#Write an R program for finding stationary distribution of markov chains


# Define prob transition matrix 
# (note matrix() takes vectors in column form so there is a transpose here to switch col's to row's)
P=t(matrix(c(c(0.5,0.4,0.1),c(0.3,0.4,0.3),c(0.2,0.3,0.5)),nrow=3))
# Check sum across = 1
apply(P,1,sum) 


# Definte initial probability vector
x0=c(0.1,0.2,0.7)
# Check sums to 1
sum(x0)


pi_bru <- (P^100)[1,]
print("Brute-force")
print(pi_bru)