When analyzing the space complexity of an algorithm, we are interested in how much additional memory is required to perform the given task. In the case of the Selection Sort algorithm, it is an in-place sorting algorithm, meaning that it sorts the elements by swapping them within the given array itself, without requiring any additional memory allocation for intermediate results.

The space complexity of Selection Sort can be expressed as O(1), which indicates constant space usage. This is because the amount of additional space required by the algorithm does not depend on the size of the input array. Whether the array contains 10 or 1000 elements, the space requirements will remain the same.

The algorithm achieves this constant space complexity by performing the sorting operation directly on the input array, using only a few temporary variables to keep track of the current minimum value and to perform swapping. The only memory required is for these temporary variables, which have a fixed size regardless of the array size.

Let’s take a look at the implementation of Selection Sort in Python to further understand its space complexity:

def selection_sort(arr):
    n = len(arr)
    for i in range(n):
        min_index = i
        for j in range(i+1, n):
            if arr[j] < arr[min_index]:
                min_index = j
        arr[i], arr[min_index] = arr[min_index], arr[i]

As you can see, the algorithm uses the input array arr to perform the sorting operation. The temporary variable min_index is used to keep track of the index of the current minimum element, and the swapping operation is done directly on the array.

In conclusion, the space complexity of Selection Sort is O(1) as it does not require any additional memory allocation that depends on the size of the input array. This makes it an efficient choice for sorting large arrays with limited memory resources.

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