Solution

Heap Sort is the most appropriate algorithm for a sorting task that requires minimal auxiliary space. It sorts an array by first building a heap data structure and then repeatedly extracting the maximum element to place it in the sorted order. Heap Sort operates in-place with a space complexity of O(1), making it efficient in terms of auxiliary space compared to algorithms like Merge Sort, which requires additional space. Why Other Options are Wrong: a) Merge Sort requires O(n) additional space for temporary arrays, making it less suitable for minimal space requirements. b) Quick Sort has an average space complexity of O(log n) due to recursion stack but is not as space-efficient as Heap Sort. c) Bubble Sort has a space complexity of O(1) but is inefficient in terms of time complexity compared to Heap Sort. e) Radix Sort, while efficient for certain data types, requires additional space for digit bins, making it less suitable for minimal space usage.