Exercise 5A (i) Write a function collatzseq(n) which computes the Collatz sequence (as a Python list) given an initial value n. For example, the output of collatzseq (5) should be [5,16,8,4,2,1] (ii) Write a function collatzcount (n) which counts the number of steps s(n) until the sequence starting at n reaches 1. For example, s(1) = 0 and as above s(11) = 14. (iii) Plot a graph of s(n) against n for n € [1,1000]. Use circles for markers instead of lines. (iv) What percentage of initial values n have the property that s(n) < n/10 for n € [1,1000]? (Write your answer as a comment, including any code you used to obtain it but commented out.) = (v) Let max(n) be the largest integer reached by the sequence with initial value n before ending at 1. That is, max(n) = max{A¡ | Ao n}. For example, in the case above, max(11) 52. Plot a graph of max(n) against n for n € [1, 1000]. Investigate using different plotting techniques such as: restricting the y-axis, logarithmic plots, using a bigger range for x (so long as this doesn't make your code too slow), or plotting additional points or lines to help identify any patterns you can see. Comment on your observations (including your answer as a comment). =
Exercise 5A (i) Write a function collatzseq(n) which computes the Collatz sequence (as a Python list) given an initial value n. For example, the output of collatzseq (5) should be [5,16,8,4,2,1] (ii) Write a function collatzcount (n) which counts the number of steps s(n) until the sequence starting at n reaches 1. For example, s(1) = 0 and as above s(11) = 14. (iii) Plot a graph of s(n) against n for n € [1,1000]. Use circles for markers instead of lines. (iv) What percentage of initial values n have the property that s(n) < n/10 for n € [1,1000]? (Write your answer as a comment, including any code you used to obtain it but commented out.) = (v) Let max(n) be the largest integer reached by the sequence with initial value n before ending at 1. That is, max(n) = max{A¡ | Ao n}. For example, in the case above, max(11) 52. Plot a graph of max(n) against n for n € [1, 1000]. Investigate using different plotting techniques such as: restricting the y-axis, logarithmic plots, using a bigger range for x (so long as this doesn't make your code too slow), or plotting additional points or lines to help identify any patterns you can see. Comment on your observations (including your answer as a comment). =
Computer Networking: A Top-Down Approach (7th Edition)
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ISBN:9780133594140
Author:James Kurose, Keith Ross
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Chapter1: Computer Networks And The Internet
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Problem R1RQ: What is the difference between a host and an end system? List several different types of end...
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![Exercise 5A (i) Write a function collatzseq(n) which computes the Collatz sequence (as a Python list)
given an initial value n. For example, the output of collatzseq (5) should be [5,16,8,4,2,1]
(ii) Write a function collatzcount (n) which counts the number of steps s(n) until the sequence starting
at n reaches 1. For example, s(1) = 0 and as above s(11) = 14.
(iii) Plot a graph of s(n) against n for n € [1,1000]. Use circles for markers instead of lines.
(iv) What percentage of initial values ʼn have the property that s(n) <n/10 for n = [1, 1000]? (Write your
answer as a comment, including any code you used to obtain it but commented out.)
(v) Let max(n) be the largest integer reached by the sequence with initial value n before ending at 1. That
is, max(n) = max{A; | A₁ = n}. For example, in the case above, max(11) = 52. Plot a graph of max(n)
against n for n € [1, 1000]. Investigate using different plotting techniques such as: restricting the y-axis,
logarithmic plots, using a bigger range for x (so long as this doesn't make your code too slow), or plotting
additional points or lines to help identify any patterns you can see. Comment on your observations (including
your answer as a comment).](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F3011c556-643e-4a01-b0e0-55d8cf24eddf%2F1a66b6c5-d465-447b-9ad2-642f668cb013%2Fcfe2yc_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Exercise 5A (i) Write a function collatzseq(n) which computes the Collatz sequence (as a Python list)
given an initial value n. For example, the output of collatzseq (5) should be [5,16,8,4,2,1]
(ii) Write a function collatzcount (n) which counts the number of steps s(n) until the sequence starting
at n reaches 1. For example, s(1) = 0 and as above s(11) = 14.
(iii) Plot a graph of s(n) against n for n € [1,1000]. Use circles for markers instead of lines.
(iv) What percentage of initial values ʼn have the property that s(n) <n/10 for n = [1, 1000]? (Write your
answer as a comment, including any code you used to obtain it but commented out.)
(v) Let max(n) be the largest integer reached by the sequence with initial value n before ending at 1. That
is, max(n) = max{A; | A₁ = n}. For example, in the case above, max(11) = 52. Plot a graph of max(n)
against n for n € [1, 1000]. Investigate using different plotting techniques such as: restricting the y-axis,
logarithmic plots, using a bigger range for x (so long as this doesn't make your code too slow), or plotting
additional points or lines to help identify any patterns you can see. Comment on your observations (including
your answer as a comment).
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