#Nathan Fox
#Homework 1
#I give permission for this work to be posted online

#Help procedure
Help:=proc() : print(`FindUPi(L,i), FindUP(L)`): end:

#L: list of numbers
#i: positive integer
#If there exists a list M of length i such that L ends with
#at least three repeated copies of M, returns M
#Otherwise, returns FAIL
#Works by checking if the last 3i elements of the list are
#the same as the last i repeated 3 times
FindUPi:=proc(L, i)
local m, n:
n:=nops(L):
m:=L[n-i+1..]:
if L[n-3*i+1..]=[op(m),op(m),op(m)] then
    m:
else
    FAIL:
fi:
end:

#L: list of numbers
#If there exists a list M such that L ends with
#at least three repeated copies of M, returns the shortest such M
#Otherwise, returns FAIL
#Works by calling FindUPi for all i values from 1 to
#the length of L divided by 3
FindUP:=proc(L)
local i, m, n:
n:=nops(L):
for i from 1 to n/3 do
    m:=L[n-i+1..]:
    if L[n-3*i+1..]=[op(m),op(m),op(m)] then
        return m:
    fi:
end do:
return FAIL:
end:

#Note: these procedures are not recursive, so we do not need option remember