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  1. import itertools
  2. import math
  3. import random
  4.  
  5.  
  6. def rank(p, elements):
  7.   k = len(p)
  8.  
  9.   if k == 1:
  10.     return len(list(e for e in elements if e < p[0]))
  11.  
  12.   head, tail = p[0], p[1:]
  13.  
  14.   n = len(elements) - 1
  15.   num_preceding = len([e for e in elements if e < head])
  16.  
  17.   preceding = num_preceding * (
  18.       math.factorial(n)
  19.       / math.factorial(n - k + 1)
  20.   )
  21.  
  22.   return int(preceding) + rank(tail, elements - {head})
  23.  
  24.  
  25. def update_p(p, i, n):
  26.   p[i] += 1
  27.   prev = p[:i]
  28.   while p[i] in prev:
  29.     p[i] += 1
  30.   for j in range(i + 1, len(p)):
  31.     p[j] = 0
  32.     prev = p[:j]
  33.     while p[j] in prev:
  34.       p[j] += 1
  35.  
  36.  
  37. def unrank(index, k, n):
  38.   elements = sorted(range(n))
  39.   p = elements[:k]
  40.   remaining = index
  41.   for i in range(k):
  42.     if p[i] == n - 1:
  43.       continue
  44.     while True:
  45.       r = rank(p, set(elements))
  46.       if r > remaining:
  47.         break
  48.       update_p(p, i, n)
  49.       print((p,r))
  50.       candidate = remaining - r
  51.     remaining = candidate
  52.   return p
  53.  
  54. n = 4
  55. k = 2
  56.  
  57. for p in sorted(itertools.chain.from_iterable(map(
  58.     lambda x: list(itertools.permutations(x)),
  59.     itertools.combinations(range(n), k)))):
  60.   print((p, rank(list(p), set(range(n)))))
  61.  
  62. n = 2048
  63. k = 24
  64. p = random.sample(range(n), k)
  65. # print((p, rank(p, set(range(n)))))
  66.  
  67. num_tests = 1
  68. max_n = 20
  69. max_k = 5
  70.  
  71. for _ in range(num_tests):
  72.   n = random.randint(5, max_n)
  73.   k = random.randint(2, min(max_k, n))
  74.  
  75.   p = random.sample(range(n), k)
  76.   p, k, n = [6, 2], 2, 14
  77.   elements = set(range(n))
  78.  
  79.   rank_p = rank(p, elements)
  80.   unranked = unrank(rank_p, k, n)
  81.  
  82.   if unranked != p:
  83.     print((p, n, rank_p, unranked, rank(unranked, elements)))
  84.     break
Success #stdin #stdout 0.15s 14196KB
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stdin
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Standard input is empty
stdout
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((0, 1), 0)
((0, 2), 1)
((0, 3), 2)
((1, 0), 3)
((1, 2), 4)
((1, 3), 5)
((2, 0), 6)
((2, 1), 7)
((2, 3), 8)
((3, 0), 9)
((3, 1), 10)
((3, 2), 11)
([1, 0], 0)
([2, 0], 13)
([3, 0], 26)
([4, 0], 39)
([5, 0], 52)
([6, 0], 65)
([7, 0], 78)
([6, 2], 14, 80, [7, 0], 91)
https://ideone.com/iNsPKN
language:
Python 3 (python  3.12)
created:
6 hours ago
visibility:
public

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