Have you ever wondered how a simple algorithm can unravel the logic behind nature, like the predictable (and sometimes unpredictable) fall of apples? 🍎
🔮 Problem Statement
Imagine you are the lucky owner of a land that extends from position s to position t on a horizontal axis. Within your property, rests a venerable apple tree. From time to time, an apple detaches from the tree, influenced by the wind or simply by the law of gravity.
As a diligent gardener (and aspiring data scientist), you record each fall. You note the distance and direction in which the apple fell from the tree: a negative number indicates that it fell to the left, while a positive number indicates that it fell to the right.
Your mission is to write a function that, given the position of the tree p, the boundaries of the land s and t, and an array apples[n] with the distances of each fall, determines how many apples ended up within the limits of your prized land.
Parameters:
s: Left boundary of your land (integer).t: Right boundary of your land (integer).p: Position of the apple tree (integer).apples[n]: Array with the distances of the apple falls (array of integers).
Return Value:
- Number of apples that fell within your land (integer).
Example:
>>> counting_apples(2, 10, 9, [5, -7, 10, 1])
2In this example, the land extends from 2 to 10. The apple tree is at position 9. Of the apples that fell, only two landed within the land: the one that fell 1 unit to the right (final position 10) and the one that fell -7 units to the left (final position 2). The apple that fell 5 units to the right (final position 14) and the one that fell 10 units to the right (final position 19) were outside the land.
🧩 Step-by-Step Solution
To solve this problem, we rely on the power of higher-order functions and lambda functions in Python, allowing us to create concise and readable code.
First, we use the filter() function. This function is like a smart sieve that reviews each element of our distance list (apples) and decides whether it should pass to the next stage based on a condition:
filter(lambda apple: s <= p + apple <= t, apples)Here, the lambda function acts as our selection criterion. For each apple (distance), we calculate the final position where the apple fell (p + apple). Then, we check if this position is within the limits of our land (s <= p + apple <= t). If the apple fell within the land, the lambda function returns True, and the apple’s distance passes to the next stage. Otherwise, it returns False, and the apple is discarded.
Next, we convert the resulting iterator from filter() into a list:
list(filter(lambda apple: s <= p + apple <= t, apples))This gives us a list with only the distances of the apples that fell within the land. Finally, we use the len() function to count the number of elements in this list, which represents the total number of apples that landed within our land.
len(list(filter(lambda apple: s <= p + apple <= t, apples)))Complete Solution:
def counting_apples(s, t, p, apples):
"level: easy; points: 2"
return len(list(filter(lambda apple: s <= p + apple <= t, apples)))🧠 Key Concepts
This problem allows us to explore the power of higher-order functions and lambda functions in Python. Higher-order functions are functions that can receive other functions as arguments or return functions as results. This allows us to create more flexible and modular code. In our case, filter() is a higher-order function that receives a lambda function as an argument.
Lambda functions, also known as anonymous functions, are functions that are defined inline and do not have an associated name. They are ideal for situations where we need a simple function for a single use, as in the case of our filter.
Did you know that the filter() function in Python returns an iterator, not a list directly? This is more memory efficient, as it only calculates the elements that meet the condition as they are needed. However, to obtain the length, we must first convert the iterator to a list.
💫 Final Thoughts
This problem, although simple, illustrates the power of functional programming in Python. We could further optimize this code by avoiding the conversion to a list if we only need to count the elements. We could use sum(1 for apple in apples if s <= p + apple <= t) to iterate over the array and add 1 for each apple that falls within the range.
It is important to remember that code readability is crucial. Although there are more concise ways to write the solution, it is important to choose the option that is easier to understand and maintain.
I hope this journey through the apple orchard has been instructive! 🌳 If you enjoyed this type of analysis and want to continue exploring the fascinating world of software development, I invite you to explore other articles on my blog. Don’t miss the opportunity to continue learning and improving your skills!