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3562. Maximum Profit from Trading Stocks with Discounts

Description

You are given an integer n, representing the number of employees in a company. Each employee is assigned a unique ID from 1 to n, and employee 1 is the CEO. You are given two 1-based integer arrays, present and future, each of length n, where:

  • present[i] represents the current price at which the ith employee can buy a stock today.
  • future[i] represents the expected price at which the ith employee can sell the stock tomorrow.

The company's hierarchy is represented by a 2D integer array hierarchy, where hierarchy[i] = [ui, vi] means that employee ui is the direct boss of employee vi.

Additionally, you have an integer budget representing the total funds available for investment.

However, the company has a discount policy: if an employee's direct boss purchases their own stock, then the employee can buy their stock at half the original price (floor(present[v] / 2)).

Return the maximum profit that can be achieved without exceeding the given budget.

Note:

  • You may buy each stock at most once.
  • You cannot use any profit earned from future stock prices to fund additional investments and must buy only from budget.

 

Example 1:

Input: n = 2, present = [1,2], future = [4,3], hierarchy = [[1,2]], budget = 3

Output: 5

Explanation:

  • Employee 1 buys the stock at price 1 and earns a profit of 4 - 1 = 3.
  • Since Employee 1 is the direct boss of Employee 2, Employee 2 gets a discounted price of floor(2 / 2) = 1.
  • Employee 2 buys the stock at price 1 and earns a profit of 3 - 1 = 2.
  • The total buying cost is 1 + 1 = 2 <= budget. Thus, the maximum total profit achieved is 3 + 2 = 5.

Example 2:

Input: n = 2, present = [3,4], future = [5,8], hierarchy = [[1,2]], budget = 4

Output: 4

Explanation:

  • Employee 2 buys the stock at price 4 and earns a profit of 8 - 4 = 4.
  • Since both employees cannot buy together, the maximum profit is 4.

Example 3:

Input: n = 3, present = [4,6,8], future = [7,9,11], hierarchy = [[1,2],[1,3]], budget = 10

Output: 10

Explanation:

  • Employee 1 buys the stock at price 4 and earns a profit of 7 - 4 = 3.
  • Employee 3 would get a discounted price of floor(8 / 2) = 4 and earns a profit of 11 - 4 = 7.
  • Employee 1 and Employee 3 buy their stocks at a total cost of 4 + 4 = 8 <= budget. Thus, the maximum total profit achieved is 3 + 7 = 10.

Example 4:

Input: n = 3, present = [5,2,3], future = [8,5,6], hierarchy = [[1,2],[2,3]], budget = 7

Output: 12

Explanation:

  • Employee 1 buys the stock at price 5 and earns a profit of 8 - 5 = 3.
  • Employee 2 would get a discounted price of floor(2 / 2) = 1 and earns a profit of 5 - 1 = 4.
  • Employee 3 would get a discounted price of floor(3 / 2) = 1 and earns a profit of 6 - 1 = 5.
  • The total cost becomes 5 + 1 + 1 = 7 <= budget. Thus, the maximum total profit achieved is 3 + 4 + 5 = 12.

 

Constraints:

  • 1 <= n <= 160
  • present.length, future.length == n
  • 1 <= present[i], future[i] <= 50
  • hierarchy.length == n - 1
  • hierarchy[i] == [ui, vi]
  • 1 <= ui, vi <= n
  • ui != vi
  • 1 <= budget <= 160
  • There are no duplicate edges.
  • Employee 1 is the direct or indirect boss of every employee.
  • The input graph hierarchy is guaranteed to have no cycles.

Solutions

Solution 1

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