题意:给定一个序列,第i个元素代表第i天这支股票的价格,问在最佳时机买入和卖出能赚多少钱?只买一次,且仅1股,假设本钱无限。

思路:要找一个最低价的时候买入,在最高价的时候卖出利润会最大。但是时间是不能冲突的,比如说在明天买入,今天卖出。因此,对于今天的价格,应该要找到今天之前的该股的最低价,买入,今天卖出。

  其实就是要为序列中的一个元素A[k],找到另一个元素A[e],位置满足e<k,结果使得A[k]-A[e]最大。

  用动态规划解决,从左扫起,遇到一个元素就更新当前最小值,再用当前元素去减这个最小值。扫完就知道结果了。

class Solution {
public:
int maxProfit(vector<int>& prices) {
int small=, ans=;
for(int i=; i<prices.size(); i++)
{
small=min(small, prices[i]); //找到i之前的最小值
ans=max( prices[i]-small, ans );
}
return ans;
}
};

AC代码

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