Introduction:
The given problem asks us to determine the time complexity of the most efficient algorithm for sorting an array A in descending order. The array A contains elements that are either 0 or 1. We need to choose the correct option among the given choices.

Explanation:
To sort the array A in descending order, we can use a counting sort algorithm. Counting sort is an efficient algorithm when the range of input values is small. In this case, the range is only 0 and 1, making counting sort a suitable choice.

Counting Sort Algorithm:
The counting sort algorithm works as follows:
1. Create an array count[] of size 2 to store the count of 0s and 1s.
2. Traverse the given array A and increment the count of the corresponding element in count[].
3. Modify the count[] array to store the cumulative sum of counts. The count[i] now contains the actual position of the element i in the sorted array.
4. Initialize an output[] array of the same size as the input array A.
5. Traverse the input array A from right to left. For each element A[i], find its correct position in the output[] array using the count[] array, decrement the count, and place the element in the output[] array.
6. The output[] array now contains the sorted elements in descending order.

Time Complexity Analysis:
1. Creating the count[] array and traversing the given array A to compute the count[] array takes O(n) time, where n is the size of the input array.
2. Modifying the count[] array to store the cumulative sum of counts can be done in O(1) time since the size of the count[] array is fixed.
3. Initializing the output[] array takes O(n) time.
4. Traversing the input array A from right to left and placing the elements in the output[] array takes O(n) time.
5. Therefore, the overall time complexity of the counting sort algorithm is O(n).

Conclusion:
The most efficient algorithm for sorting the array A in descending order is counting sort, which has a time complexity of O(n). Hence, the correct answer is option 'A'.