#OK to post homework
#TianHao Zhang,02/23/19

#################################Help######################################

Help := proc():print(`A(n)` ):end:

#################################Part2#####################################
#ArDataMV(A,v,N): inputs a pos. number A, and a vector of numbers v (given as a list), (let n:=nops(v)) and outputs a list of length N where each entry is a pair obtained by picking a random point (a list of length n) in [-A,A]^n and returns the pair [x,0] if v.x (the dot product of v and x) is negative and [x,1] if it is zero or positive.

ArDataMV:=proc(A,v,N) local i, j, ra, t, x, n, sum, L:
L:=[]:
n:=nops(v):
ra:=rand(-abs(A)..abs(A)):
for i from 1 to N do
  x:=[]:

  for j from 1 to n do
    t:=ra():
    x:=[op(x),t]:
  od:

  sum := 0:

  for j from 1 to n do
    sum := sum + x[j]*v[j]:
  od:
  if sum < 0 then
    L:=[op(L),[x,0]]:
  else
    L:=[op(L),[x,1]]:
  fi:
od:

L:
end:

#################################Part3#####################################
#PAmv(L,n): that inputs a list containing data of the form [VectorOfLenghn,ZeroOrOne] where, VectorOfLengthn is a list of length n, and n is the dimension.
PAmv:=proc(L,n) local i,j,v,x,N,sum:
v:=[seq(0,i=1..n)]:
N:=nops(L):
for i from 1 to N do
  x:=L[i]:
  sum:=0:
  for j from 1 to n do
    sum := sum + x[1][j]*v[j]:
  od:
  if sum < 0 and x[2]=1 then
     for j from 1 to n do
       v[j] := v[j] + x[1][j]:
     od
  elif sum >= 0 and x[2]=0 then
     for j from 1 to n do
       v[j] := v[j] - x[1][j]:
     od
  fi:
od:

v:

end:

#################################Part4#####################################
#TestPMV(L,v) where v is a vector (list) with n components
TestPMV:=proc(L,v) local fn, fp, i, j, sum, n, N, x:
 fn:=0:
 fp:=0:
 N:=nops(L):
 n=nops(v):
  for i from 1 to N do
    sum:=0:
    x:=L[i]:
    for j from 1 to n do
      sum := sum + x[1][j]*v[j]:
    od:
    if sum >= 0 and x[2]=0 then
       fp:=fp+1:
    elif sum < 0 and x[2]=1 then
       fn:=fn+1:
    fi:
 od:

[fn,fp,N]:

end:

#################################Part5#####################################
#PA1corrected(L): That first transfoms the list L to the format [[data,1],ZeroOrOne], and uses your procedure PAmv(L,n) with n=2 to outputs two numbes a and b such that L[i][2]=1 iff ax+b>=0. Compare its performance to PA1(L).
PA1corrected:=proc(L) local i, L1, n:
 n:=nops(L):
 L1:=L:
 for i from 1 to n do
   L1[i][1]:=[op(L1[i][1]),1]:
 od:
PAmv(L1,2):
end: