Space Complexity

Euler tour with entry-exit times uses $n$ positions for entry times. Each node occupies one entry position. Segment tree on this array uses $O(n)$ space (the tree has $4n$ nodes but that is still $O(n)$).

BIT uses $O(n)$ space directly. Total memory: $O(n)$ for the tree structure, $O(n)$ for flattened array, $O(n)$ for segment tree or BIT. All linear. For $n = 200,000$, you need around $3$ to $4$ megabytes total, well within typical memory limits.