Retrieving the top 100 numbers from one hundred million of numbers

Question

One of my friend has been asked with a question

Retrieving the max top 100 numbers from one hundred million of numbers

in a rece

Answer 1

@darius can actually be improved !!!
By "pruning" or deferring the heap-replace operation as required

Suppose we have a=1000 at the top of the heap
It has c,b siblings
We know that c,b>1000

      a=1000
  +-----|-----+
 b>a         c>a




We now read the next number x=1035
Since x>a we should discard a.
Instead we store (x=1035, a=1000) at the root
We do not (yet) bubble down the new value of 1035 
Note that we still know that b,cx
Now, we get the next number y
when yx>a then we replace x with y (the root now has (y, a=1000))
=> we saved log(m) steps here, since x will never have to bubble down

when a>y>x then we need to bubble down y recursively as required

Worst run time is still O(n log m) 
But average run time i think might be O(n log log m) or something
In any case, it is obviously a faster implementation