A tight bound on the worst-case number of comparisons for Floyd's heap construction algorithm

In this paper a tight bound on the worst-case number of comparisons for Floyd’s well known heap construction algorithm, is derived. It is shown that at most 2n-2{\mu}(n)-{\sigma}(n) comparisons are executed in the worst case, where {\mu}(n) is the number of ones and {\sigma}(n) is the number of zeros after the last one in the binary representation of the number of keys n.