Buy and Sell Stocks All Variants in DSA Python - Cheat Sheet & Quick Revision

Recall & Review

beginner

What is the main goal in the 'Buy and Sell Stocks' problem?

To find the maximum profit by choosing the best days to buy and sell stocks given their prices over time.

beginner

In the 'Buy and Sell Stocks I' variant, how many transactions are allowed?

Only one transaction is allowed: buy once and sell once.

intermediate

What is the key difference between 'Buy and Sell Stocks II' and 'Buy and Sell Stocks I'?

'Buy and Sell Stocks II' allows unlimited transactions (buy and sell multiple times), while 'I' allows only one transaction.

intermediate

What constraint does 'Buy and Sell Stocks with Cooldown' add?

After selling a stock, you must wait one day before buying again (cooldown period).

intermediate

In 'Buy and Sell Stocks with Transaction Fee', what effect does the fee have on profit calculation?

Each sell transaction reduces profit by the fee amount, so profit must be calculated after subtracting the fee.

In 'Buy and Sell Stocks I', what is the best approach to find maximum profit?

A Track the minimum price so far and calculate max profit by selling at current price

B Buy and sell every day to maximize profit

C Use dynamic programming with unlimited transactions

D Ignore prices and pick random days

Tracking the minimum price so far and calculating profit by selling at current price helps find the max profit with one transaction.

Which variant allows buying and selling stocks multiple times without restrictions?

A Buy and Sell Stocks I

B Buy and Sell Stocks II

C Buy and Sell Stocks with Cooldown

D Buy and Sell Stocks with Transaction Fee

'Buy and Sell Stocks II' allows unlimited transactions without cooldown or fees.

What does the cooldown period prevent in the 'Buy and Sell Stocks with Cooldown' variant?

A Buying multiple stocks at once

B Selling multiple times in a day

C Buying immediately after selling

D Selling before buying

Cooldown means you cannot buy a stock immediately after selling; you must wait one day.

How does a transaction fee affect the profit calculation in stock trading problems?

A It reduces profit by the fee amount on each sell

B It increases profit by the fee amount

C It has no effect on profit

D It only applies when buying

Each sell transaction reduces profit by the fee amount, so it must be subtracted.

Which data structure or technique is commonly used to solve 'Buy and Sell Stocks with Cooldown'?

A Binary search

B Greedy approach

C Sorting

D Dynamic programming

Dynamic programming is used to handle cooldown constraints and track states.

Explain how to find the maximum profit when only one buy and one sell are allowed.

Think about the lowest price before the current day.

Describe how cooldown and transaction fee change the approach to buying and selling stocks.

Consider extra rules that limit when and how profit is made.

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