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Discover how recursion works in Python with an in-depth explanation of how coins are added in a coin change problem.
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Understanding the Sequence of Execution in Recursive Python Functions

In programming, particularly in Python, recursion can sometimes become a tricky concept to grasp. One common question that arises is about the order in which lines of code are executed, especially when dealing with recursive function calls. For instance, consider a scenario where we need to make change for an amount greater than or equal to 24 using only coins of 5 and 7. In this guide, we’ll unravel the mystery behind the execution order of a specific recursive function, clarifying how appending values works within this framework.

The Problem Statement

Let’s take a closer look at a piece of code that attempts to solve the coin change problem:

[[See Video to Reveal this Text or Code Snippet]]

Upon execution of the function change(34), the output generated is [5, 5, 7, 7, 5, 5]. However, there’s a crucial question: How does the coins.append(5) line get executed in relation to the recursion?

Breaking Down the Execution Flow

To clarify this, let's visualize what happens during the execution of change(34) step by step:

First Call change(34):

The code checks the conditions until it reaches coins = change(29). Here, it makes the first recursive call with an updated amount of 29.

Second Call change(29):

This again follows the same pattern and calls change(24). This signifies we are still resolving until we hit a base case.

Third Call change(24):

Here, the base case is met, and the function returns [5, 5, 7, 7]. This forms the list of coins for the amount 24.

Returning to change(29):

After it receives the list from the third call, it proceeds to execute the line coins.append(5). Now the coins list is updated to [5, 5, 7, 7, 5], which includes the newly appended 5.

Returning to change(34):

Finally, the changed list [5, 5, 7, 7, 5] from the second call has the append(5) line executed for the first call too, resulting in the final output [5, 5, 7, 7, 5, 5].

Important Notes on Recursion

Independent Variables: Each time the function is called, a new independent coins variable is created for that call. This prevents overlaps or conflicts between different recursive instances.

The Base Case: It’s crucial to remember that each recursive function needs a base case to avoid infinite recursion. In this snippet, we currently lack a handling mechanism for amounts 23 or 28, potentially leading to assertion errors. Without appropriate base cases, your function may not behave as expected when certain inputs are given.

Conclusion

Understanding recursion may seem daunting at first, but by breaking down each layer of the function and observing how each call interacts with one another, we can clarify how operations like append utilize separate instances of variables. To effectively use recursion in Python, ensure you have all necessary base cases reached and remember the unique nature of variables in each recursive layer. As you practice these principles, you’ll find that mastering recursion opens up a whole new realm of possibilities in coding!