121-best-time-to-buy-and-sell-stock

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Description

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.

 

Constraints:

• 1 <= prices.length <= 105
• 0 <= prices[i] <= 104

Solution(Python)

class Solution:
    def maxProfit(self, prices: List[int]) -> int:
        return self.optimized(prices)

    """
    Time Complexity: O(n^2)
    Space Complexity: O(1)
    """

    def bruteforce(self, prices: List[int]) -> int:
        n = len(prices)
        maxProfit = 0
        for i in range(n):
            for j in range(i + 1, n):
                if prices[j] - prices[i] > maxProfit:
                    maxProfit = prices[j] - prices[i]

        return maxProfit

    """
    Time Complexity: O(n)
    Space Complexity: O(1)
    """

    def optimized(self, prices: List[int]) -> int:
        buyPrice = float("inf")
        profit = 0

        for sellprice in prices:
            if sellprice < buyPrice:
                buyPrice = sellprice
            elif sellprice - buyPrice > profit:
                profit = sellprice - buyPrice
        return profit