Compute moving and weighted averages from a stream

You are processing a stream of numeric events (e.g., user activity counts). You are given a fixed window size X.

Part 1: Moving average over last X values

Design a data structure / function that supports:

• next(value) -> avg

where avg is the average of the most recent X values seen so far (or fewer than X if fewer values have arrived).

Part 2 (follow-up): Weighted moving average

Modify the approach to compute a weighted moving average over the most recent X values where more recent values have higher weight.

For example, for the last k <= X values (oldest to newest):

• weights could be 1, 2, ..., k
• weighted average = $\frac{\sum_{i=1}^{k} i \cdot v_i}{\sum_{i=1}^{k} i}$

Constraint

Do this without storing all previous data points (i.e., memory should not grow with the total stream length).