def calc_prob_at_least(v,potential_e,e,i):
r = Rational()
for j in range(0,2*i):
r.multiply_by(e - j)
r.divide_by(potential_e - j)
r.multiply_by(gmpy2.comb(v - 2, i))
return r.value()
def main():
start = time.time()
results = multiprocessing.Queue()
updates = multiprocessing.Queue()
trials = 200
max_input = int(gmpy2.exp(128))
degree = int(sys.argv[2])
num_points = int(sys.argv[1])
n = multiprocessing.cpu_count()
processes = []
proc_results = []
size = int(gmpy2.comb(num_points, degree)) / n
combs = itertools.combinations(numpy.linspace(1, 2, num_points), degree)
for i in range(n):
xs = [x for _, x in zip(range(size), combs)]
proc = multiprocessing.Process(target=worker, args=(xs, results, updates, trials, max_input))
print "starting process %d" % i
proc.start()
processes.append(proc)
for i in range(2*n):
print updates.get()
for i in range(n):
proc_results.append(results.get())
for proc in processes:
proc.join()
pretty_errors(min(proc_results))
print "Time Elapsed: %.2f seconds." % (time.time() - start)
def calc_prob_at_least(v, potential_e, e, i):
r = Rational()
for j in range(0, 2 * i):
r.multiply_by(e - j)
r.divide_by(potential_e - j)
r.multiply_by(gmpy2.comb(v - 2, i))
return r.value()
def card(n,k,a):
result = 0
a.sort(reverse=True)
x = 0
for i in range(n-1,k-2,-1):
result += (a[x] * comb(i,k-1)) % mod
x+=1
return result % mod
def triangleDensity(graph):
outV = snap.TIntPrV()
snap.GetTriadParticip(graph,outV)
triangles = 0.0
for pair in outV:
triangles += (pair.GetVal1()*pair.GetVal2())
triangles=triangles / 3.0 #three triangles per node is added
print ("number of triangles: "+str(triangles))
return (triangles/gmpy2.comb(graph.GetNodes(),3))
def triangleDensity(graph):
outV = snap.TIntPrV()
snap.GetTriadParticip(graph, outV)
triangles = 0.0
for pair in outV:
triangles += (pair.GetVal1() * pair.GetVal2())
triangles = triangles / 3.0 #three triangles per node is added
print("number of triangles: " + str(triangles))
return (triangles / gmpy2.comb(graph.GetNodes(), 3))
def modulo_combs(m, n, p):
""" Uses Lucas' theorem to calculate the value of m choose n, modulo p.
For this to work p must be a prime - the output is indeterminate for
non-prime values of p.
"""
product = 1
while m > 0:
m, mi = divmod(m, p)
n, ni = divmod(n, p)
product = (product * gmpy2.comb(mi, ni)) % p
if product == 0:
return 0
return product
def badTriangleDensity(graph):
triangles = numpy.zeros(graph.GetMxNId())
i = 0
print("starting triangle density, printing every 100 nodes competed")
for currentNode in graph.Nodes():
i = i+1
if i % 100 == 0:
print(i)
for neighbourIndex in range(0, currentNode.GetOutDeg()):
neighbourId = currentNode.GetOutNId(neighbourIndex)
neighbourNode = graph.GetNI(neighbourId)
for NNI in range(0, neighbourNode.GetOutDeg()):
NNID = neighbourNode.GetOutNId(NNI)
for realNeighbourIndex in range(0, currentNode.GetOutDeg()):
realNeighbour = currentNode.GetOutNId(realNeighbourIndex)
if NNID == realNeighbour:
triangles[currentNode.GetId()] += 1
print "done with triangle density"
print "number of triangles: {}".format(ntriangles)
return ntriangles/gmpy2.comb(graph.GetNodes(), 3)
def badTriangleDensity(graph):
triangles = numpy.zeros(graph.GetMxNId())
i = 0
print("starting triangle density, printing every 100 nodes competed")
for currentNode in graph.Nodes():
i = i + 1
if i % 100 == 0:
print(i)
for neighbourIndex in range(0, currentNode.GetOutDeg()):
neighbourId = currentNode.GetOutNId(neighbourIndex)
neighbourNode = graph.GetNI(neighbourId)
for NNI in range(0, neighbourNode.GetOutDeg()):
NNID = neighbourNode.GetOutNId(NNI)
for realNeighbourIndex in range(0, currentNode.GetOutDeg()):
realNeighbour = currentNode.GetOutNId(realNeighbourIndex)
if NNID == realNeighbour:
triangles[currentNode.GetId()] += 1
print "done with triangle density"
print "number of triangles: {}".format(ntriangles)
return ntriangles / gmpy2.comb(graph.GetNodes(), 3)
def height(n, m):
'''height (n,m) = height(n,m-1) + height(n-1,m-1) +1 for n >0
we can demonstrate that height (n,m) = sum on i from 0 to min (m-1,n-1) factor(i,m-1) height(n-i,1) + constant
with constant = 1+ sum on j from 1 to m-2 ( sum on i from 0 to min(jn-1) of factor(i,j) )
with factor(i,p) defined only with n-1>=p>=i = recursive sum on index k from 1 to p-1 ( sum on index(k) from i-k to index (k-1) of sum on index ) the last one is the sum of the index itself
in total there should be i-1 sums recursively // factor (i,p) = factor(i,p-1) + factor (i-1,p-1) with factor(0,p) = 1 and factor (p,p) = 1
we need then to compute the factors f(i,p) for i from 0 to n-1 and for p from 1 to n-1
global count
if count == 0:
for i in range (1,5000):
for j in range (i,5000):
comb(i,j)
count += 1
'''
if m == 0 or n == 0:
constante = 0
elif m == 1:
constante = 1
elif n >= m:
constante = pow(2, m) - 1
else:
max_index = min(n,m)
'''
for i in range(1, max_index+1-2*(max_index%2), 2):
print(i)
constante += 2*comb(m,i)
if (max_index-1)%2 ==0:
constante += 2*comb(m - 1, max_index-1)
#constante += 2 * comb(m - 1, i)
'''
constante = 2*somme_comb(n-1, m-1)
constante += gmpy2.comb(m - 1, max_index) - 1
return constante
#!/usr/bin/env python
from gmpy2 import comb
count = 0
for n in range(1, 101):
for r in range(1, n):
c = comb(n,r)
if c > 1000000:
count += 1
print(count)
import sys
import gmpy2
tot = 0
for n in range(23, 101):
for i in range(n):
if gmpy2.comb(n,i) > 10**6:
tot += 1
print tot
import gmpy2 total = 0 for i in range(10, 101) : for j in range(1, i) : if gmpy2.comb(i, j) >= 1000000 : total += 1 print(total)
#!/usr/bin/env python
from euler import digits
from gmpy2 import comb
def is_asc(n):
ds = digits(n)
return all([a <= b for a, b in zip(ds, ds[1:])])
def is_desc(n):
ds = digits(n)
return all([a >= b for a, b in zip(ds, ds[1:])])
def count_asc(nums):
return sum(1 for n in nums if is_asc(n))
def count_desc(nums):
return sum(1 for n in nums if is_desc(n))
# (1-9)00...
# 11 -> (1-9)11 = 9*
# 45 -> (1-4)45 = C(1,1) + C(2, 1) + C(3, 1) + ... + C(9, 1)
# 54 -> (5-9)54 = same
n = 100
print(comb(n+10, n) + comb(n+9, n) - (n*10 + 2))
def bi_dist(x, n, p):
return gmpy2.comb(n, x) * (p**x) * ((1 - p)**(n - x))
import copy
import itertools
import cPickle as pickle
import gmpy2
import math
# To create the dictionaries for the workers in the coded case
# N is a multiple of K-choose-r
with open("Dict_0.txt", "rb") as myFile:
Gdict = pickle.load(myFile)
K = 10
N = 12600
r = 3
kcr = int(gmpy2.comb(K, r))
g = N / kcr
fid = [x for x in range(1, kcr + 1)]
ltemp1 = [x for x in range(1, K + 1)]
ltemp2 = itertools.combinations(ltemp1, r)
WSubsetR = {}
fidWSet = {}
fidNodes = {}
Gdist = [None] * K
for j in range(K):
Gdist[j] = {}
i1 = 1
for x in ltemp2:
WSubsetR[i1] = x
fidWSet[x] = i1
from gmpy2 import comb print comb(2 * 20,20)
#!/usr/bin/env python from gmpy2 import comb print(comb(2 * 20, 20))
#!/usr/bin/env python from gmpy2 import comb print(comb(2 * 20,20))
valueDict = {}
ltemp1 = []
ltemp2 = []
ltemp3 = []
ltemp4 = []
destPrank = [None] * (K)
srcPrank = [None] * (K)
multicastGroupMap = {}
i1 = 0
i2 = 0
i3 = 0
i4 = 0
i5 = 0
i6 = 0
maxnumber = None
kcr = int(gmpy2.comb(K, r))
g = N / kcr
#################################### Loading sub-graph dictionary into memory ###################################
with open("DictC3_%s.txt" % rank,
"rb") as myFile: # change 3 to suitable r as required
GdictLocal = pickle.load(myFile)
myFile.close()
################################ Initializing Data ##############################
Gdist = [None] * K
fid = [x for x in range(1, kcr + 1)]
# WSubsetR={}
ltemp1 = [x for x in range(1, K + 1)]
from gmpy2 import comb # Look at Problem015.mkd to understand why the possibilities are given by # the combination of (40, 20) possibilities = comb(2 * 20, 20) print(possibilities)
#!/usr/bin/env python
from gmpy2 import comb
count = 0
for n in range(1, 101):
for r in range(1, n):
c = comb(n, r)
if c > 1000000:
count += 1
print(count)