The Two-Pointer Strategy in Algorithms

Feb 122 min read

Introduction

The two-pointer strategy is a powerful technique used in various algorithmic problems, especially those related to arrays and searching. It involves maintaining two different indices (or pointers) to traverse and process data efficiently. In this blog, we will explore the two-pointer strategy using a simple yet effective problem: maximizing profit from stock prices.

Understanding the Problem

Given a list of stock prices where each element represents the stock price on a given day, we need to determine the maximum possible profit from a single buy-sell transaction. The goal is to buy at a lower price and sell at a higher price that appears later in the list.

Implementing the Two-Pointer Strategy

Below is an optimized implementation using the two-pointer technique:

def max_profit(prices: list) -> int:
    min_price = float('inf')  # Set to infinity to ensure it updates correctly
    max_profit = 0  # Start with zero profit
    
    for price in prices:
        if price < min_price:
            min_price = price  # Update the minimum price
        
        max_profit = max(max_profit, price - min_price)  # Update max profit
    
    return max_profit

Explanation of the Code

Initialize Variables:
- min_price is initialized to infinity to ensure that any price in the list will be smaller, allowing it to be updated correctly.
- max_profit is set to zero, as initially, no profit is made.
Iterate Through the Prices:
- For each price in the list, check if it is the smallest encountered so far and update min_price accordingly.
- Compute the potential profit if the stock were sold at the current price and update max_profit if the new profit is greater.

Why This Approach Works

Efficient: This approach runs in O(n) time complexity, making it ideal for large datasets.
Simple: The logic is easy to follow without requiring additional memory, maintaining an O(1) space complexity.
Optimized Decision Making: By updating min_price dynamically and computing profits simultaneously, we avoid unnecessary nested loops.

Applications of Two-Pointer Strategy

This method can be adapted to various problems, such as:

Finding pairs with a given sum in a sorted array
Removing duplicates in an array
Merging sorted lists efficiently

Conclusion

The two-pointer strategy provides an elegant solution to problems involving array traversal. By keeping track of key values efficiently, we can solve problems optimally without unnecessary computations. Try applying this technique to different challenges, and you’ll find it an invaluable addition to your algorithmic toolkit!

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