import numpy as np

# Transition matrix
#a_ij here means the probability of transitioning j->i, otherwise transpose A
A = np.array([
    [0.5, 0.3, 0.3],
    [0.4, 0.5, 0.4],
    [0.1, 0.2, 0.3]
])

# Initialize state (states are indexed 0,1,2 here)
current_state = 2
state_counts = [0, 0, 0]  # Track visits to each state
num_transitions = 1000

# Simulate transitions and count states
for _ in range(num_transitions):
    state_counts[current_state] += 1
    current_state = np.random.choice([0, 1, 2], p=A[:,current_state])

# Print the number of times each state was visited
print("State visit counts:")
print(f"State 1: {state_counts[0]}")
print(f"State 2: {state_counts[1]}")
print(f"State 3: {state_counts[2]}")