Auctions　are　important　mechanisms　for　resource　and　task　allocation　in　multi-agent　systems.　Combinatorial　auctions　where　bidders　can　bid　on　bundles　of　items　can　lead　to　more　economical　revenue.　This　is　a　winner　determination　problem.　But　determining　the　winners　is　NP-complete.　Rothkopf　et　al　presented　a　dynamic　programming　algorithm　for　this　problem.　It　is　an　optimal　algorithm　found　so　far　for　the　general　case.　In　this　paper　we　analyzes　its　computational　complexity　exactly,　prove　that　the　computational　complexity　of　the　algorithm　is　O(3n)　for　n　items.　Comparing　with　the　result　O(3n)　of　Rothkopf　et　al,　it　is　more　exact.　This　will　help　to　research　on　the　approximate　algorithm　for　the　winner　determination　problem　in　combinatorial　auctions,　and　for　the　optimal　coalition　structure　generation　in　multi-agent　systems.