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 A.1, Problem 5E
Program Plan Intro
To evaluate the sum of the given equation.
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Consider the following function:
• 2 sin(n+ #),
n=o
√√√3
f(n)=
n so
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€ [1,1], Include
plot both f(n) and f'(n) for
enough point so that the curve you
plots
appears smooth. Use different colors and separate
label to represent
represent the function and it's derivative
respectively, label the axes x and y, and use
grid. You must use
Sympy and Matplotlit,
Manual differention
should
be avoid
Ql: The Collatz conjecture function is defined for a positive integer m as
follows. (COO1)
g(m) = 3m+1 if m is odd
= m/2 if m is even
=1 if m=1
The repeated application of the Collatz conjecture function, as follows:
g(n), g(g(n)), g(g(g(n))), ...
e.g. If m=17, the sequence is
1. g(17) = 52
2. g(52) = 26
3. g(26) = 13
4. g(13) = 40
5. g(40) = 20
6. g(20) = 10
7. g(10) = 5
8. g(5) = 16
9. g(16) = 8
10. g(8) = 4
11. g(4) = 2
12. g(2) = 1
Thus if m=17, apply the function 12 times in order to reach m=1. Use
Recursive Function.
If F1(A, B, C, D) = Sum(0, 1, 3, 8, 9, 14, 15) and d=Sum(4, 5, 11, 12, 13), the F1 =
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