Added Math Library

math library

math library

math library

Fixed Py2

Update polygon.py

Update math.py

Author: kkksc03

cyaron/__init__.py

@@ -4,6 +4,7 @@
 It has tools for graphs and IO files.
 """
 
+from __future__ import absolute_import
 from .io import IO
 from .graph import Graph, Edge
 from .str import String
@@ -13,5 +14,6 @@
 from .vector import Vector
 from .polygon import Polygon
 from .compare import Compare
+from .math import *
 from random import randint, randrange, uniform, choice, random
 

cyaron/consts.py

@@ -1,3 +1,4 @@
+from __future__ import absolute_import
 import math
 import string
 

cyaron/math.py

@@ -0,0 +1,360 @@
+#coding=utf8
+''' 
+forked from https://blog.dreamshire.com/common-functions-routines-project-euler/
+'''
+from __future__ import absolute_import
+from math import sqrt, ceil
+from functools import reduce
+import random
+import itertools
+
+
+fact = (1, 1, 2, 6, 24, 120, 720, 5040, 40320, 362880)
+
+def factorial(n): return reduce(lambda x,y:x*y,range(1,n+1),1)
+
+def is_perm(a,b): return sorted(str(a))==sorted(str(b))
+
+def is_palindromic(n): n=str(n); return n==n[::-1]
+
+def is_pandigital(n, s=9): n=str(n); return len(n)==s and not '1234567890'[:s].strip(n)
+
+#--- Calculate the sum of proper divisors for n--------------------------------------------------
+def d(n):
+    s = 1
+    t = sqrt(n)
+    for i in range(2, int(t)+1):
+        if n % i == 0: s += i + n/i
+    if t == int(t): s -= t    #correct s if t is a perfect square
+    return s
+
+#--- Create a list of all palindromic numbers with k digits--------------------------------------
+def pal_list(k):
+    if k == 1:
+        return [1, 2, 3, 4, 5, 6, 7, 8, 9]
+    return [sum([n*(10**i) for i,n in enumerate(([x]+list(ys)+[z]+list(ys)[::-1]+[x]) if k%2
+                                else ([x]+list(ys)+list(ys)[::-1]+[x]))])
+            for x in range(1,10)
+            for ys in itertools.product(range(10), repeat=int(k/2)-1)
+            for z in (range(10) if k%2 else (None,))]
+
+
+#--- sum of factorial's digits-------------------------------------------------------------------
+def sof_digits(n):
+    if n==0: return 1
+    s = 0
+    while n > 0:
+        s, n = s + fact[n % 10], n // 10
+    return s
+
+
+
+#--- find the nth Fibonacci number---------------------------------------------------------------
+def fibonacci(n):
+    """
+    Find the nth number in the Fibonacci series.  Example:
+    
+    >>>fibonacci(100)
+    354224848179261915075
+
+    Algorithm & Python source: Copyright (c) 2013 Nayuki Minase
+    Fast doubling Fibonacci algorithm
+    http://nayuki.eigenstate.org/page/fast-fibonacci-algorithms
+    """
+    if n < 0:
+        raise ValueError("Negative arguments not implemented")
+    return _fib(n)[0]
+
+# Returns a tuple (F(n), F(n+1))
+def _fib(n):
+    if n == 0:
+        return (0, 1)
+    else:
+        a, b = _fib(n // 2)
+        c = a * (2 * b - a)
+        d = b * b + a * a
+        if n % 2 == 0:
+            return (c, d)
+        else:
+            return (d, c + d)
+
+
+#--- sum of squares of digits-------------------------------------------------------------------
+def sos_digits(n):
+    s = 0
+    while n > 0:
+        s, n = s + (n % 10)**2, n // 10
+    return s
+
+#--- sum of the digits to a power e-------------------------------------------------------------
+def pow_digits(n, e):
+    s = 0
+    while n > 0:
+        s, n = s + (n % 10)**e, n // 10
+    return s
+
+
+
+#--- check n for prime--------------------------------------------------------------------------
+def is_prime(n):
+    if n <= 1: return False
+    if n <= 3: return True
+    if n%2==0 or n%3 == 0: return False
+    r = int(sqrt(n))
+    f = 5
+    while f <= r:
+        if n%f == 0 or n%(f+2) == 0: return False
+        f+= 6
+    return True
+
+
+
+
+#--- Miller-Rabin primality test----------------------------------------------------------------
+def miller_rabin(n):
+    """
+    Check n for primalty:  Example:
+
+    >miller_rabin(162259276829213363391578010288127)    #Mersenne prime #11
+    True
+
+    Algorithm & Python source:
+    http://en.literateprograms.org/Miller-Rabin_primality_test_(Python)
+    """
+    d = n - 1
+    s = 0
+    while d % 2 == 0:
+        d >>= 1
+        s += 1
+    for repeat in range(20):
+        a = 0
+        while a == 0:
+            a = random.randrange(n)
+        if not miller_rabin_pass(a, s, d, n):
+            return False
+    return True
+
+def miller_rabin_pass(a, s, d, n):
+    a_to_power = pow(a, d, n)
+    if a_to_power == 1:
+        return True
+    for i in range(s-1):
+        if a_to_power == n - 1:
+            return True
+        a_to_power = (a_to_power * a_to_power) % n
+    return a_to_power == n - 1
+
+
+
+#--- factor a number into primes and frequency----------------------------------------------------
+"""
+    find the prime factors of n along with their frequencies. Example:
+
+    >>> factor(786456)
+    [(2,3), (3,3), (11,1), (331,1)]
+    
+    Source: Project Euler forums for problem #3
+"""
+def factor(n):
+    f, factors, prime_gaps = 1, [], [2, 4, 2, 4, 6, 2, 6, 4]
+    if n < 1:
+        return []
+    while True:
+        for gap in ([1, 1, 2, 2, 4] if f < 11 else prime_gaps):
+            f += gap
+            if f * f > n:  # If f > sqrt(n)
+                if n == 1:
+                    return factors
+                else:
+                    return factors + [(n, 1)]
+            if not n % f:
+                e = 1
+                n //= f
+                while not n % f:
+                    n //= f
+                    e += 1
+                factors.append((f, e))
+
+
+#--- greatest common divisor----------------------------------------------------------------------
+def gcd(a, b):
+    """
+    Compute the greatest common divisor of a and b. Examples:
+    
+    >>> gcd(14, 15)    #co-prime
+    1
+    >>> gcd(5*5, 3*5)
+    5
+    """
+    if a < 0:  a = -a
+    if b < 0:  b = -b
+    if a == 0: return b
+    while (b): a, b = b, a%b
+    return a
+
+
+
+
+#--- generate permutations-----------------------------------------------------------------------
+def perm(n, s):
+    """
+    requires function factorial()
+    Find the nth permutation of the string s. Example:
+
+    >>>perm(30, 'abcde')
+    bcade
+    """
+    if len(s)==1: return s
+    q, r = divmod(n, factorial(len(s)-1))
+    return s[q] + perm(r, s[:q] + s[q+1:])
+
+
+
+
+#--- binomial coefficients-----------------------------------------------------------------------
+def binomial(n, k):
+    """
+    Calculate C(n,k), the number of ways can k be chosen from n. Example:
+    
+    >>>binomial(30,12)
+    86493225
+    """
+    nt = 1
+    for t in range(min(k, n-k)):
+        nt = nt * (n-t) // (t+1)
+    return nt
+
+
+#--- catalan number------------------------------------------------------------------------------
+def catalan_number(n):
+    """
+    Calculate the nth Catalan number. Example:
+    
+    >>>catalan_number(10)
+    16796
+    """
+    nm = dm = 1
+    for k in range(2, n+1):
+        nm, dm = (nm*(n+k), dm*k)
+    return nm / dm
+
+
+
+#--- generate prime numbers----------------------------------------------------------------------
+def prime_sieve(n):
+    """
+    Return a list of prime numbers from 2 to a prime < n. Very fast (n<10,000,000) in 0.4 sec.
+    
+    Example:
+    >>>prime_sieve(25)
+    [2, 3, 5, 7, 11, 13, 17, 19, 23]
+
+    Algorithm & Python source: Robert William Hanks
+    http://stackoverflow.com/questions/17773352/python-sieve-prime-numbers
+    """
+    sieve = [True] * int(n/2)
+    for i in range(3,int(n**0.5)+1,2):
+        if sieve[int(i/2)]:
+            sieve[i*int(i/2)::i] = [False] * (int((n-i*i-1)/(2*i))+1)
+    return [2] + [2*i+1 for i in range(1,int(n/2)) if sieve[i]]
+
+
+#--- bezout coefficients--------------------------------------------------------------------------
+def exgcd(a,b):
+    """
+    Bézout coefficients (u,v) of (a,b) as:
+
+        a*u + b*v = gcd(a,b)
+
+    Result is the tuple: (u, v, gcd(a,b)). Examples:
+
+    >>> bezout(7*3, 15*3)
+    (-2, 1, 3)
+    >>> bezout(24157817, 39088169)    #sequential Fibonacci numbers
+    (-14930352, 9227465, 1)
+
+    Algorithm source: Pierre L. Douillet
+    http://www.douillet.info/~douillet/working_papers/bezout/node2.html
+    """
+    u,  v,  s,  t = 1, 0, 0, 1
+    while b !=0:
+        q, r = divmod(a,b)
+        a, b = b, r
+        u, s = s, u - q*s
+        v, t = t, v - q*t
+
+    return (u, v, a)
+
+    
+    
+def mod_inverse(a,b):
+    x,y,z = exgcd(a,b) 
+    return x;
+
+def phi(x):
+    if x==1:
+        return 1;
+    factors = factor(x);
+    ans = x;
+    for prime in factors:
+        ans=int(ans / prime[0]*(prime[0]-1))
+    return ans
+
+def miu(x):
+    if x==1:
+        return 1;
+    factors = factor(x)
+    for prime in factors:
+        if prime[1]>1:
+            return 0;
+    return 1-(len(factors) and 1)*2
+
+    
+#--- number base conversion -------------------------------------------------------------------
+#source: http://interactivepython.org/runestone/static/pythonds/Recursion/pythondsConvertinganIntegertoaStringinAnyBase.html
+def dec2base(n,base):
+   convertString = "0123456789ABCDEF"
+   if n < base:
+      return convertString[n]
+   else:
+      return dec2base(n//base,base) + convertString[n%base]
+
+#--- number to words ----------------------------------------------------------------------------
+#this function copied from stackoverflow user: Developer, Oct 5 '13 at 3:45
+def n2words(num,join=True):
+    '''words = {} convert an integer number into words'''
+    units = ['','One','Two','Three','Four','Five','Six','Seven','Eight','Nine']
+    teens = ['','Eleven','Twelve','Thirteen','Fourteen','Fifteen','Sixteen', \
+             'Seventeen','Eighteen','Nineteen']
+    tens = ['','Ten','Twenty','Thirty','Forty','Fifty','Sixty','Seventy', \
+            'Eighty','Ninety']
+    thousands = ['','Thousand','Million','Billion','Trillion','Quadrillion', \
+                 'Quintillion','Sextillion','Septillion','Octillion', \
+                 'Nonillion','Decillion','Undecillion','Duodecillion', \
+                 'Tredecillion','Quattuordecillion','Sexdecillion', \
+                 'Septendecillion','Octodecillion','Novemdecillion', \
+                 'Vigintillion']
+    words = []
+    if num==0: words.append('zero')
+    else:
+        numStr = '%d'%num
+        numStrLen = len(numStr)
+        groups = int((numStrLen+2)/3)
+        numStr = numStr.zfill(groups*3)
+        for i in range(0,groups*3,3):
+            h,t,u = int(numStr[i]),int(numStr[i+1]),int(numStr[i+2])
+            g = groups-(int(i/3)+1)
+            if h>=1:
+                words.append(units[h])
+                words.append('Hundred')
+            if t>1:
+                words.append(tens[t])
+                if u>=1: words.append(units[u])
+            elif t==1:
+                if u>=1: words.append(teens[u])
+                else: words.append(tens[t])
+            else:
+                if u>=1: words.append(units[u])
+            if (g>=1) and ((h+t+u)>0): words.append(thousands[g]+'')
+    if join: return ' '.join(words)
+    return words

cyaron/polygon.py

@@ -1,3 +1,4 @@
+from __future__ import absolute_import
 from .utils import *
 from .consts import *
 import random