Why Buy and Sell Stocks All Variants in DSA Python?

The Big Idea

What if you could find the best day to buy and sell stocks without guessing or stress?

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.

The Problem

Doing this by hand is slow and confusing. You might miss the best days or make mistakes counting profits.

It's hard to keep track of many days and all possible buy-sell pairs.

The Solution

Using algorithms, you can quickly find the best days to buy and sell stocks to maximize profit.

The algorithm checks prices step-by-step and remembers the best choices without errors.

Before vs After

✗ Before

prices = [7,1,5,3,6,4]
max_profit = 0
for i in range(len(prices)):
    for j in range(i+1, len(prices)):
        profit = prices[j] - prices[i]
        if profit > max_profit:
            max_profit = profit
print(max_profit)

✓ After

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)

What It Enables

You can quickly find the best buy and sell days to maximize profit from stock prices.

Real Life Example

Investors use these algorithms to decide when to buy or sell stocks to earn the most money without guessing.

Key Takeaways

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

Algorithms help find the best buy/sell days efficiently.

This saves time and increases profit accuracy.

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