in LintCode Algorithm Array ~ read.

Best Time to Buy and Sell Stock III

LintCode-151.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.

Notice: You may not engage in multiple transactions at the same time (ie, you must sell the stock before you buy again).

Example: Given an example [4,4,6,1,1,4,2,5], return 6.

class Solution {  
    /**
     * @param prices: Given an integer array
     * @return: Maximum profit
     */
    public int maxProfit(int[] prices) {
        if (prices == null || prices.length < 2) {
            return 0;
        }

        int[] left = new int[prices.length];
        int[] right = new int[prices.length];

        left[0] = 0;
        int min = prices[0];

        // DP from left to right
        for (int i = 1; i < prices.length; i++) {
            min = Math.min(min, prices[i - 1]);
            left[i] = Math.max(left[i - 1], prices[i] - min);
        }

        // DP from right to left
        right[prices.length - 1] = 0;
        int max = prices[prices.length - 1];

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

        int profit = 0;
        for (int i = 0; i < prices.length; i++) {
            profit = Math.max(profit, left[i] + right[i]);
        }

        return profit;
    }
}

Hope this helps,
Michael