Question

I have a file that has 1,000,000 float values in it. I need to find the 10,000 largest values.

I was thinking of:

1. Reading the file
2. Converting the strings to floats
3. Placing the floats into a max-heap (a heap where the largest value is the root)
4. After all values are in the heap, removing the root 10,000 times and adding those values to a list/arraylist.

I know I will have

1. 1,000,000 inserts into the heap
2. 10,000 removals from the heap
3. 10,000 inserts into the return list

Would this be a good solution? This is for a homework assignment.

Answer 1

Your solution is mostly good. It’s basically a heapsort that stops after getting K elements, which improves the running time from O(NlogN) (for a full sort) to O(N + KlogN). Here N = 1000000 and K = 10000.

However, you should not do N inserts to the heap initially, as this would take O(NlogN) – instead, use a heapify operation which turns an array to a heap in linear time.

If the K numbers don’t need to be sorted, you can find the Kth largest number in linear time using a selection algorithm, and then output all numbers larger than it. This gives an O(n) solution.