Why Buy and Sell Stocks All Variants in DSA C++?

The Big Idea

What if you could instantly know the best day to buy and sell stocks to make the most money?

The Scenario

Imagine you want to make money by buying and selling stocks. You try to track prices every day on paper and decide when to buy or sell manually.

You write down prices and try to find the best days to buy low and sell high, but it quickly becomes confusing as prices change every day.

The Problem

Manually checking every possible day to buy and sell is slow and tiring. You might miss the best days or make mistakes because there are too many price combinations to consider.

It's easy to get overwhelmed and lose money because you can't quickly find the best profit.

The Solution

Using algorithms to analyze stock prices helps you quickly find the best days to buy and sell for maximum profit. These methods check prices efficiently without trying every possibility manually.

They handle different rules like buying and selling once, multiple times, or with cooldowns, so you don't have to think about all the details.

Before vs After

✗ Before

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

✓ After

int minPrice = INT_MAX;
int maxProfit = 0;
for (int price : prices) {
  minPrice = std::min(minPrice, price);
  maxProfit = std::max(maxProfit, price - minPrice);
}

What It Enables

You can find the best profit from stock prices quickly and correctly, even with complex buying and selling rules.

Real Life Example

Investors use these algorithms to decide when to buy or sell stocks automatically, helping them make smarter decisions and avoid losses.

Key Takeaways

Manual checking of stock prices is slow and error-prone.

Algorithms find the best buy/sell days efficiently.

Different variants handle various trading rules easily.

Practice

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

easy

A. Sell before buying to maximize profit

B. Minimize the buying price regardless of selling price

C. Buy and sell on the same day to avoid loss

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

Solution

1. Step 1: Understand the problem constraints

   The problem allows only one buy and one sell, so the goal is to find the maximum profit from one pair of days where buying day is before selling day.

2. Step 2: Identify the profit calculation

   Profit = selling price - buying price. We want to maximize this difference with the buying day before selling day.

3. Final Answer:

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

4. Quick Check:

   Profit = sell price - buy price [OK]

Hint: Find max difference with buy day before sell day [OK]

Common Mistakes:

• Ignoring the order of buy and sell days
• Trying to minimize price without considering selling
• Assuming multiple transactions allowed

2. Which of the following C++ code snippets correctly initializes a vector of stock prices for the Buy and Sell Stocks problem?

easy

A. std::vector prices = (7, 1, 5, 3, 6, 4);

B. std::vector<int> prices = {7, 1, 5, 3, 6, 4};

C. vector prices = [7, 1, 5, 3, 6, 4];

D. std::vector<int> prices = (7, 1, 5, 3, 6, 4);

Solution

1. Step 1: Recall correct vector initialization syntax

   In C++, a vector of integers is initialized with curly braces and type specified: std::vector<int> prices = {values};

2. Step 2: Check each option

   std::vector<int> prices = {7, 1, 5, 3, 6, 4}; uses correct syntax with std::vector<int> and curly braces. Options A, B, and D use incorrect syntax for vector initialization.

3. Final Answer:

   std::vector<int> prices = {7, 1, 5, 3, 6, 4}; -> Option B

4. Quick Check:

   Use std::vector<int> and braces {} [OK]

Hint: Use std::vector<int> and curly braces {} to initialize [OK]

Common Mistakes:

• Using square brackets [] instead of curly braces {}
• Omitting the type <int>
• Using parentheses () instead of braces

3. What is the output of the following C++ code that finds the maximum profit with unlimited transactions allowed?

std::vector<int> prices = {7, 1, 5, 3, 6, 4};
int maxProfit = 0;
for (int i = 1; i < prices.size(); i++) {
    if (prices[i] > prices[i - 1]) {
        maxProfit += prices[i] - prices[i - 1];
    }
}
std::cout << maxProfit << std::endl;

medium

A. 7

B. 5

C. 8

D. 6

Solution

1. Step 1: Understand the loop and profit calculation

   The code adds profit for every day where price increases from previous day, summing all positive differences.

2. Step 2: Calculate profits day by day

   Day 1 to 2: 1 - 7 = -6 (no profit)
   Day 2 to 3: 5 - 1 = 4 (add 4)
   Day 3 to 4: 3 - 5 = -2 (no profit)
   Day 4 to 5: 6 - 3 = 3 (add 3)
   Day 5 to 6: 4 - 6 = -2 (no profit)
   Total profit = 4 + 3 = 7

3. Final Answer:

   7 -> Option A

4. Quick Check:

   Sum of positive differences = 7 [OK]

Hint: Sum all positive price differences for unlimited transactions [OK]

Common Mistakes:

• Adding negative differences as profit
• Only considering one transaction
• Miscounting indices in loop

4. Identify the bug in this C++ code snippet that tries to find the maximum profit with only one transaction allowed:

std::vector<int> prices = {7, 1, 5, 3, 6, 4};
int minPrice = INT_MAX;
int maxProfit = 0;
for (int i = 0; i < prices.size(); i++) {
    if (prices[i] < minPrice) {
        minPrice = prices[i];
    } else if (prices[i] - minPrice > maxProfit) {
        maxProfit = prices[i] - minPrice;
    }
}
std::cout << maxProfit << std::endl;

medium

A. No bug, code works correctly

B. minPrice should be initialized to 0

C. maxProfit should be initialized to INT_MIN

D. Loop should start from i = 1 instead of 0

Solution

1. Step 1: Analyze initialization and loop

   minPrice is set to INT_MAX to find minimum price correctly. maxProfit starts at 0. Loop from 0 to end checks each price.

2. Step 2: Check logic correctness

   For each price, update minPrice if current price is lower. Else, calculate profit and update maxProfit if higher. This correctly finds max profit with one transaction.

3. Final Answer:

   No bug, code works correctly -> Option A

4. Quick Check:

   Correct minPrice and maxProfit updates [OK]

Hint: Initialize minPrice to INT_MAX and loop from 0 [OK]

Common Mistakes:

• Starting loop from 1 and missing first price
• Initializing minPrice to 0 causing wrong min
• Initializing maxProfit to INT_MIN causing negative profits

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

hard

A. 5

B. 7

C. 6

D. 8

Solution

1. Step 1: Understand two transactions limit

   We can buy and sell at most twice. We must find two pairs of buy-sell days maximizing total profit without overlap.

2. Step 2: Calculate max profit with two transactions

   First transaction: Buy at 3 (day 1), sell at 5 (day 3) profit = 2
   Second transaction: Buy at 0 (day 4), sell at 4 (day 8) profit = 4
   Total profit = 2 + 4 = 6

3. Final Answer:

   6 -> Option C

4. Quick Check:

   Sum of two best transactions = 6 [OK]

Hint: Split prices into two parts, sum max profits [OK]

Common Mistakes:

• Counting overlapping transactions
• Only considering one transaction
• Misidentifying buy/sell days