leetcode—Best Time to Buy and Sell stocks III

1.题目描述

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

Design an algorithm to find the maximum profit. You may complete at most two transactions.

Note:

You may not engage in multiple transactions at the same time (ie, you must sell the stock before you buy again).

2.解法分析

限定了交易次数之后题目就需要我们略微思考一下了，由于有两次交易的机会，那么我们选定一个时间点t_i，将此时间点作为两次交易的支点的话，必然有：

      t₀….t_i之内满足最佳交易原则，t_i-t_n天也满足最佳交易原则，那么这就是一个动态规划的策略了，于是有下面的代码：

 

class Solution {

public:

    int maxProfit(vector<int> &prices) {

        // Start typing your C/C++ solution below

        // DO NOT write int main() function

        if(prices.size() <=1)return 0;

        vector<int>::iterator iter;

        for(iter=prices.begin();iter!=prices.end()-1;++iter)

        {

            *iter = *(iter+1) - *iter;

        }

        prices.pop_back();

        vector<int>accum_forward;

        vector<int>accum_backward;

        int max = 0;

        int subMax = 0;

        for(iter=prices.begin();iter!=prices.end();++iter)

        {

            subMax += *iter;

            if(subMax > max)max=subMax;

            else

                if(subMax<0)subMax = 0;

            accum_forward.push_back(max);

        }

        vector<int>::reverse_iterator riter;

        max =0 ;

        subMax = 0;

        for(riter=prices.rbegin();riter!=prices.rend();++riter)

        {

            subMax +=*riter;

            if(subMax >max)max = subMax;

            else

                if(subMax<0)subMax=0;

            accum_backward.push_back(max);

        }

        max =0;

        int len = accum_forward.size();

        for(int i=0;i<len-1;++i)

        {

            if((accum_forward[i]+accum_backward[len-i-2])>max)    

                max = accum_forward[i]+accum_backward[len-i-2];

        }

        return max>accum_forward[len-1]?max:accum_forward[len-1];

    }

};

 

ps:做完题之后提交，发现老是AC不了，有个case总是解决不了，本来以为是自己代码写得有问题，检查了半天没发现错误，于是开始看别人怎么写，结果发现别人AC的代码也过不了，猜想可能系统还是做得不完善，应该是后台的线程相互干扰了，过了一段时间果然同样的代码又可以AC了。在这段过程中，看别人写的代码，发现了一个比我简洁一些的写法，虽然我么你的复杂度是一样的，但是此君代码量比我的小一点，以后学习学习，另外，一直不知道vector还可以预先分配大小，从这个代码里面也看到了，算是有所收获。附代码如下：

class Solution {

public:

    int maxProfit(vector<int> &prices) {

        // null check

        int len = prices.size();

        if (len==0) return 0;

        vector<int> historyProfit;

        vector<int> futureProfit;

        historyProfit.assign(len,0);

        futureProfit.assign(len,0);

        int valley = prices[0];

        int peak = prices[len-1];

        int maxProfit = 0;

        // forward, calculate max profit until this time

        for (int i = 0; i<len; ++i)

        {

            valley = min(valley,prices[i]);

            if(i>0)

            {

                historyProfit[i]=max(historyProfit[i-1],prices[i]-valley);

            }

        }

        // backward, calculate max profit from now, and the sum with history

        for (int i = len-1; i>=0; --i)

        {

            peak = max(peak, prices[i]);

            if (i<len-1)

            {

                futureProfit[i]=max(futureProfit[i+1],peak-prices[i]);

            }

            maxProfit = max(maxProfit,historyProfit[i]+futureProfit[i]);

        }

        return maxProfit;

    }

};