# 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).

## Solution

dp. max profit = max { l2r[0...i] + r2l[i+1...N-1] }. 0 <= i <= N-1

## Code

``````int maxProfit(int[] prices){
if (prices == null || prices.length < 2) {
return 0;
}

//highest profit in 0 ... i
int[] left = new int[prices.length];
int[] right = new int[prices.length];

// DP from left to right
left[0] = 0;
int min = prices[0];
for (int i = 1; i < prices.length; i++) {
min = Math.min(min, prices[i]);
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]);
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;
}
``````