def f(m,s, justValue=False, returnProcedure=False, checkCorrect=False): #put it all together and calculate f(m,s)
if m <= s:
print("scott's algorithm only works for m>s")
return
m = Fraction(m)
s = Fraction(s)
V = interval.findV(m,s)
sV, sVm1 = interval.getShares(m,s,V)
#sV are majors, sVm1 are minors
muffins, majors, minors = scott((m,Fraction(1),Fraction(2)),(sV,m/s,V),(sVm1,m/s,V-1))
if checkCorrect:
if checkProcedure(muffins, majors + minors, m, s):
print("procedure is correct")
else:
print("procedure is not valid!!")
if justValue:
return max(min([piece for muffin in muffins for piece in muffin]), Fraction(1,3))
if returnProcedure:
if muffins[0][0] < Fraction(1,3):
print("scott's algorithm only works if f(m,s) > 1/3")
return (muffins, majors, minors)
for muffin in muffins:
print("Muffin: " + pfmap(muffin))
for student in majors+minors:
print("Student: " + pfmap(student))
def f(m,s):
m = Fraction(m)
s = Fraction(s)
V = interval.findV(m,s)
sV, sVm1 = interval.getShares(m,s,V)
#sV are majors, sVm1 are minors
return scott((m,1,2),(sV,m/s,V),(sVm1,m/s,V-1))
def doit(m, s):
V = interval.findV(m, s)
Q = findq.findQ(m, s, spew=False)
(sV, sVm1) = interval.getShares(m, s, V)
intervals = getIntervals(m, s, Q, V)
#print (sV, sVm1, V)
return intervals
def genMatchFunctions(m, s): """Given an (m,s), generate a tuple (MVm1, MV) which has the match functions. There are two match functions because which one is to be used depends on weather the piece is a V share or a V-1 share. The MV works for V shares, and the MVm1 works for V-1 shares.""" m, s = Fraction(m), Fraction(s) V = interval.findV(m,s) MV = (-o/(V-1), m/s/(V-1)) MVm1 = (-o/(V-2), m/s/(V-2)) return (MV, MVm1)
def findQ(m, s, spew=True):
m = Fraction(m)
s = Fraction(s)
if (m < s and spew):
print("The interval therum only works when m>s")
return 1
V = interval.findV(m, s)
(sV, sVm1) = interval.getShares(m, s, V)
if sV == 0 or sVm1 == 0: #TODO: tell bill about this
return 1 #this means everyone gets same number of pieces
dat = (m, s, V, sV, sVm1)
if spew: print("V: " + str(V))
if spew: print("sV: " + str(sV))
if spew: print("sVm1: " + str(sVm1))
if (sVm1 == 0 and spew):
print(
"sVm1 is zero, so this in not a case handled by the interval theorum."
)
return 1
Q1 = findQ1(dat)
Q2 = findQ2(dat)
Q3 = (V - (m / s) - Fraction(3, 2)) / (V - 2)
if not PREM3(dat, Q3):
Q3 = 1
Q4 = (m / s - Fraction(1, 2)) / (V - 1)
if not PREM4(dat, Q4):
Q4 = 1
#Q5 = (V - 2) / (2*V - 3)
Q5 = (m / s - Fraction(1) / 2) / (V - 1)
if not PREM5(dat, Q5):
Q5 = 1
#Q6 = (V - 2) / (2*V - 3)
Q6 = (V - Fraction(3) / 2 - m / s) / (V - 2)
if not PREM6(dat, Q6):
Q6 = 1
Q7 = findQ7(m, s, sV, sVm1, V)
Q8 = findQ8(m, s, sV, sVm1, V)
Q9 = findQ9(m, s, sV, sVm1, V)
Q10 = findQ10(m, s, sV, sVm1, V)
if spew:
print("Qs: " + str([Q1, Q2, Q3, Q4, Q5, Q6, Q7, Q8, Q9, Q10]))
Q = min([Q1, Q2, Q3, Q4, Q5, Q6, Q7, Q8])
return max(Fraction(1) / 3, m / (s * (V + 1)), 1 - m / (s * (V - 2)), Q)
def constrain(m, s, Qs):
m, s = Fraction(m), Fraction(s)
V = interval.findV(m, s)
sV, sVm1 = interval.getShares(m, s, V)
Q = Value(1, 0)
M = [Interval(Q, 1 + -1 * Q)]
A = [Interval(Q, 1 + -1 * Q)]
B = [Interval(Q, 1 + -1 * Q)]
Qmin = 0 #Qs
#note to self: adding thing where if A or B is [], then just return current Qmin
while True:
print("A, B")
print(A)
print(B)
print("with Qmin = " + str(Qmin))
oldA, oldB, oldM = A, B, M
(M, Qminm) = constrainToSumT(M, 2, 1, Qs)
(A, Qmina) = constrainToSumT(A, V - 1, m / s, Qs)
(B, Qminb) = constrainToSumT(B, V, m / s, Qs)
Qmin = max(Qmin, Qmina, Qminb, Qminm)
print("with Qmin after constrain = " + str(Qmin) +
"and Qmina=%s, Qminb=%s, Qminc=%s" %
(str(Qmina), str(Qminb), str(Qminm)))
print("A, B, M after constrain")
print(A)
print(B)
print(M)
(A, Qmina) = intersection(A, M, Qs)
(B, Qminb) = intersection(B, M, Qs)
(M, Qminm) = union(A + B, Qs)
Qmin = max(Qmin, Qmina, Qminb, Qminm)
#print("with Qmin after intersection = " + str(Qmin))
if oldA == A and oldB == B and oldM == M:
break
if A == [] or B == []:
print('breaking because empty: A = ' + str(A) + ' B = ' + str(B))
break
return M, Qmin