Buy and Sell Stocks All Variants in DSA Go - 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 simplest variant, how many transactions are allowed?

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

intermediate

What does the 'Best Time to Buy and Sell Stock II' variant allow that the first variant does not?

It allows multiple transactions (buy and sell multiple times) to maximize total profit.

intermediate

How does the cooldown period affect the 'Buy and Sell Stocks' problem?

After selling a stock, you must wait one day before buying again, which restricts consecutive transactions.

intermediate

What is the impact of transaction fees in the 'Buy and Sell Stocks' problem?

Each transaction reduces profit by the fee amount, so the algorithm must consider fees to maximize net profit.

In the single transaction variant, what is the best strategy to maximize profit?

A Buy at the highest price and sell at the lowest price

B Buy multiple times without selling

C Buy and sell on the same day

D Buy at the lowest price before the highest price

To maximize profit, buy at the lowest price before the highest price to sell later at a higher price.

Which variant allows unlimited transactions to maximize profit?

A Multiple transactions without cooldown

B Single transaction with fees

C Multiple transactions with cooldown

D Single transaction only

The variant allowing multiple transactions without cooldown lets you buy and sell as many times as you want.

What does a cooldown period mean in stock trading problems?

A You must wait one day after selling before buying again

B You pay a fee for each transaction

C You cannot buy and sell on the same day

D You can only buy once

Cooldown means after selling, you must wait one day before buying again.

How do transaction fees affect the profit calculation?

A They increase the profit

B They have no effect

C They reduce the profit by the fee amount per transaction

D They allow unlimited transactions

Transaction fees reduce profit by the fee amount for each transaction made.

In the 'Buy and Sell Stocks with at most k transactions' variant, what is the main challenge?

A Finding the lowest price only

B Maximizing profit with limited number of transactions

C Ignoring transaction fees

D Buying and selling on the same day

The challenge is to maximize profit while not exceeding the allowed number of transactions.

Explain the difference between the single transaction and multiple transactions variants of the Buy and Sell Stocks problem.

Think about how many times you can buy and sell stocks.

Describe how cooldown and transaction fees change the approach to solving Buy and Sell Stocks problems.

Consider what restrictions these add to trading.

Practice

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

easy

A. Find the day with the highest 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 maximize profit by buying and selling stocks on certain days.

2. Step 2: Identify the correct objective

   Maximizing profit means choosing days to buy low and sell high, not just counting transactions or prices.

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:

• Confusing profit with number of transactions
• Thinking only about highest price day
• Ignoring the buy day in calculations

2. Which of the following Go code snippets correctly initializes a slice to store stock prices for 5 days?

easy

A. prices := []int{7, 1, 5, 3, 6}

B. prices := [5]int{7, 1, 5, 3, 6}

C. prices := make([]int, 5, 5)

D. prices := new([]int{7, 1, 5, 3, 6})

Solution

1. Step 1: Understand slice initialization in Go

   To create a slice with values, use the literal syntax: []int{values}.

2. Step 2: Check each option

   prices := []int{7, 1, 5, 3, 6} correctly creates a slice with given values. prices := [5]int{7, 1, 5, 3, 6} creates an array, not a slice. prices := make([]int, 5, 5) creates an empty slice of length 5 but no values. prices := new([]int{7, 1, 5, 3, 6}) is invalid syntax.

3. Final Answer:

   prices := []int{7, 1, 5, 3, 6} -> Option A

4. Quick Check:

   Slice literal = []int{values} [OK]

Hint: Use []int{...} to create slices with values directly [OK]

Common Mistakes:

• Using array syntax instead of slice
• Using new() incorrectly for slices
• Creating empty slices without values

3. What is the output of the following Go code that finds the max profit with only one transaction?

func maxProfit(prices []int) int {
    minPrice := prices[0]
    maxProfit := 0
    for _, price := range prices {
        if price < minPrice {
            minPrice = price
        } else if price - minPrice > maxProfit {
            maxProfit = price - minPrice
        }
    }
    return maxProfit
}

fmt.Println(maxProfit([]int{7,1,5,3,6,4}))

medium

A. 5

B. 6

C. 4

D. 7

Solution

1. Step 1: Trace the loop to find minPrice and maxProfit

   Start minPrice=7, maxProfit=0. Iterate prices: - price=7: minPrice=7, maxProfit=0 - price=1: minPrice=1 (lower) - price=5: profit=5-1=4 >0, maxProfit=4 - price=3: profit=3-1=2 <4, maxProfit=4 - price=6: profit=6-1=5 >4, maxProfit=5 - price=4: profit=4-1=3 <5, maxProfit=5

2. Step 2: Return maxProfit

   maxProfit is 5 after loop ends.

3. Final Answer:

   5 -> Option A

4. Quick Check:

   Max profit = 5 [OK]

Hint: Track min price and update max profit during iteration [OK]

Common Mistakes:

• Not updating minPrice correctly
• Calculating profit before updating minPrice
• Returning wrong variable

4. Identify the bug in this Go function that tries to calculate max profit with unlimited transactions:

func maxProfit(prices []int) int {
    profit := 0
    for i := 0; i < len(prices); i++ {
        if prices[i] > prices[i-1] {
            profit += prices[i] - prices[i-1]
        }
    }
    return profit
}

medium

A. prices slice is not initialized

B. Incorrect profit calculation logic

C. Missing return statement

D. Index out of range error due to accessing prices[i-1] when i=0

Solution

1. Step 1: Check loop and index usage

   The loop starts at i=0, but code accesses prices[i-1], which is prices[-1] at i=0, causing index out of range error.

2. Step 2: Identify fix

   Start loop from i=1 to avoid negative index access.

3. Final Answer:

   Index out of range error due to accessing prices[i-1] when i=0 -> Option D

4. Quick Check:

   Loop index must start at 1 to avoid error [OK]

Hint: Avoid negative indices by starting loop at 1 [OK]

Common Mistakes:

• Starting loop at 0 but accessing i-1
• Ignoring runtime errors
• Not testing with small input arrays

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

hard

A. 7

B. 6

C. 5

D. 8

Solution

1. Step 1: Understand two transactions limit

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

2. Step 2: Calculate max profit with two transactions

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

3. Final Answer:

   6 -> Option B

4. Quick Check:

   Two transactions max profit = 6 [OK]

Hint: Split array, find max profit left and right, sum max [OK]

Common Mistakes:

• Counting overlapping transactions
• Ignoring zero price days
• Calculating only one transaction profit