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  1. import base64
  2. import math
  3. import random
  4.  
  5.  
  6. def next_power_of_2(x):  
  7.     return 1 if x == 0 else 2**(x - 1).bit_length()
  8.  
  9.  
  10. def prev_power_of_2(x):
  11.   return next_power_of_2(x) >> 1
  12.  
  13.  
  14. def rank_permutation(seq):
  15.   ref = sorted(seq)
  16.   if ref == seq:
  17.     return 0
  18.   else:
  19.     rank = 0
  20.     f = math.factorial(len(seq)-1)
  21.     for x in ref:
  22.         if x < seq[0]:
  23.           rank += f
  24.         else:
  25.           rank += rank_permutation(seq[1:]) if seq[1:] else 0
  26.           return rank
  27.  
  28.  
  29. def unrank_permutation(n, k):
  30.     if not (0 <= k < math.factorial(n)):
  31.         raise ValueError("Rank k is out of bounds.")
  32.  
  33.     items = list(range(n))
  34.     permutation = []
  35.     temp_k = k
  36.  
  37.     for i in range(n, 0, -1):
  38.         index = temp_k // math.factorial(i - 1)
  39.         temp_k %= math.factorial(i - 1)
  40.         permutation.append(items.pop(index))
  41.  
  42.     return permutation
  43.  
  44.  
  45. def rank(comb):
  46.   return sum([
  47.     math.comb(ci, i + 1)
  48.     for i, ci in enumerate(comb)])
  49.  
  50.  
  51. def unrank(N, k):
  52.   comb = []
  53.   n = N
  54.   for r in range(k, 0, -1):
  55.     ci = r - 1
  56.     while math.comb(ci + 1, r) <= n:
  57.       ci += 1
  58.     comb.append(ci)
  59.     n -= math.comb(ci, r)
  60.   return list(reversed(comb))
  61.  
  62.  
  63. def unget(perm, n):
  64.   k = len(perm)
  65.   zipped = zip(perm, range(k))
  66.   zipped2 = [(*a, b) for a, b in zip(sorted(zipped), range(k))]
  67.   zipped_perm = sorted(zipped2, key=lambda x: x[1])
  68.   mapped_perm = map(lambda x: x[2], zipped_perm)
  69.   return rank(list(sorted(perm))), rank_permutation(list(mapped_perm))
  70.  
  71.  
  72. def get(ci, pi, k):
  73.   comb = unrank(ci, k)
  74.   perm = unrank_permutation(k, pi)
  75.   return list(map(lambda i: comb[i], perm))
  76.  
  77.  
  78. num_tests = 100
  79.  
  80. for _ in range(num_tests):
  81.     n = random.randint(2, 2048)
  82.     k = random.randint(1, min(30, n - 1))
  83.     perm = random.sample(range(n - 1), k)
  84.  
  85.     print(n, k)
  86.     print(perm)
  87.     ci, pi = unget(perm, n)
  88.     print((ci, pi))
  89.     print(min(
  90.       next_power_of_2(ci) - ci,
  91.       ci - prev_power_of_2(ci)))
  92.     bci, bpi = (
  93.       base64.b64encode(str(ci).encode()),
  94.       base64.b64encode(str(pi).encode()))
  95.     print((bci, bpi))
  96.     result = get(ci, pi, len(perm))
  97.     if perm != result:
  98.       print('HHHEEEEEEYYYYY!!!!')
  99.       print(perm, result)
  100.  
  101. print('Done.')
  102.  
Success #stdin #stdout 0.59s 16060KB
comments (?)
stdin 
Standard input is empty
stdout 
1931 13
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1055 11
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739 8
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1283 4
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1278 7
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1363 13
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403 7
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Done.
https://ideone.com/90l7Dr
language:
Python 3 (python  3.12)
created:
7 days ago
visibility:
public

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