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Invert Method #2

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Invert Method #2

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dd06091
Added invert function
zsiegel92 Jul 12, 2017
b994e4e
Added algebraic invert
zsiegel92 Jul 12, 2017
edcb6c1
cleaned up main
zsiegel92 Jul 12, 2017
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Binary file added python/__pycache__/subsets.cpython-34.pyc
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208 changes: 123 additions & 85 deletions python/subsets.py
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Original file line number Diff line number Diff line change
Expand Up @@ -6,88 +6,126 @@
# This source is public domain.

class EnumeratedSubsets(object):
def __init__(self):
self.cache = {}
def choose(self, n, k):
# handle the simple cases
k = min(k, n-k)
if k == 0:
return 1
elif k < 0:
raise Exception("negative k?")
elif k == 1:
return n
# handle caching and subcalls
c = (n,k)
if c not in self.cache:
self.cache[c] = self.choose(n-1, k) + self.choose(n-1, k-1)
return self.cache[c]

def precacheChoose(self, n, k=None):
# adjust your bounds
if k is None:
k = (n+1)//2 - 1
for k_i in xrange(1, k+1):
for n_i in xrange(k_i, n+1):
self.choose(n_i, k_i)

def generateSubset(self, n, k, i):
# non-recursive generateSubset(n, k, i), which will choose the i'th
# subset of size k from n items (numbered 0..n-1)
b = None
offset = 0
while 1:
if b is None:
b = set()

upperBound = self.choose(n,k)
if i >= upperBound:
return None

zeros = 0
low = 0
high = self.choose(n-1, k-1)
while i >= high:
zeros += 1
low = high
high += self.choose(n-zeros-1, k-1)

if (zeros + k) > n:
raise Exception("Too many zeros!")

b.add(offset + zeros)
if k == 1:
return sorted(b)
else:
n -= zeros + 1
k -= 1
i -= low
offset += zeros+1

def test(self):
for l in xrange(1, 10):
for k in xrange(1, min(l, 5)):
i = 0
while 1:
b = self.generateSubset(l, k, i)
if b is None:
break
print "%i %i %s: %s"%(l, k, i, b)
i += 1

i = 0
while 1:
b = self.generateSubset(25, 24, i)
if b is None:
break
print "%i %i %s: %s"%(25, 24, i, b)
i += 1

self.precacheChoose(10000, 12)
i = 160000
b = self.generateSubset(100, 3, i)
print "%i %i %s: %s"%(100, 3, i, b)

i = 160000000000000000000000000000
b = self.generateSubset(10000, 12, i)
print "%i %i %s: %s"%(10000, 12, i, b)
def __init__(self):
self.cache = {}
def choose(self, n, k):
# handle the simple cases
if (k>n):
return 0
k = min(k, n-k)
if k == 0:
return 1
elif k < 0:
raise Exception("negative k?")
elif k == 1:
return n
# handle caching and subcalls
c = (n,k)
if c not in self.cache:
self.cache[c] = self.choose(n-1, k) + self.choose(n-1, k-1)
return self.cache[c]

def precacheChoose(self, n, k=None):
# adjust your bounds
if k is None:
k = (n+1)//2 - 1
for k_i in xrange(1, k+1):
for n_i in xrange(k_i, n+1):
self.choose(n_i, k_i)

def generateSubset(self, n, k, i):
# non-recursive generateSubset(n, k, i), which will choose the i'th
# subset of size k from n items (numbered 0..n-1)
b = None
offset = 0
while 1:
if b is None:
b = set()

upperBound = self.choose(n,k)
if i >= upperBound:
return None

zeros = 0
low = 0
high = self.choose(n-1, k-1)
while i >= high:
zeros += 1
low = high
high += self.choose(n-zeros-1, k-1)

if (zeros + k) > n:
raise Exception("Too many zeros!")

b.add(offset + zeros)
if k == 1:
return sorted(b)
else:
n -= zeros + 1
k -= 1
i -= low
offset += zeros+1

def test(self):
for l in xrange(1, 10):
for k in xrange(1, min(l, 5)):
i = 0
while 1:
b = self.generateSubset(l, k, i)
if b is None:
break
print("%i %i %s: %s"%(l, k, i, b))
i += 1

i = 0
while 1:
b = self.generateSubset(25, 24, i)
if b is None:
break
print("%i %i %s: %s"%(25, 24, i, b))
i += 1

self.precacheChoose(10000, 12)
i = 160000
b = self.generateSubset(100, 3, i)
print("%i %i %s: %s"%(100, 3, i, b))

i = 160000000000000000000000000000
b = self.generateSubset(10000, 12, i)
print("%i %i %s: %s"%(10000, 12, i, b))

def invert(self,n,l):
k=len(l)
assert(k<=n) #assert subset of {1,...,n}
assert(k==len(set(l)))#assert unique elements
assert(max(l)<n)
l.sort()
if k==1:
return l[0]
elif k==0:
return 0
else:
return self.choose(n,k)-self.choose(n-l[0],k)+self.invert(n-l[0]-1,list(map(lambda x: x-l[0]-1,l[1:])))
def algebraicInvert(self,n,l):
k=len(l)
l.sort()
return self.choose(n,k) - self.choose(n-l[0],k) + sum([self.choose(n-l[i-1]-1,k-i) - self.choose(n-l[i],k-i) for i in range(1,k)])


if __name__=='__main__':
a = EnumeratedSubsets()
max_n = 15
for n in range(1,max_n):
for k in range(1,n+1):
for i in range(0,a.choose(n,k)):
l= a.generateSubset(n,k,i)
assert(a.invert(n,l)==i)
assert(a.invert(n,l)==a.algebraicInvert(n,l))

print("generateSubset(" + str(n) + "," + str(k) + "," + str(i) + ") = " + str(l))
print("invert(" + str(n) + "," + str(l) + ") = " + str(a.invert(n,l)))
print("algebraicInvert(" + str(n) + "," + str(l) + ") = " + str(a.algebraicInvert(n,l)))
print()

else:
print("Passed all tests")