Buy and Sell Stocks All Variants in DSA Python - Practice Problems & Challenges

Challenge - 5 Problems

❓ Predict Output

intermediate

Maximum Profit with One Transaction

What is the output of the following code that calculates the maximum profit from a single buy-sell transaction?

DSA Python

def max_profit(prices):
    min_price = float('inf')
    max_profit = 0
    for price in prices:
        if price < min_price:
            min_price = price
        elif price - min_price > max_profit:
            max_profit = price - min_price
    return max_profit

print(max_profit([7,1,5,3,6,4]))

A 5

B 6

C 4

D 7

💡 Hint

Track the lowest price and calculate profit by subtracting it from current price.

The lowest price is 1, the highest price after that is 6, so max profit is 6 - 1 = 5.

❓ Predict Output

intermediate

Maximum Profit with Unlimited Transactions

What is the output of this code that calculates the maximum profit with unlimited buy-sell transactions?

DSA Python

def max_profit(prices):
    profit = 0
    for i in range(1, len(prices)):
        if prices[i] > prices[i-1]:
            profit += prices[i] - prices[i-1]
    return profit

print(max_profit([7,1,5,3,6,4]))

A 6

B 8

C 5

D 7

💡 Hint

Add all positive differences between consecutive days.

Profits: (5-1)=4 + (6-3)=3 total 7.

❓ Predict Output

advanced

Maximum Profit with At Most Two Transactions

What is the output of this code that calculates the maximum profit with at most two buy-sell transactions?

DSA Python

def max_profit(prices):
    n = len(prices)
    if n == 0:
        return 0
    left_profits = [0]*n
    right_profits = [0]*n

    min_price = prices[0]
    for i in range(1, n):
        min_price = min(min_price, prices[i])
        left_profits[i] = max(left_profits[i-1], prices[i] - min_price)

    max_price = prices[-1]
    for i in range(n-2, -1, -1):
        max_price = max(max_price, prices[i])
        right_profits[i] = max(right_profits[i+1], max_price - prices[i])

    max_profit = 0
    for i in range(n):
        max_profit = max(max_profit, left_profits[i] + right_profits[i])
    return max_profit

print(max_profit([3,3,5,0,0,3,1,4]))

A 6

B 7

C 5

D 8

💡 Hint

Use two arrays to track max profit from left and right sides.

Best two transactions: buy at index 3 (price 0) sell at index 5 (price 3), buy at index 6 (price 1) sell at index 7 (price 4), total profit 3 + 3 = 6.

❓ Predict Output

advanced

Maximum Profit with Cooldown

What is the output of this code that calculates the maximum profit with cooldown (one day after selling you cannot buy)?

DSA Python

def max_profit(prices):
    if not prices:
        return 0
    n = len(prices)
    sell, prev_sell = 0, 0
    buy, prev_buy = -prices[0], 0
    for i in range(1, n):
        prev_buy = buy
        buy = max(buy, prev_sell - prices[i])
        prev_sell = sell
        sell = max(sell, prev_buy + prices[i])
    return sell

print(max_profit([1,2,3,0,2]))

A 2

B 4

C 3

D 5

💡 Hint

Track buy and sell states with cooldown constraints.

Transactions: buy at 1, sell at 3, cooldown day 4, buy at 0, sell at 2, total profit 3.

🧠 Conceptual

expert

Understanding State Transitions in Stock Trading with Cooldown

In the cooldown variant of the stock trading problem, which state transition correctly represents the update of the 'buy' state on day i?

A buy[i] = max(buy[i-1], sell[i-1] - price[i])

B buy[i] = max(buy[i-1], sell[i-2] - price[i])

C buy[i] = max(buy[i-2], sell[i-1] - price[i])

D buy[i] = max(buy[i-1], sell[i] - price[i])

💡 Hint

Remember cooldown means you cannot buy immediately after selling the previous day.

You can only buy today if you were not holding stock yesterday or you sold stock two days ago (due to cooldown). So buy[i] depends on sell[i-2].

Practice

1. What is the main goal when solving the Buy and Sell Stocks problem variants?

easy

A. Find the day with the lowest stock price only

B. Minimize the number of transactions regardless of profit

C. Maximize the profit by choosing the best days to buy and sell stocks

D. Calculate the average stock price over all days

Solution

1. Step 1: Understand the problem goal

   The problem asks to find the best days to buy and sell stocks to get the highest profit.

2. Step 2: Identify the objective

   Maximizing profit means buying low and selling high at the right times.

3. Final Answer:

   Maximize the profit by choosing the best days to buy and sell stocks -> Option C

4. Quick Check:

   Goal = Maximize profit [OK]

Hint: Focus on profit maximization, not just prices or counts [OK]

Common Mistakes:

• Thinking the goal is to minimize transactions
• Only finding lowest price day without selling
• Calculating averages instead of profit

2. Which of the following Python code snippets correctly initializes variables to track minimum price and maximum profit for the stock problem?

easy

A. min_price = float('inf'); max_profit = 0

B. min_price = 0; max_profit = float('-inf')

C. min_price = None; max_profit = None

D. min_price = 0; max_profit = 0

Solution

1. Step 1: Understand initialization needs

   We want min_price to start very high so any price is lower, and max_profit to start at zero.

2. Step 2: Check each option

   min_price = float('inf'); max_profit = 0 sets min_price to infinity and max_profit to zero, which is correct for tracking minimum and maximum values.

3. Final Answer:

   min_price = float('inf'); max_profit = 0 -> Option A

4. Quick Check:

   Initialization = min_price high, max_profit zero [OK]

Hint: Use infinity for min_price start, zero for max_profit [OK]

Common Mistakes:

• Setting min_price to zero causes wrong minimum tracking
• Using None without checks causes errors
• Setting max_profit to negative infinity can confuse logic

3. What is the output of the following code snippet for prices = [7,1,5,3,6,4]?

min_price = float('inf')
max_profit = 0
for price in prices:
    if price < min_price:
        min_price = price
    elif price - min_price > max_profit:
        max_profit = price - min_price
print(max_profit)

medium

A. 6

B. 7

C. 4

D. 5

Solution

1. Step 1: Trace the loop with given prices

   Prices: 7,1,5,3,6,4 - Start min_price=inf, max_profit=0 - price=7: min_price=7 - price=1: min_price=1 (lower) - price=5: profit=5-1=4 > 0, max_profit=4 - price=3: profit=3-1=2 < 4, no change - price=6: profit=6-1=5 > 4, max_profit=5 - price=4: profit=4-1=3 < 5, no change

2. Step 2: Final max_profit after loop

   max_profit is 5 after checking all prices.

3. Final Answer:

   5 -> Option D

4. Quick Check:

   Max profit = 5 [OK]

Hint: Track min price and update max profit on higher prices [OK]

Common Mistakes:

• Confusing max profit with max price
• Not updating min_price correctly
• Calculating profit incorrectly

4. Identify the error in this code snippet for the stock problem:

prices = [7,1,5,3,6,4]
min_price = 0
max_profit = 0
for price in prices:
    if price < min_price:
        min_price = price
    elif price - min_price > max_profit:
        max_profit = price - min_price
print(max_profit)

medium

A. Loop should start from second element

B. min_price initialized to 0 instead of a high value

C. max_profit should start at float('inf')

D. Using elif instead of if causes logic error

Solution

1. Step 1: Check variable initialization

   min_price is set to 0, but prices include values greater than 0, so min_price never updates to actual minimum (1).

2. Step 2: Effect of wrong min_price initialization

   Since min_price=0, price < min_price is never true, so min_price stays 0, causing incorrect profit calculations.

3. Final Answer:

   min_price initialized to 0 instead of a high value -> Option B

4. Quick Check:

   min_price must start high to track minimum [OK]

Hint: Initialize min_price to infinity, not zero [OK]

Common Mistakes:

• Starting min_price at zero causes wrong minimum tracking
• Confusing max_profit initialization
• Thinking elif causes logic error here

5. Given the prices array [3,3,5,0,0,3,1,4], what is the maximum profit with at most two transactions?

hard

A. 6

B. 7

C. 5

D. 4

Solution

1. Step 1: Understand two transactions limit

   We can buy and sell stocks at most twice to maximize total profit.

2. Step 2: Calculate profits for two transactions

   First transaction: buy at 3, sell at 5 = 2 profit Second transaction: buy at 0, sell at 4 = 4 profit Total profit = 2 + 4 = 6

3. Final Answer:

   6 -> Option A

4. Quick Check:

   Two transactions max profit = 6 [OK]

Hint: Split array, find max profit in two parts [OK]

Common Mistakes:

• Counting overlapping transactions
• Only considering one transaction
• Adding profits incorrectly