# 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