 2 to get the maximum capital.
Therefore, output the final maximized capital, which is 0 + 1 + 3 = 4.
**Example 2:**
**Input:** k = 3, w = 0, profits = [1,2,3], capital = [0,1,2]
**Output:** 6
**Constraints:**
* 1 <= k <= 105
* 0 <= w <= 109
* `n == profits.length`
* `n == capital.length`
* 1 <= n <= 105
* 0 <= profits[i] <= 104
* 0 <= capital[i] <= 109