Buy and Sell Stocks All Variants in DSA C - Execution Trace

Concept Flow - Buy and Sell Stocks All Variants

Start with prices array

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Choose variant: single, multiple, cooldown, fee

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Initialize variables: buy, sell, cooldown, fee

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Iterate over prices

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Update buy/sell states based on variant rules

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At end, return max profit

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Done

The flow starts with the prices array, selects the variant, updates buy/sell states per day, and ends with the max profit.

Execution Sample

DSA C

int maxProfit(int* prices, int n) {
  int buy = -prices[0], sell = 0;
  for (int i = 1; i < n; i++) {
    buy = buy > -prices[i] ? buy : -prices[i];
    sell = sell > buy + prices[i] ? sell : buy + prices[i];
  }
  return sell;
}

This code calculates max profit for single transaction by tracking buy and sell states.

Execution Table

Step	Operation	Day (i)	Price	Buy State	Sell State	Action	Profit So Far
0	Initialize	0	7	-7	0	Buy at price 7	0
1	Iterate	1	1	-1	0	Update buy: max(-7,-1)=-1	0
2	Iterate	2	5	-1	4	Update sell: max(0,-1+5)=4	4
3	Iterate	3	3	-1	4	No change buy or sell	4
4	Iterate	4	6	-1	5	Update sell: max(4,-1+6)=5	5
5	Iterate	5	4	-1	5	No change buy or sell	5
6	End	-	-	-1	5	Return sell as max profit	5

💡 Reached end of prices array, max profit is sell state = 5

Variable Tracker

Variable	Start	After Day 1	After Day 2	After Day 3	After Day 4	After Day 5	Final
buy	-7	-1	-1	-1	-1	-1	-1
sell	0	0	4	4	5	5	5

Key Moments - 3 Insights

Why does buy state become -1 on day 1 instead of staying -7?

On day 1, buy is updated to max(-7, -1) = -1, meaning buying at price 1 is better than previous buy at 7 (see execution_table row 1).

Why does sell state not change on day 3 even though price changes?

On day 3, sell remains 4 because max(4, -1 + 3) = 4, so selling at price 3 doesn't improve profit (see execution_table row 3).

Why return sell state as max profit at the end?

Sell state tracks max profit after selling, so at end it holds max profit achievable (see execution_table row 6).

Visual Quiz - 3 Questions

Look at the execution_table, what is the buy state at day 2?

A -1

B -7

C 0

D 4

💡 Hint

Check the 'Buy State' column at Step 2 in execution_table.

At which day does the sell state first increase above 0?

A Day 1

B Day 2

C Day 3

D Day 4

💡 Hint

Look at 'Sell State' column in execution_table rows for days 1 to 4.

If price on day 4 was 7 instead of 6, how would sell state change at day 4?

A Remain 5

B Increase to 7

C Increase to 6

D Decrease below 5

💡 Hint

Calculate max(sell at day 3, buy + new price) using variable_tracker values.

Concept Snapshot

Buy and Sell Stocks Variants:
- Track buy and sell states per day
- buy = max(buy, -price)
- sell = max(sell, buy + price)
- Variants add cooldown, fees, or multiple transactions
- Return sell state as max profit
- Update states iteratively over prices array

Full Transcript

This visualization shows how to find max profit from stock prices by tracking buy and sell states daily. We start by buying at the first price, then update buy and sell states each day to reflect best decisions. Buy state means best cost to hold stock, sell state means best profit after selling. We update buy as max of previous buy or buying today after selling. Sell updates as max of previous sell or selling today after buying. At the end, sell state holds max profit. The example uses prices [7,1,5,3,6,4] and shows step-by-step updates. Key moments clarify why buy changes on day 1 and why sell stays same on day 3. Quiz questions test understanding of state changes and effects of price changes.