A permutation is an ordered arrangement of objects. For example, 3124 is one possible permutation of the digits 1, 2, 3 and 4. If all of the permutations are listed numerically or alphabetically, we call it lexicographic order. The lexicographic permutations of 0, 1 and 2 are:
012 021 102 120 201 210
What is the millionth lexicographic permutation of the digits 0, 1, 2, 3, 4, 5, 6, 7, 8 and 9?
In [1]:
factorials = [1]
prod = 1
for k in range(1, 10):
prod *= k
factorials.append(prod)
factorials.reverse()
def base_factorial(n):
seq = []
for f in factorials:
seq.append(n//f)
n %= f
return seq
def get_perm(n):
L = list(range(10))
perm = ''
for d in base_factorial(n):
perm += str(L[d])
del L[d]
return perm
print(get_perm(10**6 - 1))
In [ ]: