leetcode(121). Best Time to Buy and Sell Stock

股票买卖最大利润算法

最新推荐文章于 2025-09-06 17:22:57 发布

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本文介绍了一种寻找股票交易中最大利润的算法。该算法通过遍历价格数组并记录最低买入价格来确定最大利润。举例说明了算法如何运作并给出了Python实现。

problem

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

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

Example 1: Input: [7, 1, 5, 3, 6, 4] Output: 5

max. difference = 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

In this case, no transaction is done, i.e. max profit = 0.

分析

In formal terms, we need to find $\max(prices[j] - prices[i])$ , for every i and j such that j > i.
接下来再进一步抽象这个问题：对每一个元素都减去它之前最小的元素，这样得到的最大值就是要求的结果， $\max (price[j]-\min(price[:j]))$ ，因此我们只要用minprice保存 $\min(price[:j])$ 并不断更新即可。

class Solution(object):
    def maxProfit(self, prices):
        """
        :type prices: List[int]
        :rtype: int
        """
        minprice =  float('inf')
        ans = 0

        for i in prices:
            if i < minprice:
                minprice = i
            else:
                ans = max(ans, i-minprice)
        return ans