The max_profit function calculates the maximum possible profit from a list of stock prices by iterating through the list and adding up the differences between each pair of consecutive prices. The function returns 0 as the total profit if the input list is empty, contains only one price, or has prices in descending order.

Cell 8

def max_profit(prices):
    """Find maximum profit possible."""
    profit = 0
    for i in range(len(prices)-1):
        if prices[i+1] > prices[i]:
            profit += prices[i+1] - prices[i]
    return profit

assert max_profit([]) == 0
assert max_profit([100]) == 0
assert max_profit([1,6,5,2,8,1,4,5]) == 15
assert max_profit(range(100, 0, -1)) == 0
print('All passed')

def max_profit(prices):
    """
    Find the maximum possible profit from a list of prices.

    Args:
        prices (list): A list of prices where each price is a positive integer.

    Returns:
        int: The maximum possible profit.

    Raises:
        ValueError: If prices is empty or contains non-positive values.
    """
    if not prices:
        raise ValueError("Prices cannot be empty")
    for price in prices:
        if price <= 0:
            raise ValueError("All prices must be positive")
    
    return sum(max(0, prices[i+1] - prices[i]) for i in range(len(prices)-1))

assert max_profit([]) == 0
assert max_profit([100]) == 0
assert max_profit([1,6,5,2,8,1,4,5]) == 15
assert max_profit(range(100, 0, -1)) == 0

# TODO: Implement a more efficient solution using a single pass through the prices list
#       (currently has a time complexity of O(n^2))

Code Breakdown

Function Definition

def max_profit(prices):

• This line defines a function named max_profit that takes one argument: prices.

Function Documentation

"""Find maximum profit possible."""

• This is a docstring that provides a brief description of the function's purpose.

Variable Initialization

profit = 0

• This line initializes a variable named profit and sets its value to 0. This variable will be used to store the total profit.

Loop Through Prices

for i in range(len(prices)-1):

• This line begins a loop that will iterate over the indices of the prices list.
• The -1 is used to prevent an IndexError when accessing prices[i+1].

Calculate Profit

if prices[i+1] > prices[i]:
    profit += prices[i+1] - prices[i]

• Within the loop, this line checks if the price at the next index (prices[i+1]) is greater than the current price (prices[i]).
• If the condition is true, it calculates the profit by subtracting the current price from the next price and adds it to the total profit.

Return Total Profit

return profit

• After the loop completes, this line returns the total profit.

Test Cases

assert max_profit([]) == 0
assert max_profit([100]) == 0
assert max_profit([1,6,5,2,8,1,4,5]) == 15
assert max_profit(range(100, 0, -1)) == 0
print('All passed')

• These lines test the max_profit function with different input scenarios:
  • An empty list.
  • A list with a single price.
  • A list with multiple prices.
  • A list with prices in descending order.
• If all assertions pass, the message "All passed" is printed.