在O（K）时间中找到大小为N的最大堆中最大K个数的算法？

Question

The O(K * logK) algorithm for finding the largest K numbers in a max heap of size N is well known. I heard about that there is an O(K) algorithm for solving this problem. I do not find the literature on this. Could anyone give any pointers on this? Thanks!

Answer 1

I finally find the paper that describes the algorithm. There is a similar question on Quora .

The paper, " An Optimal Algorithm for Selection in a Min-Heap ", by GN Frederickson, describes the algorithm. The following is the abstract:

An O(k)-time algorithm is presented for selecting the kth smallest element in a binary min-heap of size n⪢k. The approach uses recursively defined data structures that impose a hierarchical grouping on certain elements in the heap. The result establishes a further example of a partial order for which the kth smallest element can be determined in time proportional to the information theory lower bound. Two applications, to a resource allocation problem and to the enumeration of the k smallest spanning trees, are identified.