The Merge Sort algorithm is a classic example of the Divide and Conquer paradigm in algorithm design. It follows the following steps:

1. Divide: The unsorted array is divided into two halves until each subarray contains only one element.

2. Conquer: Each subarray is recursively sorted.

3. Combine: The sorted subarrays are merged back together to obtain the final sorted array.

The complexity analysis of Merge Sort involves considering the time complexity and space complexity.

Time Complexity:

- Best case: Merge Sort has a consistent time complexity of O(n log n) for all cases, including the best case. This is because it always divides the array into halves and recursively sorts them. The merging step takes O(n) time for each level of recursion, and there are log n levels of recursion.

- Worst case: The worst-case time complexity of Merge Sort is also O(n log n). This occurs when the array is in reverse order or contains duplicate elements. In such cases, each level of recursion still takes O(n) time for merging, and there are log n levels of recursion.

- Average case: The average-case time complexity of Merge Sort is O(n log n) as well, considering that the algorithm consistently divides the array into halves and merges them back together.

Space Complexity:

Merge Sort has a space complexity of O(n) in the worst case. This is because it requires additional space to store the merged subarrays during the merging step. The space required is proportional to the size of the input array.

In conclusion, Merge Sort has a time complexity of O(n log n) in all cases (best, worst, and average) and a space complexity of O(n) in the worst case. It is an efficient sorting algorithm, especially for large datasets, and its performance remains consistent regardless of the initial order of the array.

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