{ "data": { "question": { "questionId": "3854", "questionFrontendId": "3562", "categoryTitle": "Algorithms", "boundTopicId": 3684091, "title": "Maximum Profit from Trading Stocks with Discounts", "titleSlug": "maximum-profit-from-trading-stocks-with-discounts", "content": "
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.
\n\nNote:
\n\nbudget
.\n
Example 1:
\n\nInput: n = 2, present = [1,2], future = [4,3], hierarchy = [[1,2]], budget = 3
\n\nOutput: 5
\n\nExplanation:
\n\n4 - 1 = 3
.floor(2 / 2) = 1
.3 - 1 = 2
.1 + 1 = 2 <= budget
. Thus, the maximum total profit achieved is 3 + 2 = 5
.Example 2:
\n\nInput: n = 2, present = [3,4], future = [5,8], hierarchy = [[1,2]], budget = 4
\n\nOutput: 4
\n\nExplanation:
\n\n8 - 4 = 4
.Example 3:
\n\nInput: n = 3, present = [4,6,8], future = [7,9,11], hierarchy = [[1,2],[1,3]], budget = 10
\n\nOutput: 10
\n\nExplanation:
\n\n7 - 4 = 3
.floor(8 / 2) = 4
and earns a profit of 11 - 4 = 7
.4 + 4 = 8 <= budget
. Thus, the maximum total profit achieved is 3 + 7 = 10
.Example 4:
\n\nInput: n = 3, present = [5,2,3], future = [8,5,6], hierarchy = [[1,2],[2,3]], budget = 7
\n\nOutput: 12
\n\nExplanation:
\n\n8 - 5 = 3
.floor(2 / 2) = 1
and earns a profit of 5 - 1 = 4
.floor(3 / 2) = 1
and earns a profit of 6 - 1 = 5
.5 + 1 + 1 = 7 <= budget
. Thus, the maximum total profit achieved is 3 + 4 + 5 = 12
.\n
Constraints:
\n\n1 <= 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
hierarchy
is guaranteed to have no cycles.给你一个整数 n
,表示公司中员工的数量。每位员工都分配了一个从 1 到 n
的唯一 ID ,其中员工 1 是 CEO。另给你两个下标从 1 开始的整数数组 present
和 future
,两个数组的长度均为 n
,具体定义如下:
present[i]
表示第 i
位员工今天可以购买股票的 当前价格 。future[i]
表示第 i
位员工明天可以卖出股票的 预期价格 。公司的层级关系由二维整数数组 hierarchy
表示,其中 hierarchy[i] = [ui, vi]
表示员工 ui
是员工 vi
的直属上司。
此外,再给你一个整数 budget
,表示可用于投资的总预算。
公司有一项折扣政策:如果某位员工的直属上司购买了自己的股票,那么该员工可以以 半价 购买自己的股票(即 floor(present[v] / 2)
)。
请返回在不超过给定预算的情况下可以获得的 最大利润 。
\n\n注意:
\n\nbudget
。\n\n
示例 1:
\n\n输入: n = 2, present = [1,2], future = [4,3], hierarchy = [[1,2]], budget = 3
\n\n输出: 5
\n\n解释:
\n\n4 - 1 = 3
。floor(2 / 2) = 1
购买股票。3 - 1 = 2
。1 + 1 = 2 <= budget
,因此最大总利润为 3 + 2 = 5
。示例 2:
\n\n输入: n = 2, present = [3,4], future = [5,8], hierarchy = [[1,2]], budget = 4
\n\n输出: 4
\n\n解释:
\n\n8 - 4 = 4
。示例 3:
\n\n输入: n = 3, present = [4,6,8], future = [7,9,11], hierarchy = [[1,2],[1,3]], budget = 10
\n\n输出: 10
\n\n解释:
\n\n7 - 4 = 3
。floor(8 / 2) = 4
,获得利润 11 - 4 = 7
。4 + 4 = 8 <= budget
,因此最大总利润为 3 + 7 = 10
。示例 4:
\n\n输入: n = 3, present = [5,2,3], future = [8,5,6], hierarchy = [[1,2],[2,3]], budget = 7
\n\n输出: 12
\n\n解释:
\n\n8 - 5 = 3
。floor(2 / 2) = 1
,获得利润 5 - 1 = 4
。floor(3 / 2) = 1
,获得利润 6 - 1 = 5
。5 + 1 + 1 = 7 <= budget
,因此最大总利润为 3 + 4 + 5 = 12
。\n\n
提示:
\n\n1 <= 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
hierarchy
保证 无环 。max_profit[u]
and max_profit1[u]
for each node u
",
"- max_profit[u]
= maximum profit in the subtree of u
assuming the parent of u
has not bought the stock",
"- max_profit1[u]
= maximum profit in the subtree of u
assuming the parent of u
has bought the stock",
"For each node u
, consider two cases:",
"Buy the stock for u
(at present[u]
price if parent did not buy, or at floor(present[u]/2)
if parent bought), then add the best max_profit1
values of its children",
"Skip buying for u
, then add the best max_profit
values of its children"
],
"solution": null,
"status": null,
"sampleTestCase": "2\n[1,2]\n[4,3]\n[[1,2]]\n3",
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