def test_fact(self):
self.assertEqual(utils.fact(0), 1)
self.assertEqual(utils.fact(5), 120)
self.assertEqual(utils.fact(3), 6)
with self.assertRaises(ValueError):
utils.fact(-5)
pass
def test_fact(self):
# with self.assertRaises(ValueError):
# utils.fact(-1)
self.assertEqual(utils.fact(0), 1)
self.assertEqual(utils.fact(1), 1)
self.assertEqual(utils.fact(2), 2)
self.assertEqual(utils.fact(5), 120)
def test_fact(self):
# À compléter...
self.assertEqual(utils.fact(6), 720)
self.assertEqual(utils.fact(0), 1)
with self.assertRaises(ValueError):
utils.fact(-5)
def nperms_with_part(part):
ret = multinomial(part)
for p in part:
ret *= fact(p - 1)
for n in same_ns(part):
ret //= fact(n)
return ret
def test_fact(self):
# À compléter...
self.assertEqual(utils.fact(4), 24)
self.assertEqual(utils.fact(7), 5040)
self.assertEqual(utils.fact(0), 1)
with self.assertRaises(ValueError):
utils.fact(-2)
def test_fact(self):
list=[1,1,2,6,24,120,720,5040,40320,362880,3628800]
for i in range(10):
self.assertEqual(utils.fact(i),list[i])
with self.assertRaises(ValueError):
utils.fact(-1)
with self.assertRaises(TypeError):
utils.fact('a')
def pb15():
"""
Problem 15 : Lattice paths
One could prove that the number of such paths are Catalan Numbers i.e. (2n)!/(n!)^2 or (2n n).
See utils.fact for implementation of the factorial function.
"""
res = utils.fact(40) // (utils.fact(20)**2)
return res
def bin(n, r):
"""
Computes the binomial factor
>>> bin(2,1)
2
>>> bin(23,10)
1144066
"""
return fact(n) / (fact(r) * fact(n - r))
def do( N ):
ways = ( choose( 25, N )
* product( xrange( 75, 100 - N ) )
* fact( 75 ) )
all = fact( 100 )
ret = ways * 10 ** 50 / all
import sys
print >>sys.stderr, (ret, N)
return ret
def test_fact(self):
results_fact = (1,1,2,6,24,120,720,5040,40320,362880)
for i in range(10):
self.assertEqual(utils.fact(i) , results_fact[i])
with self.assertRaises(ValueError):
utils.fact(-1)
with self.assertRaises(TypeError):
utils.fact("2")
def postfact():
numinput= int(request.forms.get('factorial'))
fact= utils.fact(numinput)
return '''
the results: {}<br /><br />
<a href= https://boiling-beach-99041.herokuapp.com>Home</a>
'''.format(fact)
def pb20():
"""
Problem 20 : Factorial digits sum.
Basic implementation as we convert multiple times.
"""
n = utils.fact(100)
return sum(list(map(int, list(str(n)))))
def main(): print 'task 20' res = 0 s = str(utils.fact(100)) for c in s: res += int(c) print res
def T(n, k):
if k == 0:
return 1
else:
ans = 1
for j in xrange(k):
ans *= (n + j)
return ans / fact(k)
def prob12():
limit = 500
nbDiv = 0
i = 1
while nbDiv < limit:
triangular = (i * (i + 1)) / 2
nbDiv = len(utils.fact(triangular))
i += 1
return triangular
def Answer_fact(self, number):
try:
nbr = int(number)
x = str(utils.fact(nbr))
return {"number": number, "fact": x}
except:
return {"number": number, "fact": "None"}
def logP( k, n ):
total = 0
curr = choose( n, k / 2 + k % 2 )
for r in xrange( k / 2 + k % 2, k + 1 ):
total += curr
curr = curr * ( n - r ) / ( r + 1 )
return log( total ) + log( fact( k ) )
def p( k, n ):
total = 0
curr = choose( n, k / 2 + k % 2 )
for r in xrange( k / 2 + k % 2, k + 1 ):
total += curr
curr = curr * ( n - r ) / ( r + 1 )
return total * fact( k )
def prob12():
limit = 500
nbDiv = 0
i = 1
while nbDiv < limit:
triangular = (i * (i+1))/2
nbDiv = len(utils.fact(triangular))
i+=1
return triangular
def factorial_page():
decoded = request.forms.decode("utf-8")
print(decoded)
try:
number = int(decoded.get("Number"))
except ValueError:
return "<h1> Please enter a <strong>valid</strong> number</h1>"
try:
result = fact(number)
except ValueError:
result = None
return "The factorial of {} is {}".format(number, result)
def c(n, r):
n_fact = fact(n)
r_fact = fact(r)
nr_fact = fact(n - r)
return n_fact / (r_fact * nr_fact)
def test_fact2():
assert fact(4) == 24
def test_fact(self):
self.assertEqual(utils.fact(4), 24)
with self.assertRaises(ValueError):
utils.fact(-1)
def fact(n) :
var = int(n)
result = utils.fact(var)
return template('La factorielle de {{a}} est {{b}}', a=n,b=result)
def test_fact2():
assert fact(4) == 24
def test_fact ( self ):
self.assertEqual(utils.fact(1),1)
with self.assertRaises(ValueError):
utils.fact(-2)
self.assertEqual ( utils . fact (0) , 1)
def test_fact(self):
self.assertEqual(utils.fact(0), 0)
self.assertEqual(utils.fact(4), 24)
self.assertRaises(ValueError, utils.fact(-1))
pass
def test_fact3():
with pytest.raises(ValueError):
n = fact(-1)
#! python3 """How many such routes are there through a 20×20 grid?""" import sys from os.path import dirname sys.path.insert(0, dirname(dirname(__file__))) from utils import fact print(fact(2 * 20) // (fact(20)**2)) # 2n! / n!^2
def test_fact(self):
# À compléter...
self.assertEqual(utils.fact(0), 1)
self.assertIsNone(utils.fact("zetze"))
self.assertEqual(utils.fact(9), 362880)
def good(n):
return (sum(fact(int(x)) for x in str(n)) == n)
def test_fact3():
with pytest.raises(ValueError):
n = fact(-1)
def test_fact(self):
self.assertEqual(utils.fact(0), 1)
self.assertEqual(utils.fact(1), 1)
self.assertEqual(utils.fact(5), 120)
def test_fact(self):
self.assertEqual(utils.fact(0) , 1)
self.assertEqual(utils.fact(5) , 120)
def test_some_number(self):
self.assertEquals(fact(4), 24)
def test_fact(self):
self.assertEqual(utils.fact(5), 120)
self.assertEqual(utils.fact(2), 2)
pass
def test_fact(self):
self.assertEqual(utils.fact(5), 120)
with self.assertRaises(ValueError):
utils.fact(-5)
def test_fact():
assert fact(3) == 6
def test_simple_value(self):
self.assertEquals(fact(0), 1)
def C(n, r):
return fact(n) / (fact(r) * fact(n - r))
#!/usr/bin/env python
# -*- coding: utf-8 -*-
# Project Euler
# Problem 74
#
# Determine the number of factorial chains that contain exactly sixty
# non-repeating terms.
from utils import fact
LIMIT = 1000000
FACTS = [fact(n) for n in xrange(0,10)]
def fact_digits(n):
result = 0
while n:
result += FACTS[n%10]
n //= 10
return result
def p074():
untried = set(xrange(1,LIMIT))
lengths = {}
while(untried):
n = untried.pop()
seen = []
in_cycle = n in seen
in_lengths = n in lengths
while not in_cycle and not in_lengths:
seen.append(n)
def test_fact():
with pytest.raises(ValueError):
utils.fact(-2)
assert utils.fact(0) == 1
assert utils.fact(4) == 24
assert utils.fact(5) == 120
def test_fact(self):
self.assertEqual(utils.fact(3), 6)
pass
def binom(n, k):
return utils.fact(n) // (utils.fact(k) * utils.fact(n - k))
from __future__ import division
from plotty import *
from utils import fact,Fibn
import itertools
savefigs=[3]
for fig in savefigs:
if fig==1:
N=30
p=[]
for h in range(31):
p.append(fact(N)/fact(h)/fact(N-h) * (0.5)**N)
h=range(31)
figure(1)
#lineplot(h,p)
plot(h,p,'--o',linewidth=3,markersize=10)
xlabel('Number of heads')
ylabel('$P(h,N=30)$')
grid(True)
draw()
savefig('../../figs/coinflips1.pdf')
elif fig==2:
# solution for streaks http://marknelson.us/2011/01/17/20-heads-in-a-row-what-are-the-odds/
N=50
def test_fact(self): self.assertEqual(1, utils.fact(0)) self.assertEqual(1, utils.fact(1)) self.assertEqual(6, utils.fact(3)) with self.assertRaises(ValueError): utils.fact(-1)
def test_fact(self):
self.assertEqual(utils.fact(3), 6)
self.assertEqual(utils.fact(7), 5040)
self.assertEqual(utils.fact(0), 1)
self.assertEqual(utils.fact(-4), ValueError)
def test_fact(self):
self.assertEqual(utils.fact(3), 6)
self.assertEqual(utils.fact(4), 24)
# pour tester si la fonction lance une exception
with self.assertRaises(ValueError):
utils.fact(-1)
def test_fact():
assert fact(3) == 6
def prob_20():
return sum(int(x) for x in str(fact(100)))
def c(n, r):
return (fact(n) / fact(r)) / fact(n - r)
def test_fact(self):
self.assertEqual(utils.fact(3), 6)
self.assertEqual(utils.fact(4), 24)
self.assertEqual(utils.fact(0), 1)
with self.assertRaises(ValueError):
utils.fact(-5)
def dfsum(n):
s = 0
for i in range(numDigits(n, 10)):
s += fact(nthDigit(n, i, 10))
return s
def test_fact(self):
self.assertEqual(utils.fact(3),6)
with self.assertRaises(ValueError):
utils.fact(-1)
def test_fact(self):
self.assertEqual(utils.fact(0), 2)
pass
def test_fact(self):
# À compléter...
self.assertEqual(utils.fact(3), 6)
def test_fact(self):
with self.assertRaises(ValueError):
utils.fact(-1)
self.assertEqual(utils.fact(5),120)
pass
