Leetcode #2291: Maximum Profit From Trading Stocks
In this guide, we solve Leetcode #2291 Maximum Profit From Trading Stocks in Python and focus on the core idea that makes the solution efficient.
You will see the intuition, the step-by-step method, and a clean Python implementation you can use in interviews.
Problem Statement
You are given two 0-indexed integer arrays of the same length present and future where present[i] is the current price of the ith stock and future[i] is the price of the ith stock a year in the future. You may buy each stock at most once.
Quick Facts
- Difficulty: Medium
- Premium: Yes
- Tags: Array, Dynamic Programming
Intuition
The problem breaks into overlapping subproblems, so caching results prevents exponential repetition.
A carefully chosen DP state captures exactly what we need to build the final answer.
Approach
Define the DP state and recurrence, then compute states in the correct order.
Optionally compress space once the recurrence is clear.
Steps:
- Choose a DP state definition.
- Write the recurrence and base cases.
- Compute states in the correct order.
Example
Input: present = [5,4,6,2,3], future = [8,5,4,3,5], budget = 10
Output: 6
Explanation: One possible way to maximize your profit is to:
Buy the 0th, 3rd, and 4th stocks for a total of 5 + 2 + 3 = 10.
Next year, sell all three stocks for a total of 8 + 3 + 5 = 16.
The profit you made is 16 - 10 = 6.
It can be shown that the maximum profit you can make is 6.
Python Solution
class Solution:
def maximumProfit(self, present: List[int], future: List[int], budget: int) -> int:
f = [[0] * (budget + 1) for _ in range(len(present) + 1)]
for i, w in enumerate(present, 1):
for j in range(budget + 1):
f[i][j] = f[i - 1][j]
if j >= w and future[i - 1] > w:
f[i][j] = max(f[i][j], f[i - 1][j - w] + future[i - 1] - w)
return f[-1][-1]
Complexity
The time complexity is , and the space complexity is . The space complexity is .
Edge Cases and Pitfalls
Watch for boundary values, empty inputs, and duplicate values where applicable. If the problem involves ordering or constraints, confirm the invariant is preserved at every step.
Summary
This Python solution focuses on the essential structure of the problem and keeps the implementation interview-friendly while meeting the constraints.