Fall 2002 ALG: Page 1 of 1
QUESTION CODE: ALG
CS Diagnostic Exam
Fall 2002
Algorithm (CS 600)
Part I
Consider a hardware register inside a CPU. Operations available on
this register are common machine-level operations:
- load and store register contents from memory
- rotate with wrap around register contents 1 bit left (or right)
- arithmetic between the register and either memory locations
or constant values
- bitwise logical operations between the register and either
memory locations or constant values
- jump (to an address) if the sign bit is set,
- jump (to an address) if the register is zero
a) Give an algorithm to efficiently determine if any single bit in the
register is zero (ie is it false that the register has all ones).
b) Give an algorithm to efficiently determine if any two consecutive bits in
the register are zero.
c) Give an algorithm to efficiently determine if any three consecutive bits
in the register are zero. Generalize this procedure to detecting k
consecutive zero bits?
(Note that for the purpose of efficiency all of the operations are considered
as taking the same amount of time. Thus a load operation takes the same
amount of time as a rotate.)
Part II
a. Consider the problem of determining if a string of length n has two
consecutive zeros. The basic operation is to examine a position in the
string to see if it is a 0 or a 1. For each n =2,3,4,5 either give an
adversary strategy to force any algorithm to examine every bit, or give an
algorithm that solves the problem by examining less than n bits.
b. Give a general solution for n = 3k + 1 for k >= 2.