Selected Topics in Algorithms Jeff Achter and Roberto Tamassia Summary: Selected Topics in Algorithms Jeff Achter and Roberto Tamassia Department of Computer Science Brown University Providence, RI 02912­1910 {jda,rt}@cs.brown.edu September 1993 Copyright c 1990, 1991, 1992, 1993 by J.D. Achter and R. Tamassia Contents 1 Recurrence Relations 3 1.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Fundamental Recurrence Relations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2.1 T(N) = T(N/2) + 1; T(1) = 1 . . . . . . . . . . . . . . . . . . . . . . . . . 4 1.2.2 Induction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2.3 T(N) = T(N/2) + N; T(1) = 1 . . . . . . . . . . . . . . . . . . . . . . . . . 6 1.2.4 T(N) = T(N) + N; T(1) = 1 (0 < < 1) . . . . . . . . . . . . . . . . . 7 1.2.5 T(N) = 2T(N/2) + N; T(1) = 1 . . . . . . . . . . . . . . . . . . . . . . . . 8 1.2.6 T(N) = 2T(N/2) + N ; T(1) = 1; = 1 . . . . . . . . . . . . . . . . . . 9 1.3 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10 Collections: Environmental Sciences and Ecology; Mathematics