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DIS-algo (n): =========== r = 0 i = n* n while i 1 do for j = 1 to i do r = r + 1 i = 1/2 return r In the above, i/2 is integer division, i.e., it returns an integer, truncating any decimal part of the result of the division- so, as one concrete example (not necessarily one that comes up in this exercise!), 5/2 would return 2, not 2.5. (a) What is the final value of r returned by this function? Express it as a function of n. (b) Express the running time (as a function of n) of DIS-algo using e-notation. (c) Express the space complexity (as a function of n) of DIS-algo using e-notation.

DIS-algo (n): =========== r = 0 i = n* n while i 1 do for j = 1 to i do r = r + 1 i = 1/2 return r In the above, i/2 is integer division, i.e., it returns an integer, truncating any decimal part of the result of the division- so, as one concrete example (not necessarily one that comes up in this exercise!), 5/2 would return 2, not 2.5. (a) What is the final value of r returned by this function? Express it as a function of n. (b) Express the running time (as a function of n) of DIS-algo using e-notation. (c) Express the space complexity (as a function of n) of DIS-algo using e-notation.

Computer Networking: A Top-Down Approach (7th Edition)
Computer Networking: A Top-Down Approach (7th Edition)
7th Edition
ISBN:9780133594140
Author:James Kurose, Keith Ross
Publisher:James Kurose, Keith Ross
Chapter1: Computer Networks And The Internet
Section: Chapter Questions
Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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DIS-algo (n): =========== r = 0 in n while i 1 do for j = 1 to i do r = r + 1 i = 1/2 return r In the above, i/2 is integer division, i.e., it returns an integer, truncating any decimal part of the result of the division- so, as one concrete example (not necessarily one that comes up in this exercise!), 5/2 would return 2, not 2.5. (a) What is the final value of r returned by this function? Express it as a function of n. (b) Express the running time (as a function of n) of DIS-algo using e-notation. (c) Express the space complexity (as a function of n) of DIS-algo using -notation. As usual, be sure to give concise but convincing explanations for your answers. NOTE: Here are some hints, which might be especially helpful for part la of this exercise: • You are welcome to assume that the input value n is a power of 2, if it simplifies your analysis. •Using summation notation may help. There's a common "trick" in algorithm analysis involving summation- for some exponent x, = (). Here's a quick derivation of that: 1 12 2x 2x because 1 1 for any r by properties of exponents This "trick" might be useful in your analysis of this algorithm. . Please be careful of off-by-one errors! = -note that
Transcribed Image Text:DIS-algo (n): =========== r = 0 in n while i 1 do for j = 1 to i do r = r + 1 i = 1/2 return r In the above, i/2 is integer division, i.e., it returns an integer, truncating any decimal part of the result of the division- so, as one concrete example (not necessarily one that comes up in this exercise!), 5/2 would return 2, not 2.5. (a) What is the final value of r returned by this function? Express it as a function of n. (b) Express the running time (as a function of n) of DIS-algo using e-notation. (c) Express the space complexity (as a function of n) of DIS-algo using -notation. As usual, be sure to give concise but convincing explanations for your answers. NOTE: Here are some hints, which might be especially helpful for part la of this exercise: • You are welcome to assume that the input value n is a power of 2, if it simplifies your analysis. •Using summation notation may help. There's a common "trick" in algorithm analysis involving summation- for some exponent x, = (). Here's a quick derivation of that: 1 12 2x 2x because 1 1 for any r by properties of exponents This "trick" might be useful in your analysis of this algorithm. . Please be careful of off-by-one errors! = -note that
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