Python codes

Vertification of an assignment from Stochastic Processing. Using Brute Force and "itertools" library.

import itertools
 
dim = 100
m = list(range(1, dim+1))
w = list(range(-1, -dim-1, -1))
num = 0
global zero_num
zero_num = 0
 
m_all = list(itertools.permutations(m,dim))
w_all = list(itertools.permutations(w,dim))
 
num = len(m_all) * len(w_all)
for m in m_all:
    for w in w_all:
        for i in range(dim):
            if m[i] + w[i] == 0:
                zero_num += 1
                break
 
print(zero_num)
print(num)
print((num-zero_num)/num)

As dim goes to infinity, the final ratio should be approaching to 1/e.