Best Time to Buy and Sell Stock III

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) {
if (prices == null || prices.length < 2) return 0;
int[] forwardMax = new int[prices.length];
int[] backwardMax = new int[prices.length];

int buyPoint = prices[0];
int sellPoint = prices[0];
int maxProfit = 0;
forwardMax[0] = 0;

for (int i = 1; i < prices.length; i++) {
if (prices[i] < buyPoint) {
buyPoint = prices[i];
}
forwardMax[i] = Math.max(prices[i] - buyPoint, forwardMax[i - 1]);
}
sellPoint = prices[prices.length - 1];
backwardMax[prices.length - 1] = 0;

for (int i = prices.length - 2; i >= 0; i--) {
if (prices[i] > sellPoint) {
sellPoint = prices[i];
}
backwardMax[i] = Math.max(sellPoint - prices[i], backwardMax[i + 1]);
}

int max = 0;
for (int i = 0; i < prices.length - 1; i++) {
if (forwardMax[i] + backwardMax[i + 1] > max) {
max = forwardMax[i] + backwardMax[i + 1];
}
}
if (max < Math.max(forwardMax[prices.length - 1], backwardMax[0])) {
max = Math.max(forwardMax[prices.length - 1], backwardMax[0]);
}
return max;
}
}