level3_3.py

from fractions import Fraction

def transposeMatrix(m):
	return map(list,zip(*m))

def getMatrixMinor(m,i,j):
    return [row[:j] + row[j+1:] for row in (m[:i]+m[i+1:])]

def getMatrixDeternminant(m):
    if len(m) == 2:
        return m[0][0]*m[1][1]-m[0][1]*m[1][0]

    determinant = 0
    for c in range(len(m)):
        determinant += ((-1)**c)*m[0][c]*getMatrixDeternminant(getMatrixMinor(m,0,c))
    return determinant

def getMatrixInverse(m):
    determinant = getMatrixDeternminant(m)
    if len(m) == 2:
        return [[m[1][1]/determinant, -1*m[0][1]/determinant],
                [-1*m[1][0]/determinant, m[0][0]/determinant]]

    cofactors = []
    for r in range(len(m)):
        cofactorRow = []
        for c in range(len(m)):
            minor = getMatrixMinor(m,r,c)
            cofactorRow.append(((-1)**(r+c)) * getMatrixDeternminant(minor))
        cofactors.append(cofactorRow)
    cofactors = transposeMatrix(cofactors)
    for r in range(len(cofactors)):
        for c in range(len(cofactors)):
            cofactors[r][c] = cofactors[r][c]/determinant
    return cofactors

s=int(input("Enter number of states "))
m = [[int(input()) for x in range (s)] for y in range(s)]

terms=[]
termlen=0
t=[([0]*s) for i in range(s)]

for i in range(s):
	if m[i].count(0)==len(m[i]):
		m[i][i]=1
		termlen+=1
	else:
		m[i]=[j/sum(m[i]) for j in m[i]]

# for i in range(s):
# 	print(m[i])
# print("\n")

for i in range(s):
	for j in range(s):
		t[(i+termlen)%s][(j+termlen)%s]=m[i][j]

r=[[0 for i in range(termlen)] for j in range(s-termlen)]
q=[[0 for i in range(s-termlen)] for j in range(s-termlen)]

for i in range(s-termlen):
	for j in range(termlen):
		r[i][j]=t[i+termlen][j]

for i in range(s-termlen):
	for j in range(s-termlen):
		q[i][j]=-1*t[i+termlen][j+termlen]
	q[i][i]=1+q[i][i]

f=getMatrixInverse(q)

fr=[[0 for i in range(termlen)] for j in range(s-termlen)]

for i in range(s-termlen):
	for j in range(termlen):
		for k in range(s-termlen):
			fr[i][j]+=f[i][k]*r[k][j]

for i in range(s):
	print(t[i])
print("\n")

for i in range(s-termlen):
	print(r[i])
print("\n")

for i in range(s-termlen):
	print(q[i])
print("\n")

for i in range(s-termlen):
	print(f[i])
print("\n")

for i in range(s-termlen):
	print(fr[i])
print("\n")

num=[]
den=[]
for i in fr[0]:
	stringo=str(Fraction(i).limit_denominator())
	print(stringo)
	try:
		num.append(int(stringo.split("/")[0]))
	except:
		num.append(0)
	try:
		den.append(int(stringo.split("/")[1]))
	except:
		den.append(0)

maxden=max(den)

for i in range(len(num)):
	if num[i]==0:
		terms.append(0)
		continue
	if den[i]<maxden:
		terms.append(int(num[i]*maxden/den[i]))
	else:
		terms.append(num[i])

terms.append(maxden)
# print(num,"\n",den)
print(terms)