Problem 1. For each integer n > 1 we define a tree Tn, recursively, as follows. T1 and T2 consistof only a single node. For n 2 3, T, is obtained from three copies of Tn/3, one copy of Tn/3, andthree additional nodes, by connecting them as follows:Notations [r] and [x] represent the floor and ceiling functions; the first one rounds a real numberr to the largest integer a r.Let l(n) be the number of nodes in Tn-(a) Give a recurrence equation for t(n) and justify it.(b) Draw T19. (You can use a drawing software or draw it by hand, and include a pdf file in thelatex source.)(c) Give the asymptotic formula for t(n), by using Master Theorem to solve the recurrence frompart (a). Justify your solution.

Problem 1. For each integer n 21 we define a tree Tn, recursively, as follows. Tị and T2 consist of only a single node. For n 2 3, T, is obtained from three copies of Tn/3, one copy of Tn/3, and three additional nodes, by connecting them as follows: Notations [r] and [x] represent the floor and ceiling functions; the first one rounds a real number z to the largest integer a < r and the second one rounds z to the smallest integer b> r. Let l(n) be the number of nodes in Tn- (a) Give a recurrence equation for t(n) and justify it. (b) Draw T19. (You can use a drawing software or draw it by hand, and include a pdf file in the latex source.) (c) Give the asymptotic formula for t(n), by using Master Theorem to solve the recurrence from part (a). Justify your solution.

Problem 1. For each integer n 21 we define a tree Tn, recursively, as follows. Tị and T2 consist of only a single node. For n 2 3, T, is obtained from three copies of Tn/3, one copy of Tn/3, and three additional nodes, by connecting them as follows: Notations [r] and [x] represent the floor and ceiling functions; the first one rounds a real number z to the largest integer a < r and the second one rounds z to the smallest integer b> r. Let l(n) be the number of nodes in Tn- (a) Give a recurrence equation for t(n) and justify it. (b) Draw T19. (You can use a drawing software or draw it by hand, and include a pdf file in the latex source.) (c) Give the asymptotic formula for t(n), by using Master Theorem to solve the recurrence from part (a). Justify your solution.

Operations Research : Applications and Algorithms

4th Edition

ISBN:9780534380588

Author:Wayne L. Winston

Publisher:Wayne L. Winston

Chapter18: Deterministic Dynamic Programming

Section18.4: Resource-allocation Problems

Problem 3P

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