{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,1]],"date-time":"2026-05-01T14:12:52Z","timestamp":1777644772521,"version":"3.51.4"},"reference-count":0,"publisher":"SAGE Publications","issue":"1","license":[{"start":{"date-parts":[[2012,1,1]],"date-time":"2012-01-01T00:00:00Z","timestamp":1325376000000},"content-version":"tdm","delay-in-days":0,"URL":"https:\/\/journals.sagepub.com\/page\/policies\/text-and-data-mining-license"}],"content-domain":{"domain":["journals.sagepub.com"],"crossmark-restriction":true},"short-container-title":["Fundamenta Informaticae"],"published-print":{"date-parts":[[2012,11]]},"abstract":"<jats:p>\n                    The worst-case behavior of the heap-construction phase of Heapsort escaped mathematically precise characterization by a closed-form formula for almost five decades. This paper offers a proof that the exact number of comparisons of keys performed in the worst case during construction of a heap of size N is: 2N \u2212 2s\n                    <jats:sub>2<\/jats:sub>\n                    (N) \u2212 e\n                    <jats:sub>2<\/jats:sub>\n                    (N), where s\n                    <jats:sub>2<\/jats:sub>\n                    (N) is the sum of all digits of the binary representation of N and e\n                    <jats:sub>2<\/jats:sub>\n                    (N) is the exponent of 2 in the prime factorization of N. It allows for derivation of this best-known upper bound on the number of comparisons of Heapsort: (2N \u2212 1)$\\lceil$lgN$\\rceil$ \u2212 2\n                    <jats:sup>$\\lceil$lgN$\\rceil$+1<\/jats:sup>\n                    \u2212 2s\n                    <jats:sub>2<\/jats:sub>\n                    (N) \u2212 e\n                    <jats:sub>2<\/jats:sub>\n                    (N) + 5.\n                  <\/jats:p>","DOI":"10.3233\/fi-2012-751","type":"journal-article","created":{"date-parts":[[2019,12,3]],"date-time":"2019-12-03T00:13:38Z","timestamp":1575332018000},"page":"75-92","update-policy":"https:\/\/doi.org\/10.1177\/sage-journals-update-policy","source":"Crossref","is-referenced-by-count":3,"title":["Elementary Yet Precise Worst-Case Analysis of Floyd's Heap-Construction Program"],"prefix":"10.1177","volume":"120","author":[{"given":"Marek A.","family":"Suchenek","sequence":"first","affiliation":[{"name":"Department of Computer Science, California State University Dominguez Hills, Suchenek@csudh.edu"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"179","published-online":{"date-parts":[[2012,1,1]]},"container-title":["Fundamenta Informaticae"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2012-751","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/journals.sagepub.com\/doi\/pdf\/10.3233\/FI-2012-751","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2026,4,29]],"date-time":"2026-04-29T06:30:18Z","timestamp":1777444218000},"score":1,"resource":{"primary":{"URL":"https:\/\/journals.sagepub.com\/doi\/10.3233\/FI-2012-751"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2012,1,1]]},"references-count":0,"journal-issue":{"issue":"1","published-print":{"date-parts":[[2012,11]]}},"alternative-id":["10.3233\/FI-2012-751"],"URL":"https:\/\/doi.org\/10.3233\/fi-2012-751","relation":{},"ISSN":["0169-2968","1875-8681"],"issn-type":[{"value":"0169-2968","type":"print"},{"value":"1875-8681","type":"electronic"}],"subject":[],"published":{"date-parts":[[2012,1,1]]}}}