Leetcode Best Time to Buy and Sell Stock III

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).

1 兩段分段思想
2 前往後，後往前都可以處理數列的思想

時間復雜度是O(n)，不掌握這種思想是很難做出來的。

class Solution {
public:
    int maxProfit(vector &prices) 
	{
		vector profit(prices.size()+1);

		int buy = INT_MAX;
		for (int i = 0; i < prices.size(); i++)
		{
			if (prices[i] < buy) buy = prices[i];
			else profit[i+1] = max(profit[i], prices[i]-buy);
		}

		int sale = INT_MIN , max_profit = 0, res = 0;
		for (int i = prices.size() - 1; i >= 0 ; i--)
		{
			if (prices[i] > sale) sale = prices[i];
			else max_profit = max(max_profit, sale - prices[i]);
			profit[i+1] = profit[i+1]+ max_profit;
			res = max(profit[i+1], res);
		}
		return res;
	}
};