Question

I have a sequence of elements, say a1,a2,…,an. (n ~ 4*10^7)

The input will be mostly sorted. More specifically any element less than a_i will be either to the left, or very close to the right(~ 300 elements).

How can I sort this sequence efficiently?

Answer 1

You could do this using a heap of N elements where N is the maximum overlap (N=300 in your case).

Start with an empty heap.

For each element in the sequence:

1. Add element to the heap

2. If the heap has more than N elements, output (and remove from the heap) the smallest element

Finally output the remaining elements in the heap.

This will have complexity O(nlogN)