Best Time to Buy and Sell Stock III

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).

 

Code:

Method1:

class Solution {
public:
    int maxProfit(vector<int> &prices) {
        int oneTry=0,oneHis=0,twoTry=0,twoHis=0; //Try: attempt to buy; His: the max-profit record; One/Two: one/two transaction(s)
        int n = prices.size() - 1;
        for (int i=0;i<n;i++){ 
            int diff = prices[i+1] - prices[i];
            if(i>0){
                twoTry = max(twoTry, oneHis) + diff;
                twoHis = max(twoTry,twoHis); // the max-profit by totally two transactions
            }
            oneTry = max(oneTry, 0) + diff;
            oneHis = max(oneTry,oneHis); // the max-profit by totally one transaction
        }
        return max(oneHis,twoHis);
    }
};

 

Method2:

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;
    }
};