The first homework focuses on Python fundamentals and Amdahl$$s law, which include:

$1.($a$)$ Define a list with $20$ elements and assign the elements with random integers

between $(50,100),$ sort the list and print the result. After sorting the list, calculate the

sum of the elements at even locations $($i$.$e$.,$ a$[0]+$ a$[2]+$ a$[4]+$ a$[6]+...+$ a$[18])$

$($b$)$ Calculate the mean, median, standard deviation of the list. Also, calculate the $2-$based

logarithm values of the list elements. Hint: use functions in modules statistics and math.

$2.$ Using Python, define a list with $20$ elements and assign the elements with random

integers between $(0,1000).$ Then complete the following tasks: $(1)$ define a function

myfunc which take one argument and check if the argument is prime, if yes, return

True, otherwise, return False; $(2)$ apply the built$-$in map function to the list and use the

$2-$based logarithm function of the math module to calculate the value of each element

in the list, $(3)$ apply the built$-$in filter function the list and use the myfunc function to filter

the prime numbers; $(4)$ redo part $(3),$ but instead of calling the function, in the filter

function, write a lambda expression to implement the same functionality.

$3.($a$)$ Given a program, its total running time is t using a single processor $($i$.$e$.,$ running

the program serially$).$ If $90\%$ of the program $($i$.$e$.,90\%$ of t$)$ can be executed parallelly,

according to Amdahl$$s law, what will be the speedup if running the program parallelly

on a computer with $8$ processors $($or CPU cores$)?$ If unlimited processors are available

in the computer, what is the maximum speedup?

$($b$)$ What is superlinear speedup? Under what conditions will it happen?

$($c$)$ Given a program which searches the target data in a sequence of $12$ data, assume

$($i$)$ without knowing the location of the target data, the CPU will examine the data one

by one; $($ii$)$ the whole program can be executed parallelly and the program will stop

immediately once the target data is found; and $($iii$)$ the program$$s running time except

data searching can be ignored, please calculate:

$(1)$ If the target data is the $3$rd in the sequence, what is the speedup gained by

running the program using $4$ CPUs over running the program using $1$ CPU.

Note: by default, the data will be equally dispatched to the CPUs $($i$.$e$.,$ CPU $1$

processes data $1,2,3$; CPU $2$ processes data $4,5,6,$ etc.$)$

$(2)$ If the target data is the $7$th in the sequence, what is the speedup by running the

programing using $4$ CPUs?

$(3)$ If the target data is the $7$th in the sequence, what is the speedup by running the

programing using $3$ CPUs?

Turn in source code in $.$py file. Add your name, student ID and HW number at the

beginning as comments. For problem $3,$ please turn in the electronic$/$scanned

copy of your calculation.

Due: Friday, September $20,2024$