How would you sort an array of one billions integers?

Question

Sigiloso · Accepted Answer

16

Tal · Answer

I think that the trick here is to use some sort of a divide and conquer sorting algorithm
(such as merge sort or quick sort) and use this idea to divide the sorting between several computers so if you have p computers it will take O(n/p*log(n/p))
The problem arises when you need to merge all the data together back to a big array, but that only takes O(n) since the sub-arrays are already sorted.

The big con to this is that merge sort (the traditional method) requires extra memory for each iteration, so its possible to use merge sort to divide the array to p computers but in each computer use quick sort (which is in place sorting) to sort the sub-arrays. that way you save the memory (since you need to move the sub-arrays to other computer anyway) and still get sorting of O(n/plog(n/p))

lamont · Answer

The integers need not be distinct. I failed to mention that the counters are 32 bit unsigned integers. They can handle 4 billion duplicate values in the original array, which is greater than the "one billions" requirement.

This whole problem is rather contrived. When you have a billion integers they're generally going to be in a file, not an array. But if you've already got an array of 1 billion integers, what's another 4 billion?

lamont · Answer

Here's an outside of the box answer. An array a[d] = r maps a domain to a range. Assuming 32 bit integers, the domain size in this problem is on the same order as the range (about 4 billion). We can use this to design an O(n) sorting algorithm. Count the number of occurrences of each possible integer and then spit them back into the array:

RangeSort(a, n)
{
    const MAXINT = 1  0)
            a[i++] = j;
}

Both loops are O(n). MAXINT is a constant, so the memset is O(1).

Sigiloso · Answer

your answer would work only if you  knew the integers in the array are distinct. If they`re not, each entry in your array should be able to keep a number up to  one billions(in the case all integers in the array are equal)

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