#OK to post homework
#Ariana Yousafzai, 10/25/2020, Assignment 14


1.  


#CountRuns(L,k): inputs a list L of numbers (or for that matter, any objects) and outputs the #number of "runs" of length k in L




CountRuns:=proc(L,k) local fa,L1,T1,T2,t2:


option remember:


if not type(L,list) then
ERROR(`Bad input`):
fi:


if k=0 then
  RETURN({{}}):
fi:


if ( k>nops(S) or k<0 or not type(k,integer) ) then
   RETURN({}):
fi:


fa:=L[1]:


L1:=S minus {fa}:


T1:=CountRuns(L1,k):


T2:=CountRuns(L1,k-1):


T1 union { seq(t2 union {fa}, t2 in T2) }:


end:


6. 


Assume a list of length 2*n+1 with n+1 2s and n (-1)s 
Suppose L is equal to its cyclic shifts 
L=L1 k times
Sum(L) = Sum(L1)*k, where Sum(L1) is an integer and k is an integer 
If a and b are integers and a*b = 1, then a = 1 and b =1.