# hw5 - Fall 11 CSci 5421Advanced Algorithms and Data...

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Fall 11: CSci 5421—Advanced Algorithms and Data Structures Out 11/21 Homework 5 Due 12/12 Please do all problems; we will grade a subset of three to four problems. Any Exercise/Problem numbers refer to the 3rd edition of the text. (Corresponding numbers for the second edition are given, where available, in parentheses.) Please follow all of the instructions given in the handout for Homework 1. 1. (12 points) Suppose that you wish to do two types of operations on an inFnite binary counter: Increment , which is as deFned in class, and Reset , which resets all bits in the counter to zero. Explain, in words, how such a counter could be implemented so that any sequence of n Increment and Reset operations on an initially-zero counter takes O ( n ) time. Use the accounting (i.e., credits- based) method. State clearly the invariant you use and the amortized cost that you assign to each operation. Hint: Consider keeping a pointer to the high-order 1-bit. 2. (12 points) Let Q be a queue, with the usual operations Enqueue and Dequeue . We wish to implement Q using two stacks S 1 and S 2 , so that the amortized cost of each queue operation is a constant. (Assume that Q is empty initially.) Describe in words how this can be done and

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## This note was uploaded on 01/28/2012 for the course CSCI 5421 taught by Professor Sturtivant,c during the Fall '08 term at Minnesota.

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hw5 - Fall 11 CSci 5421Advanced Algorithms and Data...

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