Best Time to Buy and Sell Stock III Java

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).

The extension of of "Best Time to Buy and Sell Stock"

    Solve by DP Algo again

    this time we may complete at most two transaction instead

    of at most one transaction in previous problem of Best Time

    to Buy and Sell Stock. Think of in Big picture of problem in

    solve question by complete at most k transaction, k = 2.

    Best Time to Buy and Sell Stock III

    i: day i

    j: transaction time j that 1<=j<=k

    then we have DP formula:

    diff: Profit difference between previous and current day since at most we can do twice

            transaction a day

    Optimize Local: local[j]=Max(global[j-1]+max(diff,0), local[j]+diff) in day i-1

    Optimize Global: global[j]=Max(local[j],global[j])  in day i-1

    Time: O(N*k) k=2 in here => O(N)

    Space: O(k)

public class Solution {
public int maxProfit(int[] prices) {
if(prices.length==0) return 0;
int k=2; // k is at most 2 times
int local[]=new int[k+1];
int global[]=new int[k+1];
for(int i=0;i<prices.length-1;i++){ //days start from i-1
int diff=prices[i+1]-prices[i];
for(int j=k;j>=1;j--){
//optimize local value base on previous global[j-1] (first) transaction
local[j]=Math.max(global[j-1]+Math.max(diff,0),local[j]+diff);
global[j]=Math.max(local[j],global[j]);
}
}
return global[k];
}
}