How to rearrange an array in such a way that each element is greater/smaller than its neighbours

Question

For example, if the numbers are:

30, 12, 49, 6, 10, 50, 13

The array will be:

[10, 6, 30, 12, 49, 13, 50]

<

Answer 1

This can be done in O(n):

1. Find median in O(n) (description is available in Wikipedia
2. Put every element larger than the median on odd places and every smaller element - on even places

Of course, this assumes that all elements are distinct, otherwise sometimes it will fail.