The stock span problem is a popular algorithmic problem in the field of stock market trading. It involves calculating the span of stock prices for a given period of time. The stock span is defined as the maximum number of consecutive days (starting from the current day) for which the price of a stock is less than or equal to its price on the current day.
To solve this problem, we can use a specific data structure called a stack. In computer science, a stack is an abstract data type that follows the Last-In-First-Out (LIFO) principle. It allows two main operations: push, which adds an element to the top of the stack, and pop, which removes and returns the top element from the stack.
The stack data structure is particularly useful in solving problems where elements need to be processed in a specific order. In the case of the stock span problem, we can utilize a stack to keep track of previous stock prices and their respective spans.
Let’s take a closer look at how it works:
1. Create an empty stack and initialize an array called span with all elements set to 1. 2. Start iterating through each stock price in chronological order.
3. For each stock price, do the following:
- Push its index onto the stack.
- Pop elements from the stack as long as:
- The stack is not empty.
- The price at the index on top of the stack is less than or equal to the current price.
- Add 1 plus the difference between its index and either the index on top of the stack or -1, to the span array at the current index.
- Push the current index onto the stack.
4. Finally, return the span array.
Implementation in Python:
stack = 
span =  * len(prices) # Initialize span with all elements set to 1
for i, price in enumerate(prices):
while stack and prices[stack[-1]] <= price: stack.pop() span[i] = i - stack[-1] if stack else i + 1 stack.append(i) return span ```
Let’s consider an example to understand how this algorithm works. Suppose we have a list of stock prices for a week: [100, 80, 60, 70, 60, 75, 85]. The corresponding spans would be: [1, 1, 1, 2, 1, 4, 6].
Here’s how it is calculated step by step:
– For the first price (100), there are no previous prices to compare it with. So its span is always equal to 1. – For the second price (80), it is smaller than the previous price (100). So its span is also equal to 1. – For the third price (60), it is smaller than both previous prices (100 and 80). So its span is again equal to 1. – For the fourth price (70), it is greater than the third price (60). Thus we need to look back and count how many consecutive days had prices less than or equal to 70.
In this case, it is just the third price (60). So the span becomes 2. – For the fifth price (60), it is smaller than the fourth price (70). So its span is equal to 1. – For the sixth price (75), it is greater than the fifth price (60). We count two consecutive days with prices less than or equal to 75, which are the fifth and sixth prices. Hence, the span becomes 4. – Finally, for the seventh price (85), we count all previous prices because they are all less than or equal to 85. Therefore, the span becomes 6.
The stock span problem can be efficiently solved using a stack data structure. By leveraging its LIFO property, we can keep track of previous stock prices and calculate their respective spans. This algorithm has a time complexity of O(n) since each stock price is processed only once.
Remember to consider using a stack whenever you encounter problems that require processing elements in a specific order or retrieving elements based on certain conditions. The stack data structure can be a powerful tool in your algorithmic arsenal!