121. Best Time to Buy and Sell Stock

描述

Say you have an array for which the $i^th$ element is the price of a given stock on day i.

If you were only permitted to complete at most one transaction (i.e., buy one and sell one share of the stock), design an algorithm to find the maximum profit.

Note that you cannot sell a stock before you buy one.

Example 1:

Input: [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.
             Not 7-1 = 6, as selling price needs to be larger than buying price.

Example 2:

Input: [7,6,4,3,1]
Output: 0
Explanation: In this case, no transaction is done, i.e. max profit = 0.

解法

思路：因为只能交易一次，所以用当天的价格减去之前的最低价格得到当天的最大利润，和历史最大利润作比较获取更新后的最大利润。

class Solution:
    def maxProfit(self, prices: List[int]) -> int:
        profit = 0
        lowest = float("inf")

        for price in prices:
            lowest = min(lowest, price)
            profit = max(profit, price - lowest)

        return profit

时间复杂度：$O(n)$，只遍历一次数组。 空间复杂度：$O(1)$，只使用了几个临时变量。

引用

一个方法团灭 6 道股票问题