Explain the difference between O1 vs On space complexities

The difference between $$O(1)$$ and $$O(n)$$ space complexities lies in how the memory usage of an algorithm scales with the size of the input.

Definition: $$O(1)$$ space complexity, also known as constant space complexity, means that the amount of memory required by the algorithm does not change with the size of the input. The memory usage remains constant regardless of how large the input is.
Example: Consider a function that swaps two variables. The memory required for this operation is fixed and does not depend on the size of the input data.
```
def swap(a, b):
    temp = a
    a = b
    b = temp
```
In this example, the function uses a constant amount of memory (for the variables a, b, and temp), so its space complexity is $$O(1)$$[1][2][6].

Definition: $$O(n)$$ space complexity, also known as linear space complexity, means that the amount of memory required by the algorithm grows linearly with the size of the input. If the input size doubles, the memory usage also doubles.
Example: Consider a function that creates a new list of the same size as the input list.
```
def create_list(n):
    new_list = [0] * n
    return new_list
```
In this example, if the input size n is 10, the function creates a list of 10 elements. If n is 100, it creates a list of 100 elements. Therefore, the memory usage grows linearly with the input size, making the space complexity $$O(n)$$[1][2][12].

Memory Usage: $$O(1)$$ space complexity uses a fixed amount of memory, while $$O(n)$$ space complexity uses memory that grows linearly with the input size.
Scalability: Algorithms with $$O(1)$$ space complexity are generally more scalable in terms of memory usage because they do not require additional memory as the input size increases. In contrast, algorithms with $$O(n)$$ space complexity may face memory limitations as the input size grows, especially for ve...

Explain the difference between O(1) vs O(n) space complexities