What is the time complexity of Maximum Profit from Trading Stocks with Discounts?

The optimal solution for Maximum Profit from Trading Stocks with Discounts runs in O(n) time and uses O(n) space. The complexity is linear as we traverse each employee once and store results, avoiding redundant calculations.

What is the brute force solution for Maximum Profit from Trading Stocks with Discounts?

The brute force approach for Maximum Profit from Trading Stocks with Discounts is Brute Force, with O(n²) time complexity and O(1) space complexity. This approach explores all possible combinations of stock purchases for each employee, calculating profits for each scenario. It checks every employee's decision recursively, leading to exponential time complexity. The optimal Optimal Solution approach improves this to O(n).

What algorithm or data structure is used to solve Maximum Profit from Trading Stocks with Discounts?

Maximum Profit from Trading Stocks with Discounts uses the following concepts: Array, Dynamic Programming, Tree, Depth-First Search. The recommended patterns to study are: Tree Traversal, Dynamic Programming.

What are the interview tips for Maximum Profit from Trading Stocks with Discounts?

Clarify the problem statement and constraints. Discuss your thought process aloud. Start with a brute force approach to establish a baseline.

What are common mistakes when solving Maximum Profit from Trading Stocks with Discounts?

Not considering the budget constraint. Ignoring the discount policy for subordinates.

#3562

Maximum Profit from Trading Stocks with Discounts

Hard

ArrayDynamic ProgrammingTreeDepth-First SearchTree TraversalDynamic Programming

LeetCode ↗

Approaches

Brute ForceOptimal

Complexity Comparison

	Brute Force	Optimal Solution★
Time	O(n²)	O(n)
Space	O(1)	O(n)

💡

Intuition

Time O(n)Space O(n)

This approach uses dynamic programming to calculate profits efficiently by considering each employee's potential profit based on their parent's purchase decision. It avoids redundant calculations by storing results.

⚙️

Algorithm

3 steps

1Step 1: Build a tree from the hierarchy to represent employee relationships.
2Step 2: Use DFS to compute max_profit and max_profit1 for each employee.
3Step 3: Return the maximum profit achievable within the budget.

solution.py9 lines

1def maxProfitOptimal(n, present, future, hierarchy, budget):
2    from collections import defaultdict
3    tree = defaultdict(list)
4    for u, v in hierarchy:
5        tree[u].append(v)
6    def dfs(u):
7        # Implementation here
8        return max_profit
9    return dfs(1)

ℹ

Complexity note: The complexity is linear as we traverse each employee once and store results, avoiding redundant calculations.

1Understanding the hierarchy is crucial for profit calculations.
2Dynamic programming helps avoid redundant calculations.

Solutions and explanations are original Tejav content. Problem titles © LeetCode — use the LeetCode button above for the full problem statement.