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).

标签: Array Dynamic Programming

分析:动态规划,设left[i]表示0-i天的最大利润,right[j]表示j-n-1天的最大利润,所以状态方程为:

left[i]=max(left[i-1],prices[i]-minleft);  minleft表示0-i天的最低价

right[j]=max(right[j+1],maxright-prices[j]);  maxright表示j-n-1天的最高价;

由于只可以买卖两次,并且在第二次买进是必须把第一次的卖掉,所以最大利润为max(left[i]+right[i]);

参考代码:

public class Solution {
public int maxProfit(int[] prices) {
int len=prices.length;
if(len<2)
return 0;
int left[]=new int[len];
int right[]=new int[len];
int minleft=prices[0];
left[0]=0;
for(int i=1;i<len;i++){
minleft=Math.min(minleft, prices[i]);
left[i]=Math.max(left[i-1], prices[i]-minleft);
}
int maxright=prices[len-1];
right[len-1]=0;
for(int j=len-2;j>=0;j--){
maxright=Math.max(maxright, prices[j]);
right[j]=Math.max(right[j+1], maxright-prices[j]);
}
int maxProfit=left[0]+right[0];
for(int i=0;i<len;i++){
maxProfit=Math.max(maxProfit, left[i]+right[i]);
}
return maxProfit;
}
}

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