**Best Time to Buy and Sell Stock I**

Say you have an array for which the *i*^{th} element is the price of a given stock on day *i*.

If you were only permitted to complete at most one transaction (ie, buy one and sell one share of the stock), design an algorithm to find the maximum profit.

**Example**

Given array [3,2,3,1,2], return `1`

.

**Python**

Time complexity: O(N)

Space complexity: O(1)

class Solution: """ @param prices: Given an integer array @return: Maximum profit """ def maxProfit(self, prices): # write your code here if (not prices or len(prices) <= 1): return 0 minSoFar = prices[0] profit = 0 for v in prices[1:]: minSoFar = min(minSoFar, v) profit = max(profit, v - minSoFar) return profit

**Best Time to Buy and Sell Stock II**

Say you have an array for which the *i*^{th} element is the price of a given stock on day i.

Design an algorithm to find the maximum profit. You may complete as many transactions as you like (ie, buy one and sell one share of the stock multiple times). However, 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 [2,1,2,0,1], return `2`

.

**Java**

Time complexity: O(N)

Space complexity: O(1)

class Solution { /** * @param prices: Given an integer array * @return: Maximum profit * As a solution one can find sum of contiguous delta trades, where * 'delta trade' stands for buy-sell compound transaction. */ public int maxProfit(int[] prices) { // write your code here if (prices == null || prices.length <= 0){ return 0; } int profit = 0; for (int i = 1; i < prices.length; ++i){ profit += Math.max(0, prices[i] - prices[i-1]); } return profit; } }

**Best Time to Buy and Sell Stock III**

Say you have an array for which the *i*^{th} 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`

.

**Java**

Time complexity: O(N)

Space complexity: O(1)

class Solution { /** * @param prices: Given an integer array * @return: Maximum profit */ public int maxProfit(int[] prices) { // write your code here if (prices == null || prices.length == 0){ return 0; } int buyFirst = Integer.MIN_VALUE; int sellFirst = 0; int buySecond = Integer.MIN_VALUE; int sellSecond = 0; for (int i = 0; i < prices.length; ++i){ buyFirst = Math.max(buyFirst, -prices[i]); sellFirst = Math.max(buyFirst + prices[i], sellFirst); buySecond = Math.max(buySecond, sellFirst - prices[i]); sellSecond = Math.max(sellSecond, buySecond + prices[i]); } return sellSecond; } }