#C1.txt: Maple Code for ExpMath Spring 2021,Lecture 1, Jan. 21, 2021

Help:=proc(): print(` LC(p) , IsDer(pi), RandPer(n) `): end:

#LC(p): Inputs a RATIONAL number p and outputs a pseudo-random number
#1 with probability p and 2 with probability 1-p
LC:=proc(p) local m,n,r:

if not ( type(p,numeric) and p>=0  and p<=1) then
 RETURN(FAIL):
fi:

if p=0 then
 RETURN(2):
fi:

if p=1 then
 RETURN(1):
fi:

if not type(p,fraction) then
 RETURN(FAIL):
fi:

m:=numer(p):
n:=denom(p):
r:=rand(1..n)():

if r<=m then
  1:
else
 2:
fi:

end:


#DEF: A derangement of {1, ...,n} is a permutation such that pi[i]<>i for every i
#IsDer(pi): inputs a permutation of {1,...,n} pi (n=nops(pi))
#and outputs true iff it is a derangement
IsDer:=proc(pi) local n,i:
n:=nops(pi):
for i from 1 to n do
 if pi[i]=i then
    RETURN(false):
 fi:
od:
true:
end:

#RandDer(n): Generates a random derangement using the NAIVE approach suggested by
#Alon Itai in his not entirely-raving Math review of the Nijenhuius-Wilf classic
RandDer:=proc(n) local pi:

pi:=randperm(n):

while  not IsDer(pi) do
pi:=randperm(pi):
od:
pi:
end: