Best Time to Buy and Sell Stock I II III

Best Time to Buy and Sell Stock I II III

I

对于第一题，本质意义是求出数组中某两个元素（day[i],day[i]）的最大差值。但是，要求j>i

int maxProfit(vector<int> &prices) {
        if(prices.size() ==0)
            return 0;
        
        int min=prices[0], profit=0;
        for(int i=0; i<prices.size(); i++)
        {
            if(prices[i] - min > profit)
                profit = prices[i] - min;
                
            if(prices[i] < min)
                min = prices[i];
            
            
        }
        
        return profit;
    }

II

第二题是可以进行任意多次交易，那么对数组遍历，找到临时最小值和临时最大值。

int maxProfit(vector<int> &prices) {
        if (prices.size() == 0)
		return 0;

	int profit = 0, tmpMin=prices[0], tmpMax=prices[0];
	int n = prices.size();
	for (int i = 1; i < n; i++)
	{
	    //寻找比tmpMIN小的元素
		if (prices[i] < tmpMin)
		{
		    //比tmpMin小，则更新较小的
			tmpMin = prices[i];
		}
		else
		{
		    //比tmpMin大，则可以出手卖掉，并更新tmpMin
			profit += (prices[i]-tmpMin);
			tmpMin = prices[i];
		}
	}

	return profit;
    }

III

第三题比较复杂，只允许买卖两次，有两种方法。

其一，由于两次操作之间没有交互，即第一次买卖完成之后才能进行第二次的买卖，因此可以用分治法将[0...n]中取任意一个i，分别去求[0...i]和[i+1...n-1]的最大利润，那么两者之和就是两次操作的最大利润，但是这个算法的时间复杂度是O^2，超时了。

//取[m, n]之间的最大利润
int Profit1(vector<int>& prices, int m, int n)
{
	int size = prices.size();
	if(m >= size)
		return 0;

	int minPrice = prices[m], profit = 0;
	for (int i = m+1; i < n; i++)
	{
		if (prices[i] - minPrice > profit)
		{
			profit = prices[i] - minPrice;
		}

		if (prices[i] < minPrice)
		{
			minPrice = prices[i];
		}
	}

	return profit;
}

int maxProfit(vector<int> &prices)
{
	if(prices.size() == 0)
		return 0;

	int n = prices.size();
	int max1 = 0;
	for (int i = 1; i < n; i++)
	{
		int tmp1 = Profit1(prices, 0, i);		
		int tmp2 = Profit1(prices, i+1, n);
		if(tmp1 + tmp2 > max1)
			max1 = tmp1 + tmp2;
	}

	return max1;
}

方法二，DP，参考了一位网友的方法： http://blog.youkuaiyun.com/pickless/article/details/12034365

DP的关键是找出地推关系式

int maxProfit(vector<int> &prices)
{
	int n = prices.size();
	if(0==n || 1==n)
		return 0;

	int * l = new int[n];
	int * r = new int[n];
	memset(l, 0, sizeof(int) * n);
	memset(r, 0, sizeof(int) * n);


	int minPrice = prices[0];
	for (int i = 1; i < n; i++)
	{
		l[i] = prices[i] - minPrice > l[i-1]? prices[i] - minPrice : l[i-1];
		minPrice = prices[i] < minPrice ? prices[i] : minPrice;
	}

	int maxPrice = prices[n-1];
	for (int i = n-2; i >=0; i--)
	{
		r[i] = maxPrice - prices[i] > r[i+1] ? maxPrice - prices[i] : r[i+1];
		maxPrice = prices[i] > maxPrice ? prices[i] : maxPrice;
	}

	int profit = 0;
	for (int i = 0; i < n; i++)
	{
		profit = l[i] + r[i] > profit ? l[i] + r[i] : profit;
	}

	delete l;
	delete r;

	return profit;
}