Maximum Profit From Trading Stocks

Maximum Profit From Trading Stocks

1. What is this problem about?

The Maximum Profit From Trading Stocks interview question is a variation of the Knapsack problem. You are given the current prices and future prices of several stocks, along with a limited budget (capital). You can buy each stock at most once. Your goal is to select a subset of stocks to buy today and sell in the future to maximize your total profit without exceeding your budget.

Each stock's profit is future_price - current_price. If the profit is negative or zero, you shouldn't buy it. This is essentially the 0/1 Knapsack problem where "current_price" is the weight and "profit" is the value.

2. Why is this asked in interviews?

Companies like ServiceNow and Adobe ask the Maximum Profit From Trading Stocks coding problem to test a candidate's ability to map a real-world scenario to a fundamental algorithmic pattern. It evaluates your mastery of Dynamic Programming, specifically the 0/1 Knapsack variant. It also checks if you can perform basic data preprocessing (calculating profits and filtering out losing stocks) before applying the DP logic.

3. Algorithmic pattern used

The Array, Dynamic Programming interview pattern (0/1 Knapsack) is used.

1. For each stock, calculate profit = future_price - current_price.
2. Create a DP array dp of size budget + 1, where dp[w] is the max profit for budget w.
3. For each stock with profit > 0:
   • Iterate backwards through the dp array from budget down to current_price.
   • dp[w] = max(dp[w], dp[w - current_price] + profit)
4. The answer is dp[budget].

4. Example explanation

Budget: 10. Stocks:

• A: Buy 3, Sell 8 (Profit 5)
• B: Buy 5, Sell 12 (Profit 7)
• C: Buy 8, Sell 15 (Profit 7)

DP Transitions:

• After A (3, 5): dp[3...10] = 5
• After B (5, 7): dp[8...10] = max(5, dp[8-5]+7) = 12. dp[5...7] = 7.
• After C (8, 7): dp[8] = max(12, dp[0]+7) = 12. dp[10] = max(12, dp[2]+7) = 12.

Max profit is 12 (by buying A and B).

5. Common mistakes candidates make

In the Maximum Profit From Trading Stocks coding problem, a frequent mistake is not iterating backwards through the DP array. Iterating forwards allows you to use the same stock multiple times, which turns the problem into "Unbounded Knapsack," which is incorrect here. Another error is including stocks with zero or negative profit, which adds unnecessary computation. Finally, using a 2D DP table when a 1D array is sufficient for space optimization is a missed opportunity to show efficiency.

6. Interview preparation tip

Always identify if a problem follows the "Pick or Don't Pick" structure with a constraint. This is the hallmark of the Knapsack problem. Practice space-optimizing your Knapsack solutions from O(N*W) space to O(W) space, as this is a common follow-up question in senior-level interviews.