#OK to post homework 
#Natalya Ter-Saakov, Jan 28, 2024, Assignment 2
read "C2.txt":

#Problem 3 I

#MyIfactorI(n): Inputs a positive integer n and returns a list of prime factors in weakly increasing order using ithprime
MyIfactorI:=proc(n) local i,p:
if isprime(n) then 
	return [n]:
fi:
for i from 1 to n do
	p:=ithprime(i):
	if evalb(0=n mod p) then
		return [p,op(MyIfactorI(n/p))]:
	fi:
od:
end:

#MyIfactorN(n): Inputs a positive integer n and returns a list of prime factors in weakly increasing order using nextprime
MyIfactorN:=proc(n) local i,p:
if isprime(n) then 
	return [n]:
fi:
p:=1:
for i from 1 to n do
	p:=nextprime(p):
	if evalb(0=n mod p) then
		return [p,op(MyIfactorN(n/p))]:
	fi:
od:
end:

#Problem 3 II

#CompareIfactor(n): Inputs n and returns a list of how long it took maple to compute ifactor followed by how long MyIfactor took
CompareIfactor:=proc(n) local TI, TN, MT, tempT:
tempT:=time():
MyIfactorN(n):
TN:=time()-tempT:
tempT:=time():
ifactor(n):
MT:=time()-tempT:
tempT:=time():
MyIfactorI(n):
TI:=time()-tempT:
[MT, TI, TN]:
end:

#Having run every permutation of CompareIfactor, I conclude that, due to Maple auto-memoizing, the algorithm that takes the longest is the one I run first. Maple will not allow one to restart within a procedure or file, so to actually run a comparison, one must jump through some hoops.

#Specifically run the following on every procedure for your favorite n
#restart: read "hw2NatalyaTer-Saakov.txt": TimeFactoring(procedure,n);  

#TimeFactoring(procedure, n)
TimeFactoring:=proc(procedure, n) local st:
st:=time():
print(procedure(n)):
time()-st:
end:

#New un-fun fact: The same procedure on the same number runs a different amount of time.
 

#Just like CompareIfactor, this will not actually work.
#ComparePrimes
ComparePrimes:=proc(n) local iT, nT, tempT, p:
p:=ithprime(n-1): # this is like instantaneous
tempT:=time():
ithprime(n):
iT:=time()-tempT:
tempT:=time():
nextprime(p):
nT:=time()-tempT:
[iT,nT]:
end: