# 122\_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 (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:**

```
Input:
 [7,1,5,3,6,4]

Output:
 7

Explanation:
 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
```

## Solution:

**Idea**:

* catch all the valley and peak, add all the slope into profit
  * loop over all the elements, initiate `minprice` and `maxprice` as the first element
    * if the next element is larger than `maxprice` , update `maxprice` with the current element
    * if the next element is smaller than `maxprice,` a new valley starts. Add the last profit into total profit and update `minprice` and `maxprice` be the current element.

**Time Complexity**: $$O(n)$$

**Space Complexity**: $$O(1)$$

```python
def maxProfit(self, prices):
    """
    :type prices: List[int]
    :rtype: int
    """
    if len(prices) < 2 :
        return 0

    min_price = max_price = prices[0]
    profit = 0
    for i in range(1, len(prices)) :
        if prices[i] < max_price :
            profit += max_price - min_price
            min_price = max_price = prices[i]
        else :
            max_price = prices[i]
    profit += max_price - min_price
    return profit
```


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