Introduction to Algorithms
3rd Edition
ISBN: 9780262033848
Author: Thomas H. Cormen, Ronald L. Rivest, Charles E. Leiserson, Clifford Stein
Publisher: MIT Press
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Chapter 5.1, Problem 3E
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Let's consider a long, quiet country road with houses scattered very sparsely along it. (Picture the road as a long line segment with an eastern endpoint and a western endpoint.) Further let’s suppose that despite the bucolic setting, the residents of all these houses are avid cell phone users. You want to place cell phone base stations at certain points along the road, so that every house is within four miles of one of the base stations. Give an efficient algorithm that achieves this goal using as few base stations as possible. Prove its correctness and explain its time complexity.
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- Let’s consider a long, quiet country road with houses scattered very sparsely along it. (We can picture the road as a long line segment, with an eastern endpoint and a western endpoint.) Further, let’s suppose that despite the bucolic setting, the residents of all these houses are avid cell phone users. You want to place cell phone base stations at certain points along the road, so that every house is within four miles of one of the base stations. Give an efficient algorithm that achieves this goal, using as few base stations as possible. Give the psudo code.arrow_forwardA student is interested in computing the area under the function f(x)=x over the interval [0,1] and decides to get an accurate answer using a Monte Carlo experiment (by this we are assuming the student doesn't know the answer to such an elementary mathematical question). Which of the following R codes will give such an approximate answer? M = 10^6x = runif(M)y = runif(M)mean( y <= x ) M = 10^6x = runif(M)mean( x ) M = 10^6x = rnorm(M)mean( x ) M = 10^6x = rnorm(M)y = runif(M)mean( y <= x )arrow_forwardWrite a python program by following rules: Has ? discrete time intervals where ? is large. Generates a set of customer call arrivals with the arrival rate of ? at random locations in the ? intervals (e.g., for each interval, a call will happen with probability ?/?). Counts the number of calls that actually occurs during these ? intervals. Design your experiment to determine the Poisson distribution of this experiment (probability of having k arrivals in n intervals).arrow_forward
- no handwritten Alice and Bob are playing a match to see who is the first to win n games, for some fixed n > 0. Suppose Alice and Bob are equally competent, that is, each of them wins a game with probability 1/2. Further, suppose that they have already played i + j games, of which Alice won i and Bob won j. Give an efficient algorithm to compute the probability that Alice will go on to win the match. For example, if i = n − 1 and j = n − 3, then the probability that Alice will win the match is 7/8, since she must win any of the next three games.arrow_forwardShow that it is undecidable, given the source code of a program Q, to tell whether ornot any of the following is true:(i) Q halts on input 0.(ii) Q is total – that is, Q(y) halts for all y.(iii) Q(y) = true for all y.(iv) The set of y on which Q halts is finite.(v) There is a y such that Q(y) = y.(vi) Given a second program R, Q is equivalent to R. That is, even though Q and Rhave different source codes, they compute the same partial function – for all y,either Q(y) and R(y) both halt and return the same answer, or neither halts.Prove each of these by reducing Halting to them. That is, show to how convert aninstance (P, x) of Halting to an instance of the problem above. For instance, you canmodify P’s source code, or write a new program that calls P as a subroutine. Eachof these is asking for a Turing reduction; your reduction does not necessarily have tomap yes-instances to yes-instances and no-instances to no-instances – all that mattersis that if you could solve the problem, then…arrow_forwardAlgorithm to An iterative solution to Towers of Hanoi.in: triplet S = s0, s1, s2 representing the current game stateout: triplet R = r0, r1, r2 representing the new game statelocal: pole indices a, b, z ∈ {0, 1, 2}; disc numbers g, h ∈ [2, n]; last(Q) = Q|Q|−1, if1 ≤ |Q|, otherwise, last(Q) = +∞arrow_forward
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