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).

public class Solution {
    public int maxProfit(int[] prices) {
        int len = prices.length;
        if(len == 0){
            return 0;
        }
        int f[] = new int[len];
        int b[] = new int[len];
        f[0] = b[len-1] = 0;
        
        int minf = prices[0];        
        int maxb = prices[len-1];
        int ret = 0;
        for(int i=1; i<len; i++){
            int j = len-1-i;
            f[i] = Math.max(f[i-1], prices[i]-minf);
            b[j] = Math.max(b[j+1], maxb - prices[j]);
            minf = Math.min(minf, prices[i]);
            maxb = Math.max(maxb, prices[j]);
            ret = Math.max(f[i]+b[i], ret);
        }
        for(int i = 0; i<len; i++){
            ret = Math.max(f[i]+b[i], ret);
        }
        return ret;
    }
}