Say you have an array for which the ith 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 1: Input: 7, 1, 5, 3, 6, 4 Output: 5 max. difference  61  5 not 71  6, as selling price needs to be larger than buying price Example 2: Input: 7, 6, 4, 3, 1 Output: 0 In this case, no transaction is done, i.e. max profit  0. On2 time :type prices: Listint :rtype: int On time input: 7, 1, 5, 3, 6, 4 diff : X, 6, 4, 2, 3, 2 :type prices: Listint :rtype: int
# O(n^2) time
def max_profit_naive(prices):
    """
    :type prices: List[int]
    :rtype: int
    """
    max_so_far = 0
    for i in range(0, len(prices) - 1):
        for j in range(i + 1, len(prices)):
            max_so_far = max(max_so_far, prices[j] - prices[i])
    return max_so_far


# O(n) time
def max_profit_optimized(prices):
    """
    input: [7, 1, 5, 3, 6, 4]
    diff : [X, -6, 4, -2, 3, -2]
    :type prices: List[int]
    :rtype: int
    """
    cur_max, max_so_far = 0, 0
    for i in range(1, len(prices)):
        cur_max = max(0, cur_max + prices[i] - prices[i-1])
        max_so_far = max(max_so_far, cur_max)
    return max_so_far
