the analysis of the heap-sort algorithm shows that we can construct heap storing entries in (nlogntimeby means of successive insert operationsand then use that heap to extract the entries in order by nondecreasing key howeverif all the key-value pairs to be stored in the heap are given in advancethere is an al ternative bottom-up construction method that runs in (ntime we describe this method in this sectionobserving that it could be included as one of the constructors of class implementing heap-based priority queue for simplicity of expositionwe describe this bottom-up heap construction assuming the number of keys is an integer of the type that isthe heap is complete binary tree with every level being fullso the heap has height log( viewed nonre