Consider how counting sort traditionally uses O(n) extra space for the count array and how you might simulate this with constant space by leveraging the input array itself or mathematical properties of the data.

Explore the possibility of using the input array's indices to store cumulative counts or partial sums, ensuring that the original values can still be reconstructed during the sorting process without additional storage.

Investigate whether the problem constraints allow for assumptions about the range of input values (e.g., bounded integers) that could enable a modified counting sort to operate in-place by encoding counts within the array elements themselves, such as using bit manipulation or modular arithmetic.