Buy and Sell Stocks All Variants in DSA C# - Time & Space Complexity

Time Complexity: Buy and Sell Stocks All Variants

O(n)

Understanding Time Complexity

We want to understand how the time needed to find the best buy and sell days grows as the number of stock prices increases.

How does the number of prices affect the work our code must do?

Scenario Under Consideration

Analyze the time complexity of the following code snippet.

public int MaxProfit(int[] prices) {
    int minPrice = int.MaxValue;
    int maxProfit = 0;
    for (int i = 0; i < prices.Length; i++) {
        if (prices[i] < minPrice) {
            minPrice = prices[i];
        } else if (prices[i] - minPrice > maxProfit) {
            maxProfit = prices[i] - minPrice;
        }
    }
    return maxProfit;
}
    

This code finds the maximum profit from buying and selling a stock once by scanning prices once.

Identify Repeating Operations

Identify the loops, recursion, array traversals that repeat.

• Primary operation: Single loop through the prices array.
• How many times: Exactly once for each price, so n times if there are n prices.

How Execution Grows With Input

As the number of prices grows, the code checks each price once, so the work grows directly with the number of prices.

Input Size (n)	Approx. Operations
10	About 10 checks
100	About 100 checks
1000	About 1000 checks

Pattern observation: The work grows in a straight line with input size.

Final Time Complexity

Time Complexity: O(n)

This means the time to find the best buy and sell days grows directly with the number of prices.

Common Mistake

[X] Wrong: "We must check every pair of days, so the time is always n squared."

[OK] Correct: This code smartly tracks the lowest price so far and calculates profit in one pass, avoiding checking all pairs.

Interview Connect

Understanding this time complexity shows you can find efficient solutions by scanning data once, a key skill in many coding challenges.

Self-Check

"What if we wanted to find the maximum profit with unlimited transactions? How would the time complexity change?"

Practice

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

easy

A. Minimize the number of transactions regardless of profit

B. Find the stock price on the last day only

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 objective

   The problem asks to maximize profit by buying and selling stocks on certain days.

2. Step 2: Identify the key action

   Choosing the best days to buy low and sell high maximizes profit.

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 transactions [OK]

Common Mistakes:

• Confusing profit with number of transactions
• Ignoring the buy before sell rule
• Trying to find average price instead of max profit

2. Which of the following C# code snippets correctly initializes an array of stock prices for the Buy and Sell Stocks problem?

easy

A. int prices[] = new int[6] {7, 1, 5, 3, 6, 4};

B. int prices = {7, 1, 5, 3, 6, 4};

C. int[] prices = (7, 1, 5, 3, 6, 4);

D. int[] prices = new int[] {7, 1, 5, 3, 6, 4};

Solution

1. Step 1: Check correct array initialization syntax in C#

   In C#, arrays are initialized with int[] prices = new int[] { ... };.

2. Step 2: Verify each option

   int[] prices = new int[] {7, 1, 5, 3, 6, 4}; uses correct syntax. The other options have invalid syntax: one declares a single int without array type, another uses parentheses instead of braces, and the last has incorrect array declaration style.

3. Final Answer:

   int[] prices = new int[] {7, 1, 5, 3, 6, 4}; -> Option D

4. Quick Check:

   Correct C# array syntax = int[] prices = new int[] {7, 1, 5, 3, 6, 4}; [OK]

Hint: Use int[] arr = new int[] { ... }; for arrays [OK]

Common Mistakes:

• Omitting 'new int[]' when initializing arrays
• Using parentheses instead of braces
• Declaring arrays like in C or Java incorrectly

3. What is the output of the following C# code that finds the maximum profit with only one transaction allowed?

int[] prices = {7, 1, 5, 3, 6, 4};
int minPrice = int.MaxValue;
int maxProfit = 0;
foreach (int price in prices) {
    if (price < minPrice) minPrice = price;
    else if (price - minPrice > maxProfit) maxProfit = price - minPrice;
}
Console.WriteLine(maxProfit);

medium

A. 6

B. 5

C. 4

D. 7

Solution

1. Step 1: Trace the minimum price and max profit updates

   Prices: 7,1,5,3,6,4. Min price updates to 7 then 1. Max profit updates when price - minPrice > maxProfit: 5-1=4, 6-1=5.

2. Step 2: Identify final max profit

   Max profit is 5, achieved by buying at 1 and selling at 6.

3. Final Answer:

   5 -> Option B

4. Quick Check:

   Max profit one transaction = 5 [OK]

Hint: Track min price and update max profit on each day [OK]

Common Mistakes:

• Confusing max profit with max price
• Not updating min price correctly
• Calculating profit without checking min price

4. The following code is intended to calculate the maximum profit with unlimited transactions allowed. What is the bug?

int maxProfit = 0;
for (int i = 1; i < prices.Length; i++) {
    if (prices[i] > prices[i - 1]) {
        maxProfit += prices[i] - prices[i - 1];
    }
}
return maxProfit;

medium

A. There is no bug; code works correctly

B. The code does not handle empty price array

C. The loop should start from i = 0

D. The code incorrectly adds profit when prices decrease

Solution

1. Step 1: Understand the logic for unlimited transactions

   The code adds profit for every increase from day i-1 to i, which is correct for unlimited transactions.

2. Step 2: Check for bugs

   The loop starts at 1 to compare with previous day. It skips empty array handling but not asked here. No incorrect profit addition.

3. Final Answer:

   There is no bug; code works correctly -> Option A

4. Quick Check:

   Unlimited transactions profit logic = correct [OK]

Hint: Add profit only when price increases day-to-day [OK]

Common Mistakes:

• Starting loop at wrong index
• Adding profit on price drops
• Ignoring empty or single-element arrays

5. Given the prices array {3, 3, 5, 0, 0, 3, 1, 4} and a limit of at most two transactions, what is the maximum profit achievable?

hard

A. 8

B. 7

C. 5

D. 6

Solution

1. Step 1: Understand the two transactions limit

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

2. Step 2: Calculate max profit by splitting days

   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. But better transactions are buy at 0 sell at 3 (profit 3), then buy at 1 sell at 4 (profit 3), total 6. However, the maximum profit is actually 8 by buying at 0 and selling at 5 (profit 5), then buying at 1 and selling at 4 (profit 3).

3. Final Answer:

   8 -> Option A

4. Quick Check:

   Two transactions max profit = 8 [OK]

Hint: Split array to find best two transaction profits [OK]

Common Mistakes:

• Counting more than two transactions
• Not choosing optimal buy/sell days
• Adding profits incorrectly