What is the main strategy for solving the IPO problem?

The IPO problem is solved using a greedy approach combined with a heap to select the most profitable projects that can be completed with the available capital.

Why is a greedy approach appropriate for the IPO problem?

A greedy approach ensures that at every step, we choose the most profitable project that can be completed, which maximizes capital in the long run.

What data structure is crucial for solving the IPO problem efficiently?

A max-heap (priority queue) is crucial for efficiently selecting the most profitable projects that can be completed with the available capital.

How does the heap help in the IPO problem?

The heap helps by maintaining the projects with the highest profit that can be started with the available capital, allowing for efficient project selection and maximization of capital.

What are some common pitfalls when solving the IPO problem?

Common pitfalls include failing to correctly prioritize projects based on profitability, mismanaging the heap, and not handling capital constraints properly.

#502

Hard

auto_awesome贪心·invariant

LeetCode 题解工作台

IPO

假设力扣（LeetCode）即将开始 IPO 。为了以更高的价格将股票卖给风险投资公司，力扣希望在 IPO 之前开展一些项目以增加其资本。由于资源有限，它只能在 IPO 之前完成最多 k 个不同的项目。帮助力扣设计完成最多 k 个不同项目后得到最大总资本的方式。给你 n 个项目。对于每个…

数组贪心排序堆（优先队列）

题目描述

假设力扣（LeetCode）即将开始 IPO 。为了以更高的价格将股票卖给风险投资公司，力扣希望在 IPO 之前开展一些项目以增加其资本。由于资源有限，它只能在 IPO 之前完成最多 k 个不同的项目。帮助力扣设计完成最多 k 个不同项目后得到最大总资本的方式。

给你 n 个项目。对于每个项目 i ，它都有一个纯利润 profits[i] ，和启动该项目需要的最小资本 capital[i] 。

最初，你的资本为 w 。当你完成一个项目时，你将获得纯利润，且利润将被添加到你的总资本中。

总而言之，从给定项目中选择最多 k 个不同项目的列表，以 最大化最终资本 ，并输出最终可获得的最多资本。

答案保证在 32 位有符号整数范围内。

示例 1：

输入：k = 2, w = 0, profits = [1,2,3], capital = [0,1,1]
输出：4
解释：
由于你的初始资本为 0，你仅可以从 0 号项目开始。
在完成后，你将获得 1 的利润，你的总资本将变为 1。
此时你可以选择开始 1 号或 2 号项目。
由于你最多可以选择两个项目，所以你需要完成 2 号项目以获得最大的资本。
因此，输出最后最大化的资本，为 0 + 1 + 3 = 4。

示例 2：

输入：k = 3, w = 0, profits = [1,2,3], capital = [0,1,2]
输出：6

提示：

1 <= k <= 10⁵
0 <= w <= 10⁹
n == profits.length
n == capital.length
1 <= n <= 10⁵
0 <= profits[i] <= 10⁴
0 <= capital[i] <= 10⁹

lightbulb

解题思路

方法一：贪心 + 优先队列（双堆）

将每个项目放入优先队列 $q_1$ 中，按照启动资本从小到大排序。如果堆顶元素启动资本不超过当前已有的资金，则循环弹出，放入另一个优先队列 $q_2$ 中，按照纯利润从大到小排序。取出当前利润最大的项目，将其纯利润加入到当前资金中，重复上述操作 $k$ 次。

时间复杂度 $O(n\log n)$ ，空间复杂度 $O(n)$ 。其中 $n$ 为项目数。

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class Solution:
    def findMaximizedCapital(
        self, k: int, w: int, profits: List[int], capital: List[int]
    ) -> int:
        h1 = [(c, p) for c, p in zip(capital, profits)]
        heapify(h1)
        h2 = []
        while k:
            while h1 and h1[0][0] <= w:
                heappush(h2, -heappop(h1)[1])
            if not h2:
                break
            w -= heappop(h2)
            k -= 1
        return w

speed

复杂度分析

指标	值
时间	Depends on the final approach
空间	Depends on the final approach

psychology

面试官常问的追问

外企场景

question_mark
Candidates who effectively utilize a greedy approach and justify the decision-making process will demonstrate an understanding of the core pattern of the problem.
question_mark
Look for candidates who efficiently use a heap to manage project selection, as this is key to solving the problem within time limits.
question_mark
Successful candidates will maintain a clear focus on invariant validation, ensuring that they only choose projects that can be completed with the available capital.

warning

常见陷阱

外企场景

error
Failing to prioritize the most profitable projects or using an inefficient strategy can lead to suboptimal capital maximization.
error
Incorrectly managing the heap can cause errors in project selection, leading to incorrect answers or inefficiency.
error
Not correctly handling the situation where projects cannot be completed due to capital constraints, which might result in unnecessary calculations.

swap_horiz

进阶变体

外企场景

arrow_right_alt
Consider scenarios where capital is very large or very small compared to the project costs.
arrow_right_alt
Modify the problem to allow for additional constraints, such as limiting the number of projects from specific categories.
arrow_right_alt
Change the project selection criteria to focus on minimizing risk or maximizing return over time instead of simply maximizing total capital.

help

常见问题

外企场景

继续练习

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