121. 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.

Examples:

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.

Input: prices = [7,6,4,3,1]
Output: 0
Explanation: In this case, no transactions are done and the max profit = 0.

Sliding window / two pointer solution

• Initialize a left pointer left on day 1, and a right pointer right on day 2
• Find the current profit (buy on left, sell on right)
  • if right is less than left
    • update left to be right, and
    • update right to be the next day
  • if left is less than right (it's a profit)
    • if the profit (right - left) is more than max_profit, set it to max_profit
    • only update right (because we are buying low and selling high) to the next day
  • repeat step
• Return max_profit

The memory is O(1) because only pointers are used. The time is O(n).

Python

class Solution:
    def maxProfit(self, prices: List[int]) -> int:
        max_profit = 0
        left = 0
        right = 1

        # while we haven't reached the end
        while right < len(prices):
            left_value = prices[left]
            right_value = prices[right]

            # profitable?
            if left_value < right_value:
                profit = right_value - left_value
                max_profit = max(max_profit, profit)
            else:
                left = right
            
            right += 1
          
        return max_profit