Buy and Sell Stocks All Variants in DSA Typescript - 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 does the 'Buy and Sell Stocks II' variant allow that the first variant does not?

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

advanced

How does the 'Buy and Sell Stocks with Cooldown' variant change the problem?

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

advanced

What is the key difference in the 'Buy and Sell Stocks with Transaction Fee' variant?

Each transaction (buy + sell) incurs a fee that reduces the profit from that transaction.

In the 'Buy and Sell Stocks I' problem, what is the best strategy to maximize profit?

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

B Buy and sell every day

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

D Buy and hold without selling

You want to buy at the lowest price and sell later at a higher price to maximize profit.

Which variant allows unlimited transactions to maximize profit?

A Buy and Sell Stocks with Cooldown

B Buy and Sell Stocks I

C Buy and Sell Stocks II

D Buy and Sell Stocks with Transaction Fee

Buy and Sell Stocks II allows multiple transactions without restrictions.

What does the cooldown period mean in the stock trading problem?

A You cannot buy and sell on the same day

B You must wait one day after selling before buying again

C You cannot sell stocks

D You must buy stocks every day

Cooldown means waiting one day after selling before you can buy again.

How does a transaction fee affect the profit calculation?

A It reduces the profit by the fee amount per transaction

B It has no effect

C It doubles the profit

D It increases the profit

Each transaction reduces profit by the fee amount.

Which approach is commonly used to solve 'Buy and Sell Stocks with Cooldown'?

A Greedy algorithm

B Binary search

C Sorting

D Dynamic programming

Dynamic programming helps track states with cooldown constraints.

Explain how to find the maximum profit when only one transaction is allowed.

Think about the lowest price before the current day.

Describe how cooldown affects buying and selling decisions in stock trading.

Consider what happens right after you sell a stock.

Practice

1. What is the main goal when solving the Buy and Sell Stocks problem with only one transaction allowed?

easy

A. Maximize the difference between a later selling price and an earlier buying price

B. Minimize the number of transactions

C. Find the lowest price in the array

D. Calculate the average stock price

Solution

1. Step 1: Understand the problem goal

   The problem asks to find the maximum profit by buying and selling once, so we want the biggest positive difference between a sell price after a buy price.

2. Step 2: Identify the correct approach

   Maximizing the difference between a later selling price and an earlier buying price directly solves the problem.

3. Final Answer:

   Maximize the difference between a later selling price and an earlier buying price -> Option A

4. Quick Check:

   Goal = Maximize profit from one buy and one sell [OK]

Hint: Look for max difference with sell after buy [OK]

Common Mistakes:

• Thinking to minimize transactions instead of maximizing profit
• Confusing lowest price with max profit
• Ignoring the order of buy before sell

2. Which of the following TypeScript function signatures correctly represents a function to find max profit from multiple stock transactions?

easy

A. function maxProfit(prices: number[]): number

B. function maxProfit(prices: string): number[]

C. function maxProfit(prices: number): string

D. function maxProfit(prices: any): void

Solution

1. Step 1: Analyze the input and output types

   The input should be an array of numbers representing prices, so prices: number[]. The output is the maximum profit, a number.

2. Step 2: Match the correct function signature

   function maxProfit(prices: number[]): number matches input as number array and output as number, which is correct.

3. Final Answer:

   function maxProfit(prices: number[]): number -> Option A

4. Quick Check:

   Input array, output number [OK]

Hint: Input array of numbers, output single number [OK]

Common Mistakes:

• Using string type for prices
• Returning array instead of number
• Using void return type

3. What is the output of the following TypeScript code for max profit with unlimited transactions?

function maxProfit(prices: number[]): number {
  let profit = 0;
  for (let i = 1; i < prices.length; i++) {
    if (prices[i] > prices[i - 1]) {
      profit += prices[i] - prices[i - 1];
    }
  }
  return profit;
}

console.log(maxProfit([7,1,5,3,6,4]));

medium

A. 5

B. 7

C. 8

D. 6

Solution

1. Step 1: Trace the loop and calculate profit increments

   Prices: [7,1,5,3,6,4] - i=1: 1 > 7? No, profit=0 - i=2: 5 > 1? Yes, profit += 5-1=4 - i=3: 3 > 5? No, profit=4 - i=4: 6 > 3? Yes, profit += 6-3=3, total=7 - i=5: 4 > 6? No, profit=7

2. Step 2: Return total profit

   Total profit after loop is 7.

3. Final Answer:

   7 -> Option B

4. Quick Check:

   Sum of positive diffs = 7 [OK]

Hint: Add all positive price differences [OK]

Common Mistakes:

• Adding negative differences
• Only considering one transaction
• Misreading array indices

4. Identify the bug in this TypeScript code for max profit with one transaction:

function maxProfit(prices: number[]): number {
  let minPrice = prices[0];
  let maxProfit = 0;
  for (let i = 1; i <= prices.length; i++) {
    if (prices[i] < minPrice) {
      minPrice = prices[i];
    } else if (prices[i] - minPrice > maxProfit) {
      maxProfit = prices[i] - minPrice;
    }
  }
  return maxProfit;
}

medium

A. prices array should be sorted first

B. minPrice should be initialized to 0

C. maxProfit should start at -Infinity

D. Loop condition should be < instead of <=

Solution

1. Step 1: Check loop boundary

   The loop runs with i from 1 to prices.length inclusive, but array indices go from 0 to prices.length - 1. Using <= causes out-of-bounds access at prices[prices.length].

2. Step 2: Correct the loop condition

   Change loop condition to i < prices.length to avoid accessing undefined elements.

3. Final Answer:

   Loop condition should be < instead of <= -> Option D

4. Quick Check:

   Array index out-of-bounds fixed by < condition [OK]

Hint: Use < for array loops, not <= [OK]

Common Mistakes:

• Using <= causing runtime errors
• Initializing minPrice incorrectly
• Sorting prices unnecessarily

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. 5

B. 6

C. 7

D. 4

Solution

1. Step 1: Understand two transactions limit

   We can buy and sell at most twice. We want to split the array into two parts and maximize profit from each.

2. Step 2: Calculate max profit for each split

   Best first transaction: buy at 3, sell at 5 = 2 profit Best second transaction: buy at 0, sell at 4 = 4 profit Total max profit = 2 + 4 = 6

3. Step 3: Check for better splits

   Splitting at index 5: first part max profit = 4 (buy at 0 sell at 3), second part max profit = 3 (buy at 1 sell at 4), total = 7

4. Final Answer:

   7 -> Option C

5. Quick Check:

   Sum of two best transactions = 7 [OK]

Hint: Split array, sum max profits from two parts [OK]

Common Mistakes:

• Counting more than two transactions
• Not splitting array correctly
• Choosing wrong buy/sell days