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A positive integer N is a power if it is of the form qk, where q, k are positive
Chapter 1, Problem 1.32(choose chapter or problem)
A positive integer N is a power if it is of the form qk, where q, k are positive integers and k > 1.(a) Give an efficient algorithm that takes as input a number N and determines whether it isa square, that is, whether it can be written as q2for some positive integer q. What is therunning time of your algorithm?(b) Show that if N = qk(with N, q, and k all positive integers), then either k log N or N = 1.(c) Give an efficient algorithm for determining whether a positive integer N is a power. Analyzeits running time.
Questions & Answers
QUESTION:
A positive integer N is a power if it is of the form qk, where q, k are positive integers and k > 1.(a) Give an efficient algorithm that takes as input a number N and determines whether it isa square, that is, whether it can be written as q2for some positive integer q. What is therunning time of your algorithm?(b) Show that if N = qk(with N, q, and k all positive integers), then either k log N or N = 1.(c) Give an efficient algorithm for determining whether a positive integer N is a power. Analyzeits running time.
ANSWER:Step 1 of 4
An algorithm is a finite step-by-step procedure to solve a problem. The length of the input to the algorithm determines how long it takes to solve the problem or execute an algorithm's steps, known as time complexity. The problem in the question aims to design an algorithm that checks whether the input number is Power.