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[LeetCOde][Java] Best Time to Buy and Sell Stock III

题目:

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).

算法分析:

利用通用的算法《Best Time to Buy and Sell Stock IV》 将k变为2 就ok 

AC代码:

<span style="font-family:Microsoft YaHei;font-size:12px;">public class Solution
{
    public int maxProfit(int[] prices) 
    {
        return maxProfit(2,prices);
    }
    public int maxProfit(int k, int[] prices) 
    {
       if(prices==null || prices.length==0)
            return 0;
        if(k>prices.length)//k次数大于天数时,转化为问题《Best Time to Buy and Sell Stock II》--无限次交易的情景 
        {
            if(prices==null)
                return 0;
            int res=0;
            for(int i=0;i<prices.length-1;i++)
            {
                int degit=prices[i+1]-prices[i];
                if(degit>0)
                    res+=degit;
            }
            return res;
        }
        /*
      定义维护量:
      global[i][j]:在到达第i天时最多可进行j次交易的最大利润。此为全局最优
      local[i][j]:在到达第i天时最多可进行j次交易而且最后一次交易在最后一天卖出的最大利润。此为局部最优
      定义递推式:
      global[i][j]=max(global[i-1][j],local[i][j]);即第i天没有交易,和第i天有交易
      local[i][j]=max(global[i-1][j-1]+max(diff,0),local[i-1][j]+diff)  diff=price[i]-price[i-1];
       */
        int[][] global=new int[prices.length][k+1];
        int[][] local=new int[prices.length][k+1];
        for(int i=0;i<prices.length-1;i++)
        {
            int diff=prices[i+1]-prices[i];
            for(int j=0;j<=k-1;j++)
            {
                local[i+1][j+1]=Math.max(global[i][j]+Math.max(diff,0),local[i][j+1]+diff);
                global[i+1][j+1]=Math.max(global[i][j+1],local[i+1][j+1]);
            }
        }
        return global[prices.length-1][k];
    }
}</span>

[LeetCOde][Java] Best Time to Buy and Sell Stock III