## Description

https://leetcode.com/problems/best-time-to-buy-and-sell-stock-ii/description/

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 (i.e., buy one and sell one share of the stock multiple times).

**Note:** You may not engage in multiple transactions at the same time (i.e., you must sell the stock before you buy again).

**Example 1:**

Input:[7,1,5,3,6,4]Output:7Explanation:Buy on day 2 (price = 1) and sell on day 3 (price = 5), profit = 5-1 = 4. Then buy on day 4 (price = 3) and sell on day 5 (price = 6), profit = 6-3 = 3.

**Example 2:**

Input:[1,2,3,4,5]Output:4Explanation:Buy on day 1 (price = 1) and sell on day 5 (price = 5), profit = 5-1 = 4. Note that you cannot buy on day 1, buy on day 2 and sell them later, as you are engaging multiple transactions at the same time. You must sell before buying again.

**Example 3:**

Input:[7,6,4,3,1]Output:0Explanation:In this case, no transaction is done, i.e. max profit = 0.

## Explanation

This is a follow-up question for Best Time to Buy and Sell Stock. The difference is that it allows multiple transactions.

A single for loop could solve the problem. If a price is greater than the previous price, add their difference to the max profit.

## Java Solution

public class Solution { public int maxProfit(int[] prices) { int maxProfit = 0; if (prices.length <= 1) { return maxProfit; } for (int i = 1; i < prices.length; i++) { if (prices[i] > prices[i - 1]) { maxProfit += prices[i] - prices[i - 1]; } } return maxProfit; } }

## Python Solution

```
class Solution:
def maxProfit(self, prices: List[int]) -> int:
max_profit = 0
if prices is None:
return max_profit
for i in range(1, len(prices)):
if prices[i] > prices[i - 1]:
max_profit += prices[i] - prices[i - 1]
return max_profit
```

- Time complexity : O(N).
- Space complexity : O(1).

I found that solution is very popular and helpful : https://www.youtube.com/watch?v=HOLeZ5ct2h4

How did you find the logic that it just the sum of the difference? can you elaborate?