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  1. import base64
  2. import math
  3. import random
  4.  
  5.  
  6. def rank_permutation(seq):
  7.   ref = sorted(seq)
  8.   if ref == seq:
  9.     return 0
  10.   else:
  11.     rank = 0
  12.     f = math.factorial(len(seq)-1)
  13.     for x in ref:
  14.         if x < seq[0]:
  15.           rank += f
  16.         else:
  17.           rank += rank_permutation(seq[1:]) if seq[1:] else 0
  18.           return rank
  19.  
  20.  
  21. def unrank_permutation(n, k):
  22.     if not (0 <= k < math.factorial(n)):
  23.         raise ValueError("Rank k is out of bounds.")
  24.  
  25.     items = list(range(n))
  26.     permutation = []
  27.     temp_k = k
  28.  
  29.     for i in range(n, 0, -1):
  30.         index = temp_k // math.factorial(i - 1)
  31.         temp_k %= math.factorial(i - 1)
  32.         permutation.append(items.pop(index))
  33.  
  34.     return permutation
  35.  
  36.  
  37. def rank(comb):
  38.   return sum([
  39.     math.comb(ci, i + 1)
  40.     for i, ci in enumerate(comb)])
  41.  
  42.  
  43. def unrank(N, k):
  44.   comb = []
  45.   n = N
  46.   for r in range(k, 0, -1):
  47.     ci = r - 1
  48.     while math.comb(ci + 1, r) <= n:
  49.       ci += 1
  50.     comb.append(ci)
  51.     n -= math.comb(ci, r)
  52.   return list(reversed(comb))
  53.  
  54.  
  55. def unget(perm, n):
  56.   k = len(perm)
  57.   zipped = zip(perm, range(k))
  58.   zipped2 = [(*a, b) for a, b in zip(sorted(zipped), range(k))]
  59.   zipped_perm = sorted(zipped2, key=lambda x: x[1])
  60.   mapped_perm = map(lambda x: x[2], zipped_perm)
  61.   return rank(list(sorted(perm))), rank_permutation(list(mapped_perm))
  62.  
  63.  
  64. def get(ci, pi, k):
  65.   comb = unrank(ci, k)
  66.   perm = unrank_permutation(k, pi)
  67.   return list(map(lambda i: comb[i], perm))
  68.  
  69.  
  70. num_tests = 100
  71.  
  72. for _ in range(num_tests):
  73.     n = random.randint(2, 2048)
  74.     k = random.randint(1, min(30, n - 1))
  75.     perm = random.sample(range(n - 1), k)
  76.  
  77.     print(n, k)
  78.     print(perm)
  79.     ci, pi = unget(perm, n)
  80.     print((ci, pi))
  81.     bci, bpi = (
  82.       base64.b64encode(str(ci).encode()),
  83.       base64.b64encode(str(pi).encode()))
  84.     print((bci, bpi))
  85.     result = get(ci, pi, len(perm))
  86.     if perm != result:
  87.       print('HHHEEEEEEYYYYY!!!!')
  88.       print(perm, result)
  89.  
  90. print('Done.')
  91.  
Success #stdin #stdout 0.58s 15584KB
comments (?)
stdin 
Standard input is empty
stdout 
778 1
[468]
(468, 0)
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550 13
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1314 25
[42, 669, 195, 976, 714, 932, 127, 756, 846, 60, 1238, 419, 922, 571, 224, 152, 731, 67, 139, 1233, 613, 1310, 118, 19, 455]
(43977895894767783996648563393906656858322681198065307, 965343432669283702628492)
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1973 11
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1840 26
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417 11
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763 7
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1464 3
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1246 12
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649 10
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1071 1
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917 7
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164 3
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1559 3
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1143 24
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424 30
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1169 17
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1145 30
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1004 28
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140 7
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2030 1
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856 7
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1471 1
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331 7
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1709 24
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699 14
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51 10
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1000 21
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Done.
https://ideone.com/yByGWW
language:
Python 3 (python  3.12)
created:
8 days ago
visibility:
public

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