115 lines
3.1 KiB
Python
115 lines
3.1 KiB
Python
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# -*- coding: utf-8 -*-
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"""
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Simulation of a random walk on a finite b-ary tree of depth k
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"""
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import random as rn
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import numpy as np
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import matplotlib.pyplot as plt
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import math as mt
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rn.seed(666)
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k = 20 # depth of the tree
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b = 2 # arity of the tree
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T = 100 # number of steps taken by the MC
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E = np.zeros(exp)
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M = np.zeros(exp)
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for b in range(0,exp):
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X = np.zeros(T)
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Y = np.zeros(T)
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Z = np.zeros(T)
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for a in range(0, T):
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Z[a] = T
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X[0] = rn.randint(0,k) # setting the starting level for X
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Y[0] = rn.randint(0,k) # setting the starting level for Y
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for a in range(0, (T - 1)):
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monX = rn.randint(0,1)
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probArisX = rn.randint(0,(b + 1))
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monY = rn.randint(0,1)
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probArisY = rn.randint(0,(b + 1))
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if X[a] != Y[a]:
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if X[a] > 0 and X[a] < k:
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if monX == 1:
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X[a + 1] = X[a]
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if monX == 0:
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if probArisX == 0:
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X[a + 1] = (X[a] - 1)
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if probArisX != 0:
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X[a + 1] = (X[a] + 1)
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if X[a] == 0:
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if monX == 1:
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X[a + 1] = 0
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if monX == 0:
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X[a + 1] = 1
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if X[a] == k:
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if monX == 1:
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X[a + 1] = k
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if monX == 0:
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X[a + 1] = (k - 1)
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if Y[a] > 0 and Y[a] < k:
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if monY == 1:
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Y[a + 1] = Y[a]
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if monY == 0:
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if probArisY == 0:
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Y[a + 1] = (Y[a] - 1)
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if probArisY != 0:
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Y[a + 1] = (Y[a] + 1)
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if Y[a] == 0:
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if monY == 1:
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Y[a + 1] = 0
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if monY == 0:
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Y[a + 1] = 1
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if Y[a] == k:
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if monY == 1:
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Y[a + 1] = k
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if monY == 0:
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Y[a + 1] = (k - 1)
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if X[a] == Y[a]:
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Z[a] = a
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if X[a] > 0 and X[a] < k:
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if monX == 1:
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X[a + 1] = X[a]
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Y[a + 1] = X[a + 1]
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if monX == 0:
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if probArisX == 0:
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X[a + 1] = (X[a] - 1)
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Y[a + 1] = X[a + 1]
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if probArisX != 0:
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X[a + 1] = (X[a] + 1)
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Y[a + 1] = X[a + 1]
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if X[a] == 0:
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if monX == 1:
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X[a + 1] = 0
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Y[a + 1] = X[a + 1]
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if monX == 0:
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X[a + 1] = 1
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Y[a + 1] = X[a + 1]
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if X[a] == k:
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if monX == 1:
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X[a + 1] = k
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Y[a + 1] = X[a + 1]
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if monX == 0:
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X[a + 1] = (k - 1)
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Y[a + 1] = X[a + 1]
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E[b] = np.amin(Z)
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m = np.mean(E)
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for b in range(0,exp):
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M[b] = m
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n = (mt.pow(b,k + 1) - 1)/(b - 1)
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#plt.hist(E,histtype='bar')
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plt.plot(E,'bo',ms=0.8)
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plt.plot(M, 'r')
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plt.show()
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#if m <= 4*n:
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# print('Test passed')
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