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Task/Permutations-Rank-of-a-permutation/Python/permutations-rank-of-a-permutation-1.py

@@ -0,0 +1,86 @@
+from math import factorial as fact
+from random import randrange
+from textwrap import wrap
+
+def identity_perm(n):
+    return list(range(n))
+
+def unranker1(n, r, pi):
+    while n > 0:
+        n1, (rdivn, rmodn) = n-1, divmod(r, n)
+        pi[n1], pi[rmodn] = pi[rmodn], pi[n1]
+        n = n1
+        r = rdivn
+    return pi
+
+def init_pi1(n, pi):
+    pi1 = [-1] * n
+    for i in range(n):
+        pi1[pi[i]] = i
+    return pi1
+
+def ranker1(n, pi, pi1):
+    if n == 1:
+        return 0
+    n1 = n-1
+    s = pi[n1]
+    pi[n1], pi[pi1[n1]] = pi[pi1[n1]], pi[n1]
+    pi1[s], pi1[n1] = pi1[n1], pi1[s]
+    return s + n * ranker1(n1, pi, pi1)
+
+def unranker2(n, r, pi):
+    while n > 0:
+        n1 = n-1
+        s, rmodf = divmod(r, fact(n1))
+        pi[n1], pi[s] = pi[s], pi[n1]
+        n = n1
+        r = rmodf
+    return pi
+
+def ranker2(n, pi, pi1):
+    if n == 1:
+        return 0
+    n1 = n-1
+    s = pi[n1]
+    pi[n1], pi[pi1[n1]] = pi[pi1[n1]], pi[n1]
+    pi1[s], pi1[n1] = pi1[n1], pi1[s]
+    return s * fact(n1) + ranker2(n1, pi, pi1)
+
+def get_random_ranks(permsize, samplesize):
+    perms = fact(permsize)
+    ranks = set()
+    while len(ranks) < samplesize:
+        ranks |= set( randrange(perms)
+                      for r in range(samplesize - len(ranks)) )
+    return ranks
+
+def test1(comment, unranker, ranker):
+    n, samplesize, n2 = 3, 4, 12
+    print(comment)
+    perms = []
+    for r in range(fact(n)):
+        pi = identity_perm(n)
+        perm = unranker(n, r, pi)
+        perms.append((r, perm))
+    for r, pi in perms:
+        pi1 = init_pi1(n, pi)
+        print('  From rank %2i to %r back to %2i' % (r, pi, ranker(n, pi[:], pi1)))
+    print('\n  %i random individual samples of %i items:' % (samplesize, n2))
+    for r in get_random_ranks(n2, samplesize):
+        pi = identity_perm(n2)
+        print('    ' + ' '.join('%2i' % i for i in unranker(n2, r, pi)))
+    print('')
+
+def test2(comment, unranker):
+    samplesize, n2 = 4, 144
+    print(comment)
+    print('  %i random individual samples of %i items:' % (samplesize, n2))
+    for r in get_random_ranks(n2, samplesize):
+        pi = identity_perm(n2)
+        print('    ' + '\n      '.join(wrap(repr(unranker(n2, r, pi)))))
+    print('')
+
+if __name__ == '__main__':
+    test1('First ordering:', unranker1, ranker1)
+    test1('Second ordering:', unranker2, ranker2)
+    test2('First ordering, large number of perms:', unranker1)

Task/Permutations-Rank-of-a-permutation/Python/permutations-rank-of-a-permutation-2.py

@@ -0,0 +1,17 @@
+def ranker1(n, pi, pi1):
+    if n == 1:
+        return 0
+    n1 = n-1
+    s = pi[n1]
+    pi[n1], pi[pi1[n1]] = pi[pi1[n1]], pi[n1]
+    pi1[s], pi1[n1] = pi1[n1], pi1[s]
+    return s + n * ranker1(n1, pi, pi1)
+
+def ranker2(n, pi, pi1):
+    result = 0
+    for i in range(n-1, 0, -1):
+        s = pi[i]
+        pi[i], pi[pi1[i]] = pi[pi1[i]], pi[i]
+        pi1[s], pi1[i] = pi1[i], pi1[s]
+        result += s * fact(i)
+    return result