Stock Span Problem: Optimal Solutions Using Stack and Queue Algorithms

The Stock Span Problem is a classic algorithmic challenge that often pops up in coding interviews and competitive programming contests. It serves as a brilliant example of how Stack and Queue algorithms can simplify seemingly complex problems. In this blog, we’ll explore the fundamentals of the Stock Span Problem, understand why stacks and queues are the go-to solutions, and dive into code implementations for optimal performance.

What is the Stock Span Problem?

The Stock Span Problem revolves around calculating the span of stock prices over consecutive days. The span of a stock’s price on a particular day is defined as the number of consecutive days leading up to the current day where the price of the stock was less than or equal to its price on the current day.

Problem Statement Example:

Imagine you have stock prices for n consecutive days:
[100, 80, 60, 70, 60, 75, 85]

The span for each day would be:
[1, 1, 1, 2, 1, 4, 6]

• Day 1 (100): No previous prices, so span = 1
• Day 2 (80): Price dropped compared to Day 1, span = 1
• Day 3 (60): Price dropped again, span = 1
• Day 4 (70): Higher than Day 3 but less than Day 2, span = 2
• Day 5 (60): Same situation as Day 3, span = 1
• Day 6 (75): Higher than Days 5, 4, 3, span = 4
• Day 7 (85): Higher than all previous days, span = 6

Also Read: What Are Python’s Built-in Data Types? A Comprehensive Guide

Brute Force Approach: Why It’s Not Optimal

A straightforward way to solve the Stock Span Problem is using a nested loop to compare each day’s price with all previous prices. While this method is easy to implement, it is inefficient for large datasets.

Time Complexity:

• O(n²) because for each day, we might compare it with all preceding days.

Drawbacks:

• High computational cost for large inputs.
• Not scalable for real-world financial data.

Optimal Solutions for Stock Span Problem Using Stack and Queue Algorithms

Why Use Stacks and Queues?

• Stacks allow us to keep track of previous elements efficiently in a Last In, First Out (LIFO) manner.
• Queues can be handy in managing elements in a First In, First Out (FIFO) structure, though they are less commonly used for this specific problem compared to stacks.

Let’s break down how stacks can be utilized to optimize the Stock Span Problem.

Also Read: How to optimize performance of Python code?

Using Stack for an Optimal Solution

The stack-based solution is both efficient and elegant. Here’s how it works:

1. Initialize an empty stack to store the indices of days.
2. Iterate through the stock prices.
3. For each price, pop from the stack until the stack is empty or the top of the stack has a price greater than the current price.
4. If the stack is empty, the span is the current day index plus one.
5. If the stack is not empty, the span is the difference between the current day index and the index of the last higher price.
6. Push the current day index onto the stack.

Algorithm in Steps:

1. Initialize a stack and result array.
2. For each price:
   • While the stack is not empty and the price at the top of the stack is less than or equal to the current price, pop the stack.
   • If the stack is empty, the span is the current index + 1.
   • If the stack is not empty, the span is the difference between the current index and the index at the top of the stack.
   • Push the current index onto the stack.

Code Implementation in Python:

def calculate_stock_span(prices):
    n = len(prices)
    span = [0] * n
    stack = []

    for i in range(n):
        while stack and prices[stack[-1]] <= prices[i]:
            stack.pop()

        if not stack:
            span[i] = i + 1
        else:
            span[i] = i - stack[-1]

        stack.append(i)

    return span

# Example usage:
prices = [100, 80, 60, 70, 60, 75, 85]
print(calculate_stock_span(prices))  # Output: [1, 1, 1, 2, 1, 4, 6]

Time Complexity:

• O(n) since each element is pushed and popped at most once.

Space Complexity:

• O(n) due to the auxiliary stack.

Can Queues Be Used for the Stock Span Problem?

While queues are not the typical choice for solving the Stock Span Problem, they can be used for stream-based solutions or scenarios where you need to process data in real-time. However, using queues might complicate the logic unnecessarily compared to stacks.

Also Read: What is the Difference Between Deep Copy and Shallow Copy in Python?

Real-World Applications of the Stock Span Problem

Understanding and solving the Stock Span Problem has practical applications in:

• Financial Market Analysis: Identifying trends in stock prices over time.
• Data Stream Processing: Handling real-time data in systems like stock exchanges.
• Algorithmic Trading: Automating trading strategies based on span calculations.

Common Mistakes to Avoid

• Ignoring Edge Cases: Always test with different patterns like monotonically increasing or decreasing prices.
• Incorrect Stack Operations: Ensure you’re correctly popping and pushing indices, not values.
• Overcomplicating with Queues: While theoretically possible, queues often add unnecessary complexity for this problem.

FAQs

What is the Stock Span Problem?
The Stock Span Problem calculates how many consecutive previous days a stock price was less than or equal to today’s price.

Why are stacks used in the Stock Span Problem?
Stacks efficiently keep track of indices in a LIFO manner, allowing for quick comparisons and optimal span calculations.

Can queues be used to solve the Stock Span Problem?
While possible, queues are not the most efficient tool for this problem as they complicate the logic compared to stacks.

What is the time complexity of the stack-based solution?
The time complexity is O(n), as each element is pushed and popped only once.

How does the Stock Span Problem apply to real-world scenarios?
It’s widely used in financial markets to analyze price trends and inform trading decisions.

What are some variations of the Stock Span Problem?
Variations include calculating spans in streaming data or modifying the problem to consider greater-than conditions.

Conclusion

The Stock Span Problem is an excellent demonstration of how Stack and Queue algorithms can streamline problem-solving in computer science. While the stack-based approach provides an optimal and efficient solution, understanding both methodologies can deepen your algorithmic skills. Whether you’re preparing for coding interviews or exploring algorithmic trading, mastering this problem will give you a solid edge.