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EulerP31.py
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EulerP31.py
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def findSums( end):
Q = [[]]
perms = set([])
while Q:
currPerm = Q.pop(0)
#print currPerm
if sum(currPerm) == end:
perms.add(tuple(currPerm))
moves = [0.01, 0.02, 0.05, 0.1, 0.2, 0.5, 1.0, 2.0]
for move in moves:
newPerm = currPerm[:]
newPerm.append(move)
if sum(newPerm) <= 2 and set(newPerm) not in [set(p) for p in Q]:
Q.append(newPerm)
return perms
"""
f = findSums(2)
for p in f:
print sorted(p)
"""
coins = [0.01, 0.02, 0.05, 0.1, 0.2, 0.5, 1.0, 2.0]
"""
perms = set([])
def check(x):
if sum(x) == 2 and set(x) not in [set(p) for p in perms] :
perms.add(tuple(x))
return perms
c = [[0][:] for i in range(5)]
for c[0] in coins:
check([c[0]])
for c[1] in coins:
check(c[:2][:])
for c[2] in coins:
check(c[:2][:])
for c[3] in coins:
check(c[:3])
for c[4] in coins:
check(c[:])
for perm in perms:
print perm
print len(perms)
coins = [0] * 8 + [0.01, 0.02, 0.05, 0.1, 0.2, 0.5, 1.0]
perms = set() # invariant no repeated elements,
#from itertools import *
# return elements with length=5 repeat
def combinations_with_replacement(iterable, r):
# combinations_with_replacement('ABC', 2) --> AA AB AC BB BC CC
pool = tuple(iterable)
print pool, "poop"
n = len(pool)
if not n and r:
return
indices = [0] * r
print "indi", indices
yield tuple(pool[i] for i in indices)
while True:
for i in reversed(range(r)):
if indices[i] != n - 1:
break
else:
return
indices[i:] = [indices[i] + 1] * (r - i)
yield tuple(pool[i] for i in indices)
"""
"""
for x in combinations_with_replacement(coins,10):
print x
"""
"""
for comb in combinations:
for x in permutations(comb):
if sum(x) == 2:
perms.add(x)
for p in perms: print p
"""
"""
for i in range(5):
for j in range(5):
for I in range(5):
for J in range(5):
if i + j + I + J == 13:
print i, j, I, J
"""
"""
x = coins[:]
P = []
def r(n, L):
for i in x:
if sum(L) > 2:
return
if n <= 3:
r(n+1, L + [i])
P.append(L)
r(0, [])
l = set([])
P = [sorted(p) for p in P if sum(p) == 2]
print len(P), P
X = set(tuple(p) for p in P)
for p in X:
print list(p), "1"
"""
'''x = coins[:]
P = []
def r(n, L, t, F):
for i in x:
if sum(L) > F or (n >= t and sum(L) < 0.5):
return
#if set(L) in [set(p) for p in P]:
# break
if n <= t:
r(n+1, L + [i], t, F)
print L
P.append(L)
r(0, [], 100, 1)
P1 = [sorted(p) for p in P if round(sum(p),2) == 1]
for p in P1:
print sum(p), p
print len(P1), P1
print "P", P
'''
a1 = [[0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1], [0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.1, 0.2], [0.2, 0.2, 0.2, 0.2, 0.2], [0.1, 0.1, 0.1, 0.1, 0.1, 0.5], [0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.1, 0.2, 0.5], [0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.02, 0.1, 0.2, 0.5], [0.02, 0.02, 0.02, 0.02, 0.02, 0.02, 0.02, 0.02, 0.02, 0.02, 0.1, 0.2, 0.5], [0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.05, 0.1, 0.2, 0.5], [0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.01, 0.02, 0.05, 0.1, 0.2, 0.5], [0.01, 0.02, 0.02, 0.02, 0.02, 0.02, 0.02, 0.02, 0.05, 0.1, 0.2, 0.5], [0.05, 0.05, 0.05, 0.05, 0.1, 0.2, 0.5], [0.1, 0.1, 0.1, 0.2, 0.5], [0.1, 0.2, 0.2, 0.5], [0.5, 0.5], [1.0]]
a5 = [[0.2, 0.2, 0.1], [0.1, 0.1, 0.1, 0.1, 0.1]]
a3 = [[0.1, 0.1], [0.2], [0.02] * 10, [0.01] ]
#vals = {1: a1, 0.5: [[0.2, 0.2, 0.1], [0.1, 0.1, 0.1, 0.1, 0.1]]}
vals = {1.0: [[0.5, 0.5]], 0.5: [[0.2, 0.2, 0.1]], 0.2: [[0.1, 0.1]], 0.1: [[0.05, 0.05]], 0.05: [[0.02, 0.02, 0.01]], 0.02: [[0.01, 0.01]] }
#perms = [[0.05]]
def rec(x, perms):
for i,e in enumerate(x):
if e != 0.01:
v = vals[e]
temp = sorted([a + x[:i] + x[i+1:] for a in v])
if temp not in perms:
perms += temp
return sorted([sorted(list(p)) for p in set([tuple(sorted(p2)) for p2 in perms])])
#perms = rec(perms[0], perms)
#p1 = perms[:]
def getVal(perms):
perms = rec(perms[0], perms)[:]
while True:
prev = perms[:]
for perm in perms[:]:
perms = rec(perm, perms)[:]
#print len(perms), perms
if perms == prev or len(prev) == len(perms):
break
return perms
perms = getVal([[0.02]])[:]
vals[0.02] = perms
print len(perms), perms
perms = getVal([[0.05]])[:]
vals[0.05] = perms
print len(perms), perms
perms = getVal([[0.1]])[:]
vals[0.1] = perms
print len(perms), perms
perms = getVal([[0.5]])[:]
vals[0.5] = perms
print len(perms), perms
perms = getVal([[1.0]])[:]
print len(perms), perms
'''
for perm in perms[:]:
rec(perm)
for perm in perms[:]:
rec(perm)
for perm in perms[:]:
rec(perm)
for perm in perms[:]:
rec(perm)
for perm in perms[:]:
rec(perm)
for perm in perms[:]:
rec(perm)
for perm in perms[:]:
rec(perm)
for perm in perms[:]:
rec(perm)
for perm in perms[:]:
rec(perm)
for perm in perms[:]:
rec(perm)
'''
#perms = [sorted(perm) for perm in perms]
#print len(perms), perms
#print [0.01, 0.01, 0.01, 0.02, 0.05, 0.2, 0.2, 0.5, 1.0] in perms