# Python code for 1-D random walk. 
import random 
import numpy as np 
import matplotlib.pyplot as plt 

# Probability to move up or down 
prob = [0.05, 0.95]   

n = 1000 # number of steps

# statically defining the starting position 
start = 2  
positions = [start] 

# creating the random points 
rr = np.random.random(n) 
downp = rr < prob[0] 
upp = rr > prob[1] 

t = 1

step = (1/n)**0.5

for idownp, iupp in zip(downp, upp): 
    down = step if idownp and positions[-1] > 1 else 0
    up = step if iupp and positions[-1] < 4 else 0
    positions.append(positions[-1] - down + up) 

# plotting down the graph of the random walk in 1D 
x = [i*t/n for i in range(n+1)]
plt.plot(x, positions) 
plt.xlabel('Time (seconds)')
plt.ylabel('Distance')
plt.title(f"Random Walk ({n} steps in {t} seconds)")
plt.grid(True)
plt.savefig("random_walk.png")


plt.show()