def naive_transition_matrix( n ):
states = [ tuple(state) for state in euler.permutations( range(1,n+1) ) ]
m = len(states)
mat = numpy.zeros( (m,m) )
state2id = dict(zip(states, range(len(states))))
id2state = dict(zip(range(len(states)), states))
choices = list(euler.choose(range(n), 2))
for u in states[1:]:
for i, j in choices:
v = list(u)
v[i], v[j] = v[j], v[i]
v = tuple(v)
mat[ state2id[u], state2id[v] ] = 1.0/len(choices)
return numpy.matrix(mat)
seq = [[x[i] for i in y] for y in lst]
return seq
def clockwise(seq):
for i in range(1, 5):
if seq[0][0] >= seq[i][0]:
return False
return True
def flatten(seq):
lst = ""
for i in seq:
for j in i:
lst += str(j)
return lst
ran = range(10)
ran.reverse()
ran = [i + 1 for i in ran]
for i, v in enumerate(euler.permutations(ran)):
ss = solset(v)
sums = [sum(i) for i in ss]
if alleq(sums) and clockwise(ss):
print v, ss, sums, clockwise(ss)
gon = flatten(ss)
if len(gon) == 16:
print gon
seq = [[x[i] for i in y] for y in lst]
return seq
def clockwise(seq):
for i in range(1, 5):
if seq[0][0] >= seq[i][0]:
return False
return True
def flatten(seq):
lst = ''
for i in seq:
for j in i:
lst += str(j)
return lst
ran = range(10)
ran.reverse()
ran = [i + 1 for i in ran]
for i, v in enumerate(euler.permutations(ran)):
ss = solset(v)
sums = [sum(i) for i in ss]
if alleq(sums) and clockwise(ss):
print v, ss, sums, clockwise(ss)
gon = flatten(ss)
if len(gon) == 16:
print gon
import euler
for i in range(9):
print '----'
lst = range(1, i + 2)
lst.reverse()
for perm in euler.permutations(lst):
v = euler.seqToInt(perm)
if euler.isprime(v):
print v
break
import euler
r = xrange(1, 1000001)
s = None
for i, v in zip(r, euler.permutations(range(10))):
if i == 1000000:
s = v
break
s = [str(i) for i in s]
s = ''.join(s)
print s
import euler
r = xrange(1,1000001)
s = None
for i,v in zip(r,euler.permutations(range(10))):
if i == 1000000:
s = v
break
s = [ str(i) for i in s ]
s = ''.join(s)
print s
import euler
for i in range(9):
print '----'
lst = range(1,i+2)
lst.reverse()
for perm in euler.permutations(lst):
v = euler.seqToInt(perm)
if euler.isprime(v):
print v
break
#!/usr/bin/env python
# Copyright (c) 2008 by Steingrim Dovland <*****@*****.**>
from itertools import count, izip
from euler import permutations, findfirst
# A permutation is an ordered arrangement of objects. For example, 3124
# is one possible permutation of the digits 1, 2, 3 and 4. If all of the
# permutations are listed numerically or alphabetically, we call it
# lexicographic order. The lexicographic permutations of 0, 1 and 2 are:
#
# 012 021 102 120 201 210
#
# What is the millionth lexicographic permutation of the digits 0, 1, 2,
# 3, 4, 5, 6, 7, 8 and 9?
p = permutations('0123456789')
x = findfirst(izip(count(1), p), lambda x: x[0] == 1*1000*1000)
print ''.join(x[1])
for j in impl(i,digits-1):
yield [i] + j
for i in impl(minv,digits):
yield euler.seqToInt(i)
res = []
for i in set(increasingIter(0,6)):
fc = factorialChain(i)
fcl = len(fc)-1
if fcl == 60:
res.append( i )
final = []
for r in res:
s = set()
for p in euler.permutations(euler.intToSeq(r)):
v = euler.seqToInt(p)
if factorialChainLength(v) == 60:
s.add(v)
for item in s:
final.append(item)
cnt = 0
final = list(set(final))
final.sort()
for item in final:
cnt += 1
print cnt,item,factorialChainLength(item)
print 'soln',cnt
import euler
lst = []
for a in range(1,8):
for b in range(a+1,9):
lst.append( (range(0,a),range(a,b),range(b,9)) )
#for i in lst:
# print i
def seqToInt( seq ):
return int( ''.join( [ str(i) for i in seq ] ) )
res = set()
for i in euler.permutations(range(1,10)):
for a,b,c in lst:
a = seqToInt([ i[j] for j in a ])
b = seqToInt([ i[j] for j in b ])
c = seqToInt([ i[j] for j in c ])
if a*b == c:
res.add(c)
print a,b,c, '-', list(res)
print res
def int_permutations(x):
return map(int, map(''.join, permutations(str(x))))
for i in impl(minv, digits):
yield euler.seqToInt(i)
res = []
for i in set(increasingIter(0, 6)):
fc = factorialChain(i)
fcl = len(fc) - 1
if fcl == 60:
res.append(i)
final = []
for r in res:
s = set()
for p in euler.permutations(euler.intToSeq(r)):
v = euler.seqToInt(p)
if factorialChainLength(v) == 60:
s.add(v)
for item in s:
final.append(item)
cnt = 0
final = list(set(final))
final.sort()
for item in final:
cnt += 1
print cnt, item, factorialChainLength(item)
print 'soln', cnt
import euler
lst = []
for a in range(1, 8):
for b in range(a + 1, 9):
lst.append((range(0, a), range(a, b), range(b, 9)))
#for i in lst:
# print i
def seqToInt(seq):
return int(''.join([str(i) for i in seq]))
res = set()
for i in euler.permutations(range(1, 10)):
for a, b, c in lst:
a = seqToInt([i[j] for j in a])
b = seqToInt([i[j] for j in b])
c = seqToInt([i[j] for j in c])
if a * b == c:
res.add(c)
print a, b, c, '-', list(res)
print res
