I want a data structure that keeps elements in the way that you inserted them and allows erases in $O(log(n))$ or less.↵
For example, if the initial array is empty and you insert 5, 2, 4, then the array would be [5, 2, 4]. Erase 4 and it is [5, 2]. Insert a 3 and it is [5, 2, 3]. I know that set allows erases in $O(log(n))$ and insertions but it keeps the elements in sorted order, not in the way that I inserted them.
For example, if the initial array is empty and you insert 5, 2, 4, then the array would be [5, 2, 4]. Erase 4 and it is [5, 2]. Insert a 3 and it is [5, 2, 3]. I know that set allows erases in $O(log(n))$ and insertions but it keeps the elements in sorted order, not in the way that I inserted them.