This article presents an algorithmic problem with practical value for stock market analysis. For instance, suppose you are trading the cryptocurrency Ethereum.
How much profit in dollars can you make by buying low and selling high based on historical data?
Maximum Profit Basic Algorithm
The max profit algorithm calculates the maximum profit you’d obtain by buying low and selling high:
# Profit of a single # buying low and selling high def maximumProfit(A): m = 0 for i in range(0, len(A)): for j in range (i + 1, len(A)): m = max(m, A[j] - A[i]) return m # Ethereum daily prices in Dec 2017 ($) prices = [455, 460, 465, 451, 414, 415, 441] print(maximumProfit(prices)) # 27
Exercise: Take a guess--what is the output of this code snippet?
Maximum Profit Algorithm Description
maximumProfit takes an input sequence A, e.g. a week of Ethereum prices in December 2017. It returns the largest profit from buying low and selling high.
The algorithm works as follows:
It iterates over all sequence indices
i, i.e., the buying points, and over all sequence indices
j>i, i.e., the selling points.
For each buying/selling pair
(i,j), it calculates the profit as the difference between the prices at the selling and the buying points, i.e.,
profit maintains the largest possible profit: $27 on $414 invested capital.
💡 Algorithmic Complexity: This implementation has quadratic runtime complexity as you have to check O(n*n) different combinations of buying and selling points. You’ll learn about a linear-runtime solution later.
Alternative Maximum Profit Algorithm with Slicing
Here’s a slight variant of the above algorithm:
# Profit of a single # buying low and selling high def maximumProfit(A): m = 0 for i in range(0, len(A)-1): buy, sell = A[i], max(A[i+1:]) m = max(m, sell-buy) return m # Ethereum daily prices in Dec 2017 ($) prices = [455,460,465,451,414,415,441] print(maximumProfit(prices)) # 27
Maximum Profit Algorithm with Linear Runtime in Python
The following algorithm has linear runtime complexity and is much more efficient for a single-sell max-profit algorithm.
def maximumProfit(A): buy, m = 0, 0 for i in range(len(A)): buy = min(buy, A[i]) profit = A[i] - buy m = max(m, profit) return m # Ethereum daily prices in Dec 2017 ($) prices = [455,460,465,451,414,415,441] print(maximumProfit(prices)) # 27
The maximum profit in the above algorithm of buying low and selling high for the list of prices
You buy at $414 and sell at $441 which leads to a profit of $441-$414=$27.
Maximum Profit Python Puzzle
Before I show you the solution to the max profit example in the code—can you solve this code puzzle on our interactive Python puzzle app?
Click to solve the exercise and test your Python skills!
Are you a master coder? Test your skills now!
Would you enjoy becoming the best Python coders in your environment? Here’s a decision you won’t regret: join my Python email academy. It’s the most comprehensive Python email academy in the world!
While working as a researcher in distributed systems, Dr. Christian Mayer found his love for teaching computer science students.
To help students reach higher levels of Python success, he founded the programming education website Finxter.com. He’s author of the popular programming book Python One-Liners (NoStarch 2020), coauthor of the Coffee Break Python series of self-published books, computer science enthusiast, freelancer, and owner of one of the top 10 largest Python blogs worldwide.
His passions are writing, reading, and coding. But his greatest passion is to serve aspiring coders through Finxter and help them to boost their skills. You can join his free email academy here.