data structrue to store data and calculate average

In this problem, we are interested in a data structure that supports keeping infinite numbers of Y axis parallel vectors.

Each node contains location (X axis value) and height (Y axis value). We can assume there are no two vectors in the same location.

Please advise for an efficient data structure that supports:

1. init((x1,y1)(x2,y2)(x3,y3)...(xn,yn)) - the DS will contain all n vectors, while VECTOR#i's location is xi VECTOR#i's hieght is yi.
We also know that x1<x2<x3<...<xn (nothing is known about the y) - complexity = O(n) on average

2. insert(x,y) - add vector with location x and hieght y. - complexity = O(logn) amortized on average.

3. update(x,y) - update vector#x's height to y. - complexity = O(logn) worst case

4. average_around(x) - return the heights average of logn neighbors of x - complexity = O(1) on average

Space Complexity: O(n)

so, after the long question... please advise

Well, let me first ask you: what are your thoughts on this topic? What reasoning led you to your (initial) ideas?

well at first, due to the average complexity, I've tried to use hash table and skip list... that's didn't work... i still think it is possible, its just that i cant make the average function in O(1)

second opinion is that the insert and update complexity makes me think about going for either a tree or a list with binary search... but again, what with the average...

i think they want us to use heap/hash/skip list...