Best Time to Buy and Sell Stock

You are given an array prices where prices[i] is the price of a given stock on the ith day.

You want to maximize your profit by choosing a single day to buy one stock and choosing a different day in the future to sell that stock.

Return the maximum profit you can achieve from this transaction. If you cannot achieve any profit, return 0.

 

Example 1:

Input: prices = [7,1,5,3,6,4]

Output: 5

Explanation: Buy on day 2 (price = 1) and sell on day 5 (price = 6), profit = 6-1 = 5.

Note that buying on day 2 and selling on day 1 is not allowed because you must buy before you sell.

Example 2:

Input: prices = [7,6,4,3,1]

Output: 0

Explanation: In this case, no transactions are done and the max profit = 0.

🛠 Pattern Breakdown (Step-by-Step Thought Process)

1️⃣ Keep track of the lowest price (minPrice) so far.
2️⃣ At each step, check the profit (prices[i] - minPrice).
3️⃣ Update maxProfit if we find a better profit.
4️⃣ Repeat till the end of the array.

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class Solution {

    public int maxProfit(int[] prices) {
        int n= prices.length;int min=prices[0];

        int maxprofit=0;

        for(int i=1;i<n;i++){

          if(min>prices[i]){

            min=prices[i];

          }

           

      maxprofit=Math.max(maxprofit,prices[i]-min);

        }

       

      return maxprofit;

    }

}

Pattern → Greedy + Kadane’s Algorithm for One Transaction

Time Complexity → O(N) ✅ (Single loop)

Space Complexity → O(1) ✅ (Constant space)

💡 Brute Force Approach

• Check every possible pair of buy and sell days.
• Calculate the profit for each pair (sell - buy).
• Track the maximum profit found.

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🔥 Code (O(N²) Time Complexity)

class Solution {
public int maxProfit(int[] prices) {
int n = prices.length;
int maxProfit = 0; // Track max profit
// Try every possible buy day
for (int i = 0; i < n - 1; i++) {
// Try every possible sell day after i
for (int j = i + 1; j < n; j++) {
int profit = prices[j] - prices[i]; // Calculate profit
maxProfit = Math.max(maxProfit, profit); // Update max profit
}
}
return maxProfit;
}
}