add boilerplate for second edition

This commit is contained in:
Mia von Steinkirch 2020-02-08 17:18:16 -08:00
parent 5fd154f3fd
commit dc3ebf3173
148 changed files with 18311 additions and 0 deletions

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#!/usr/bin/env python
__author__ = "bt3"
class HashTable(object):
def __init__(self, slots=10):
self.slots = slots
self.table = []
self.create_table()
def hash_key(self, value):
return hash(value)%self.slots
def create_table(self):
for i in range(self.slots):
self.table.append([])
def add_item(self, value):
key = self.hash_key(value)
self.table[key].append(value)
def print_table(self):
for key in range(len(self.table)):
print "Key is %s, value is %s." %(key, self.table[key])
def find_item(self, item):
pos = self.hash_key(item)
if item in self.table[pos]:
return True
else:
return False
if __name__ == '__main__':
dic = HashTable(5)
for i in range(1, 40, 2):
dic.add_item(i)
dic.print_table()
assert(dic.find_item(20) == False)
assert(dic.find_item(21) == True)

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#!/usr/bin/env python
# Time: 5 min
__author__ = "bt3"
class Queue(object):
def __init__(self):
self.enq = []
self.deq = []
def enqueue(self, item):
return self.enq.append(item)
def deque(self):
if not self.deq:
while self.enq:
self.deq.append(self.enq.pop())
return self.deq.pop()
def peak(self):
if not self.deq:
while self.enq:
self.deq.append(self.enq.pop())
if self.deq:
return self.deq[-1]
def size(self):
return len(self.enq) + len(self.deq)
def isempty(self):
return not (self.enq + self.deq)
if __name__ == '__main__':
q = Queue()
for i in range(1,11):
q.enqueue(i)
print 'Size:', q.size()
print 'Is empty?', q.isempty()
print 'Peak: ', q.peak()
print
print 'Dequeuing...'
for i in range(10):
print q.deque()
print 'Size:', q.size()
print 'Is empty?', q.isempty()
print 'Peak: ', q.peak()

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#!/usr/bin/env python
__author__ = "bt3"
''' Example of how to use a bit array in python as a "counter" dict'''
def print_dupl_ba(l1):
'''
>>> l1 = [0, 1, 2, 3, 4, 2, 6, 7, 8, 9]
>>> print_dupl_ba(l1)
2
'''
bs = bytearray(10)
for i in range(len(l1)):
if i == l1[i]:
bs[i] = 1
for index, bit in enumerate(bs):
if bit == 0:
return l1[index]
return None
if __name__ == '__main__':
import doctest
doctest.testmod()

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BIT-WISE
----------------------
1. To find a number:
11000101 is 2^0+2^2+2^6+2^7 = 197
2. Left shifting:
0010 1011 << 4 ---> 1011 000
3. Right shifting:
0010 1011 >> 4 ---> 0000 0010
or it can be filled with the copy of the first bit, instead of 0:
1011 0010 >> 4 ---> 1111 1011
4. XOR can cancels out:
15 ^ 12 ^ 15 = 12
5. 2^x:
left-shift 1 by x:
0000 0001 << x
so if x = 2, 2^2 = 4 -> 100
0000 0001 << 2 ---> 0000 0100
6. Is power of 2?
just do x&(x-1).
if 0 --> yes!

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#!/usr/bin/env python
__author__ = "bt3"
''' Clear a bit in a binary number.
Like the reverse of set bit:
1) first create a number filled of 1s,
with 0 at i (can create 0001000 and ~)
2) AND the number so it clears the ith bit
'''
def clear_bit(num, i):
mask = ~ (1 << i) # -0b10001
return bin(num & mask)
def clear_all_bits_from_i_to_0(num, i):
mask = ~ ( (1 << (i+1)) - 1)
return bin(num & mask)
def clear_all_bits_from_most_sig_to_1(num, i):
mask = ( 1 << i) -1
return bin(num & mask)
if __name__ == '__main__':
num = int('10010000', 2)
print clear_bit(num, 4) # '0b10000000'
num = int('10010011', 2)
print clear_all_bits_from_i_to_0(num, 2) # '0b10010000'
num = int('1110011', 2)
print clear_all_bits_from_most_sig_to_1(num, 2) #'0b11'

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#!/usr/bin/env python
__author__ = "bt3"
''' Find how many bits a int has:
1) Start with a mask of 1
2) Mask with AND
3) if result (if true): count += 1
(obs: to find the int of a bin do int('1001', 2)) and to show in bin
do bin(int))
'''
def find_bit_len(int_num):
lenght = 0
while int_num:
int_num >>= 1
lenght += 1
return lenght
if __name__ == '__main__':
for i in range(17):
print(find_bit_len(i))
print i.bit_length()

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#!/usr/bin/env python
__author__ = "bt3"
''' Find how many 1s in the binary:
1) Start with a mask of 1
2) Mask with AND
3) if result (if true): count += 1
(obs: to find the int of a bin do int('1001',
2)) and to show in bin do bin(int))
'''
def find_how_many_1_in_a_binary(n):
'''
>>> find_how_many_1_in_a_binary(9)
2
'''
counter = 0
while n:
if n & 1:
counter += 1
n >>= 1
return counter
if __name__ == '__main__':
import doctest
doctest.testmod()

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#!/usr/bin/env python
__author__ = "bt3"
''' Get a bit in a binary number:
1) Shifts 1 over by i bits
2) make an AND with the number
3) all the other than the bit at i are clean, now compare to 0
4) if the new value is not 0, bit i is 1
'''
def get_bit(num, i):
mask = 1 << i
return num & mask != 0
if __name__ == '__main__':
num = int('0100100', 2)
get_bit(num, 0) # 0
get_bit(num, 1) # 0
get_bit(num, 2) # 1
get_bit(num, 3) # 0
get_bit(num, 4) # 0
get_bit(num, 5) # 1
get_bit(num, 6) # 0

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#!/usr/bin/env python
__author__ = "bt3"
''' Given a real number between 0 and 1 (eg: 0.72), this method print the binary
representation. If the Number cannot be represented accurately in binary, with at
most 32 chars, print error:
'''
def get_float_rep(num):
'''
>>> get_float_rep(0.72)
('Error 2', '.1011100001010001111010111000010')
>>> get_float_rep(0.1)
('Error 2', '.0001100110011001100110011001100')
>>> get_float_rep(0.5)
'.1'
'''
if num >= 1 or num <= 0: return 'Error 1'
result = '.'
while num:
if len(result) >= 32: return 'Error 2', result
r = num*2
if r >= 1:
result += '1'
num = r - 1
else:
result += '0'
num = r
return result
if __name__ == '__main__':
import doctest
doctest.testmod()

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#!/usr/bin/env python
__author__ = "bt3"
''' Given two 32-bit numbers, N and M, and two bit positions, i and j, this
method insert M into N such that M starts at bit j and ends at bit i:
1) clear the bits j thru i in N'
2) shift M so that it lines up with bits j thru i
3) merge M and N
'''
def insert_small_bin_into_big_bin(M, N, i, j):
'''
>>> N = 0b10000000000
>>> M = 0b10011
>>> j = 6
>>> i = 2
>>> insert_small_bin_into_big_bin(M, N, i, j)
'0b10001001100'
'''
allOnes = ~0
left = allOnes << (j+1) # 1110000
right = ( (1 << i) - 1) # 0000111
mask = left | right # 1110111
N_cleared = N & mask
M_shifted = M << i
return bin( N_cleared | M_shifted)
if __name__ == '__main__':
import doctest
doctest.testmod()

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#!/usr/bin/env python
__author__ = "bt3"
''' Give a positive int, print the next smallest and next largest ints with
same number of 1 bits.
The brute force is:
1) find number of 1 bits
2) loop above and down until find same, checking for each
'''
def print_prev_same_1s(num):
n1s = find_num_1s(num)
# find prev
i = num-1
while True:
n1s_here = find_num_1s(i)
if n1s_here == n1s:
return bin(i)
i -= 1
if i < 0:
return None
def print_next_same_1s(num):
n1s = find_num_1s(num)
# find next
i = num+1
while True:
n1s_here = find_num_1s(i)
if n1s_here == n1s:
return bin(i)
i += 1
if i < 0:
return None
def find_num_1s(num):
counter = 0
while num:
if num & 1:
counter += 1
num >>= 1
return counter
if __name__ == '__main__':
num = 0b1001
n = '0b1010'
p = '0b110'
print_prev_same_1s(num) == p
print_next_same_1s(num) == n

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#!/usr/bin/env python
__author__ = "bt3"
''' This method returns the number of bits that are necessary to change to convert two
numbers A and B:
1) XOR
2) count 1s
'''
def count_bits_swap2(a, b):
count = 0
m = a^b
while m:
count +=1
m = m & (m-1)
return count
def count_bits_swap(a, b):
m = a^b
return count_1s(m)
def count_1s(m):
count = 0
while m:
if m& 1 :
count +=1
m >>= 1
return count
if __name__ == '__main__':
a = int('10010000', 2)
b = int('01011010', 2)
print count_bits_swap(a, b) #4
print count_bits_swap2(a, b) #4

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#!/usr/bin/env python
__author__ = "bt3"
''' Set a bit in a binary number:
1) Shifts 1 over by i bits
2) make an OR with the number, only the value at bit i will change and all the others bit
of the mask are zero so will not affect the num
'''
def set_bit(num, i):
mask = 1 << i
return bin( num | mask )
if __name__ == '__main__':
num = int('0100100', 2)
print set_bit(num, 0) #'0b100101'
print set_bit(num, 1) #'0b100110'
print set_bit(num, 2) # nothing change '0b100100'
print set_bit(num, 3) #'0b101100'
print set_bit(num, 4) #'0b110100'
print set_bit(num, 5) # nothing change '0b100100'

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#!/usr/bin/env python
__author__ = "bt3"
'''
swapping values in place without extra memory
'''
def swap_bit(a, b):
'''
>>> swap_bit(14, 73)
(73, 14)
'''
a = a^b
b = a^b
a = a^b
return a, b
if __name__ == '__main__':
import doctest
doctest.testmod()

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#!/usr/bin/env python
__author__ = "bt3"
''' Swap odd and even bits in a smart way in a binary:
1) first for odds, take n and move the odd:
(a) Mask all odd bits with 10101010 (0xAA)
(b) shift by right by 1
2) do the same to ints with 01010101
3) merge
'''
def swap_odd_even(num):
'''
>>> num = 0b11011101
>>> result = '0b1101110'
>>> swap_odd_even(num) == result
True
'''
mask_odd = 0xAA # 0b10101010
mask_even = 0x55 # 0b1010101
odd = num & mask_odd
odd >>= 1
even = num & mask_even
even >>= 1
return bin(odd | even)
if __name__ == '__main__':
import doctest
doctest.testmod()

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#!/usr/bin/env python
__author__ = "bt3"
''' This method merges set bit and clean bit:
1) first clear the bit at i using a mask such as 1110111
2) then shift the intended value v by i bits
3) this will create a number with bit i to v and all other to 0
4) finally update the ith bit with or
'''
def update_bit(num, i, v):
mask = ~ (1 << i)
return bin( (num & mask) | (v << i) )
if __name__ == '__main__':
num = int('10010000', 2)
print update_bit(num, 2, 1) # '0b10010100'

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#!/usr/bin/python3
__author__ = "bt3"
from functools import wraps
from do_benchmark import benchmark
def memo(func):
''' an example of dynamic programming using a memoizing decorator '''
cache = {}
@wraps(func)
def wrap(*args):
if args not in cache:
cache[args] = func(*args)
return cache[args]
return wrap
@memo
def find_fibonacci_seq_rec(n):
''' implements the nth fibonacci value in a recursive exponential runtime '''
if n < 2: return n
return find_fibonacci_seq_rec(n - 1) + find_fibonacci_seq_rec(n - 2)
def test_memo():
n = 50
# find_fibonacci_seq_rec = memo(find_fibonacci_seq_rec)
# @benchmark
print(find_fibonacci_seq_rec(n))
if __name__ == '__main__':
test_memo()

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#!/usr/bin/python3
__author__ = "bt3"
from itertools import combinations
from bisect import bisect
from memo import memo
from do_benchmark import benchmark
def naive_longest_inc_subseq(seq):
''' naive (exponential) solution to the longest increasing subsequence problem '''
for length in range(len(seq), 0, -1):
for sub in combinations(seq, length):
if list(sub) == sorted(sub):
return len(sub)
def longest_inc_subseq1(seq):
''' an iterative algorithm for the longest increasing subsequence problem '''
end = []
for val in seq:
idx = bisect(end, val)
if idx == len(end): end.append(val)
else: end[idx] = val
return len(end)
def longest_inc_subseq2(seq):
''' another iterative algorithm for the longest increasing subsequence problem '''
L = [1] * len(seq)
for cur, val in enumerate(seq):
for pre in range(cur):
if seq[pre] <= val:
L[cur] = max(L[cur], 1 + L[pre])
return max(L)
def memoized_longest_inc_subseq(seq):
''' a memoized recursive solution to find the longest increasing subsequence problem '''
@memo
def L(cur):
res = 1
for pre in range(cur):
if seq[pre] <= seq[cur]:
res = max(res, 1 + L(pre))
return res
return max(L(i) for i in range(len(seq)))
@benchmark
def test_naive_longest_inc_subseq():
print(naive_longest_inc_subseq(s1))
benchmark
def test_longest_inc_subseq1():
print(longest_inc_subseq1(s1))
@benchmark
def test_longest_inc_subseq2():
print(longest_inc_subseq2(s1))
@benchmark
def test_memoized_longest_inc_subseq():
print(memoized_longest_inc_subseq(s1))
if __name__ == '__main__':
from random import randrange
s1 = [randrange(100) for i in range(25)]
print(s1)
test_naive_longest_inc_subseq()
test_longest_inc_subseq1()
test_longest_inc_subseq2()
test_memoized_longest_inc_subseq()

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#!/usr/bin/env python
__author__ = "bt3"
import os
import sys
import shutil
def change_file_ext():
""" read a file and an extension from the command line and produces a copy with its extension changed"""
if len(sys.argv) < 2:
print("Usage: change_ext.py filename.old_ext 'new_ext'")
sys.exit()
name = os.path.splitext(sys.argv[1])[0] + "." + sys.argv[2]
print (name)
try:
shutil.copyfile(sys.argv[1], name)
except OSError as err:
print (err)
if __name__ == '__main__':
change_file_ext()

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#!/usr/bin/python
__author__ = "bt3"
import collections
import string
import sys
def count_unique_word_file():
if len(sys.argv) < 2:
print "Usage: python count_unique_word.py NAMEFILE"
words = collections.defaultdict(int)
strip = string.whitespace + string.punctuation + string.digits + "\"'"
for filename in sys.argv[1:]:
with open(filename) as file:
for line in file:
for word in line.lower().split():
word = word.strip(strip)
if len(word) > 2:
words[word] = +1
for word in sorted(words):
print("'{0}' occurs {1} times.".format(word, words[word]))
if __name__ == '__main__':
count_unique_word_file()

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#!/usr/bin/python
__author__ = "bt3"
import collections
import sys
def count_unique_word_freq():
return collections.Counter(\
sys.stdin.read().lower().split()).most_common(n)
if __name__ == '__main__':
count_unique_word_freq()

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#!/usr/bin/env python
__author__ = "bt3"
import sys
def grep_word_from_files():
''' using iterator enumerate to create a grep command '''
word = sys.argv[1]
for filename in sys.argv[2:]:
with open(filename) as file:
for lino, line in enumerate(file, start=1):
if word in line:
print("{0}:{1}:{2:.40}".format(filename, lino, line.rstrip()))
if __name__ == '__main__':
if len(sys.argv) < 2:
print("Usage: grep_word_from_files.py word infile1 [infile2...]")
sys.exit()
else:
grep_word_from_files()

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#!/usr/bin/env python
__author__ = "bt3"
import os
import sys
def read_data(filename):
lines = []
fh = None
try:
fh = open(filename)
for line in fh:
if line.strip():
lines.append(line)
except (IOError, OSError) as err:
print(err)
finally:
if fh is not None:
fh.close()
return lines
def write_data(lines, filename):
fh = None
try:
fh = open(filename, "w")
for line in lines:
fh.write(line)
except (EnvironmentError) as err:
print(err)
finally:
if fh is not None:
fh.close()
def remove_blank_lines():
""" read a list of filenames on the command line and for each one produces another file with the same content but with no blank lines """
if len(sys.argv) < 2:
print ("Usage: noblank.py infile1 [infile2...]")
for filename in sys.argv[1:]:
lines = read_data(filename)
if lines:
write_data(lines, filename)
if __name__ == '__main__':
remove_blank_lines()

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#!/usr/bin/env python
__author__ = "bt3"
from collections import OrderedDict
def OrderedDict_example():
''' show some examples for OrderedDict '''
''' keep the order of insertion.
maintains a doubly linked list, so size is more than twice than normal dict'''
pairs = [('a', 1), ('b',2), ('c',3)]
d1 = {}
for key, value in pairs:
if key not in d1:
d1[key] = []
d1[key].append(value)
for key in d1:
print(key, d1[key])
d2 = OrderedDict(pairs)
for key in d2:
print(key, d2[key])
if __name__ == '__main__':
OrderedDict_example()

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#!/usr/bin/env python
__author__ = "bt3"
def simple2(a, *args):
print args
def simple(*args):
print args
def simple3(**kwargs):
print kwargs
simple(1, 2, 3)
simple2(1, 2, 3)
simple3(x=1, y=2)

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#!/usr/bin/env python
__author__ = "bt3"
import random
def benchmark(func):
import time
def wrapper(*args, **kwargs):
t = time.clock()
res = func(*args, **kwargs)
print("\t%s" % func.__name__, time.clock()-t)
return res
return wrapper
@benchmark
def random_tree(n):
temp = [n for n in range(n)]
for i in range(n+1):
temp[random.choice(temp)] = random.choice(temp)
return temp
if __name__ == '__main__':
random_tree(10000)

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#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
import math
class Point(object):
def __init__(self, x=0, y=0): # self: object reference to the object itself
self.x = x # data attribute
self.y = y
def distance_from_origin(self):
return math.hypot(self.x, self.y)
def __eq__(self, other):
return self.x == other.x and self.y == other.y
def __repr__(self):
return "point ({0.x!r}, {0.y!r})".format(self)
def __str__(self): # cannot be passed to eval
return "({0.x!r}, {0.y!r})".format(self)
class Circle(Point):
def __init__(self, radius, x=0, y=0):
super().__init__(x,y) # creates and initializes self.x and self.y
self.radius = radius
def edge_distance_from_origin(self):
return abs(self.distance_from_origin() - self.radius)
def area(self):
return math.pi*(self.radius**2)
def circumference(self):
return 2*math.pi*self.radius
def __eq__(self, other): # let us avoid infinite recursion
return self.radius == other.radius and super().__eq__(other)
def __repr__(self):
return "circle ({0.radius!r}, {0.x!r})".format(self)
def __str__(self):
return repr(self)
if __name__ == '__main__':
a = Point(3,4)
print(a.distance_from_origin())
c = Circle(3,2,1)
print(c)
print(c.circumference())
print(c. edge_distance_from_origin())

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#!/usr/bin/env python
__author__ = "bt3"
a = [3, 4, 5, 6, 7]
# Filter elements greater than 4
# Bad:
b = []
for i in a:
if i > 4:
b.append(i)
print b
# Good:
print [i for i in a if i > 4]
# Or:
print filter(lambda x: x > 4, a)
# Add three to all list members:
# Bad
b = []
for i in range(len(a)):
b.append(a[i] + 3)
print b
# Good:
print [i + 3 for i in a]
# Or:
print map(lambda i: i + 3, a)

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#!/usr/bin/env python
__author__ = "bt3"
from collections import Counter
def Counter_example():
''' it is a dictionary that maps the items to the number of occurrences '''
seq1 = [1, 2, 3, 5, 1, 2, 5, 5, 2, 5, 1, 4]
seq_counts = Counter(seq1)
print(seq_counts)
''' we can increment manually or use the update() method '''
seq2 = [1, 2, 3]
seq_counts.update(seq2)
print(seq_counts)
seq3 = [1, 4, 3]
for key in seq3:
seq_counts[key] += 1
print(seq_counts)
''' also, we can use set operations such as a-b or a+b '''
seq_counts_2 = Counter(seq3)
print(seq_counts_2)
print(seq_counts + seq_counts_2)
print(seq_counts - seq_counts_2)
if __name__ == '__main__':
Counter_example()

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#!/bin/python
#
# An example of Python Decorator
#
def pretty_sumab(func):
def inner(a,b):
print(str(a) + " + " + str(b) + " is ", end="")
return func(a,b)
return inner
@pretty_sumab
def sumab(a,b):
summed = a + b
print(summed)
if __name__ == "__main__":
sumab(5,3)

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#!/usr/bin/env python
__author__ = "bt3"
def logger(func):
def inner(*args): #1
print "Arguments were: {0}".format(args)
return func(*args)
return inner
@logger
def foo(x, y):
return x+y
print foo(1, 2)
def sum(func):
s = 0
for i in func():
s += i
return s
@sum
def interate():
a = []
for i in range(10):
a.append(i)
return a
print interate
# which is the same as
def interate():
a = []
for i in range(10):
a.append(i)
return a
print sum(interate)

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#!/usr/bin/env python
__author__ = "bt3"
from collections import defaultdict
def defaultdict_example():
''' show some examples for defaultdicts '''
pairs = {('a', 1), ('b',2), ('c',3)}
d1 = {}
for key, value in pairs:
if key not in d1:
d1[key] = []
d1[key].append(value)
print(d1)
d2 = defaultdict(list)
for key, value in pairs:
d2[key].append(value)
print(d2)
if __name__ == '__main__':
defaultdict_example()

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@ -0,0 +1,15 @@
#!/usr/bin/python
__author__ = "bt3"
'''
The doctest module automatically runs any statement beginning with >>>
and compares the following line with the output from the interpreter.
>>> 1 == 1
False
'''
if __name__ == '__main__':
import doctest
doctest.testmod()

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#!/usr/bin/env python
__author__ = "bt3"
from fractions import Fraction
def rounding_floats(number1, places):
return round(number1, places)
def float_to_fractions(number):
return Fraction(*number.as_integer_ratio())
def get_denominator(number1, number2):
a = Fraction(number1, number2)
return a.denominator
def get_numerator(number1, number2):
a = Fraction(number1, number2)
return a.numerator
def test_testing_floats(module_name='this module'):
number1 = 1.25
number2 = 1
number3 = -1
number4 = 5/4
number6 = 6
assert(rounding_floats(number1, number2) == 1.2)
assert(rounding_floats(number1*10, number3) == 10)
assert(float_to_fractions(number1) == number4)
assert(get_denominator(number2, number6) == number6)
assert(get_numerator(number2, number6) == number2)
s = 'Tests in {name} have {con}!'
print(s.format(name=module_name, con='passed'))
if __name__ == '__main__':
test_testing_floats()

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@ -0,0 +1,27 @@
#!/usr/bin/env python
__author__ = "bt3"
def interate(x):
for i in range(x):
yield i
def gen1():
a = interate(10)
print a.next()
print a.next()
print a.next()
def reverse(data):
for i in range(len(data)-1, -1, -1):
yield data[i]
def gen2():
for c in reverse('awesome'):
print c
if __name__ == '__main__':
gen1()
gen2()

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#!/usr/bin/env python
__author__ = "bt3"
test = lambda x: x**2
print test(3)

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@ -0,0 +1,21 @@
#!/usr/bin/env python
__author__ = "bt3"
import logging
LOG_FILENAME = 'logging_example.out'
logging.basicConfig(filename=LOG_FILENAME,
level=logging.DEBUG,
)
logging.debug('This message should go to the log file')
f = open(LOG_FILENAME, 'rt')
try:
body = f.read()
finally:
f.close()
print 'FILE:'
print body

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@ -0,0 +1,18 @@
#!/usr/bin/env python3
__author__ = "bt3"
from functools import lru_cache
@lru_cache(maxsize=20)
def fib(n):
if n < 2:
return n
return fib(n-1) + fib(n-2)
if __name__ == '__main__':
print([fib(n) for n in range(10)])
print(fib.cache_info())

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#!/usr/bin/env python
__author__ = "bt3"
import time
import numpy as np
def testing_numpy():
''' tests many features of numpy '''
ax = np.array([1,2,3])
ay = np.array([3,4,5])
print(ax)
print(ax*2)
print(ax+10)
print(np.sqrt(ax))
print(np.cos(ax))
print(ax-ay)
print(np.where(ax<2, ax, 10))
m = np.matrix([ax, ay, ax])
print(m)
print(m.T)
grid1 = np.zeros(shape=(10,10), dtype=float)
grid2 = np.ones(shape=(10,10), dtype=float)
print(grid1)
print(grid2)
print(grid1[1]+10)
print(grid2[:,2]*2)
def trad_version():
t1 = time.time()
X = range(10000000)
Y = range(10000000)
Z = []
for i in range(len(X)):
Z.append(X[i] + Y[i])
return time.time() - t1
def numpy_version():
t1 = time.time()
X = np.arange(10000000)
Y = np.arange(10000000)
Z = X + Y
return time.time() - t1
if __name__ == '__main__':
testing_numpy()
print(trad_version())
print(numpy_version())
'''
3.23564291
0.0714290142059
'''

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@ -0,0 +1,10 @@
#!/usr/bin/env python
__author__ = "bt3"
filename = raw_input('Enter a file name: ')
try:
f = open(filename, "r")
except:
print 'There is no file named', filename

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#!/usr/bin/env python
__author__ = "bt3"
import pickle
def import_pickle(filename):
fh = None
try:
fh = open(filename, "rb")
mydict2 = pickle.load(fh)
return mydict2
except (EnvironmentError) as err:
print ("{0}: import error: {0}".format(os.path.basename(sys.arg[0]), err))
return false
finally:
if fh is not None:
fh.close()
def test_import_pickle():
pkl_file = 'test.dat'
mydict = import_pickle(pkl_file)
print(mydict)
def export_pickle(data, filename='test.dat', compress=False):
fh = None
try:
if compress:
fh = gzip.open(filename, "wb") # write binary
else:
fh = open(filename, "wb") # compact binary pickle format
pickle.dump(data, fh, pickle.HIGHEST_PROTOCOL)
except(EnvironmentError, pickle.PickingError) as err:
print("{0}: export error: {1}".format(os.path.basename(sys.argv[0], err)))
return False
finally:
if fh is not None:
fh.close()
def test_export_pickle():
mydict = {'a': 1, 'b': 2, 'c': 3}
export_pickle(mydict)
if __name__ == '__main__':
test_export_pickle()
test_import_pickle()

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@ -0,0 +1,13 @@
#!/usr/bin/env python
__author__ = "bt3"
import Queue
q = Queue.Queue()
for i in range(10):
q.put(i)
for i in range(10):
print q.get(i)

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@ -0,0 +1,27 @@
#!/usr/bin/env python
__author__ = "bt3"
import random
def testing_random():
''' testing the module random'''
values = [1, 2, 3, 4]
print(random.choice(values))
print(random.choice(values))
print(random.choice(values))
print(random.sample(values, 2))
print(random.sample(values, 3))
''' shuffle in place '''
random.shuffle(values)
print(values)
''' create random integers '''
print(random.randint(0,10))
print(random.randint(0,10))
if __name__ == '__main__':
testing_random()

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@ -0,0 +1,38 @@
#!/usr/bin/env python
__author__ = "bt3"
def usual_dict(dict_data):
newdata = {}
for k, v in dict_data:
if k in newdata:
newdata[k].append(v)
else:
newdata[k] = [v]
return newdata
def setdefault_dict(dict_data):
newdata = {}
for k, v in dict_data:
newdata.setdefault(k, []).append(v)
return newdata
def test_setdef(module_name='this module'):
dict_data = (('key1', 'value1'),
('key1', 'value2'),
('key2', 'value3'),
('key2', 'value4'),
('key2', 'value5'),)
print(usual_dict(dict_data))
print(setdefault_dict(dict_data))
s = 'Tests in {name} have {con}!'
print(s.format(name=module_name, con='passed'))
if __name__ == '__main__':
test_setdef()

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@ -0,0 +1,37 @@
#!/usr/bin/env python
__author__ = "bt3"
def difference(l1):
""" return the list with duplicate elements removed """
return list(set(l1))
def intersection(l1, l2):
""" return the intersection of two lists """
return list(set(l1) & set(l2))
def union(l1, l2):
""" return the union of two lists """
return list(set(l1) | set(l2))
def test_sets_operations_with_lists():
l1 = [1,2,3,4,5,9,11,15]
l2 = [4,5,6,7,8]
l3 = []
assert(difference(l1) == [1, 2, 3, 4, 5, 9, 11, 15])
assert(difference(l2) == [8, 4, 5, 6, 7])
assert(intersection(l1, l2) == [4,5])
assert(union(l1, l2) == [1, 2, 3, 4, 5, 6, 7, 8, 9, 11, 15])
assert(difference(l3) == [])
assert(intersection(l3, l2) == l3)
assert(sorted(union(l3, l2)) == sorted(l2))
print('Tests passed!')
if __name__ == '__main__':
test_sets_operations_with_lists()

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@ -0,0 +1,35 @@
#!/usr/bin/env python
__author__ = "bt3"
import socket
def netcat(hostname, port, content):
s = socket.socket(socket.AF_INET, socket.SOCK_STREAM)
s.connect((hostname, port))
s.sendall(content)
adata = []
while 1:
data = s.recv(1024)
if data == '':
break
adata.append(data)
s.close()
return adata
if __name__ == '__main__':
PORT = 12345
HOSTNAME = '54.209.5.48'
message = netcat(HOSTNAME, PORT, 'Hello!')[1]
print message

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@ -0,0 +1,11 @@
#!/usr/bin/env python
__author__ = "bt3"
foo = 'foo'
bar = 'bar'
print '%s%s' % (foo, bar) # It is OK
print '{0}{1}'.format(foo, bar) # It is better
print '{foo}{bar}'.format(foo=foo, bar=bar) # It is best

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@ -0,0 +1,8 @@
#!/usr/bin/env python
__author__ = "bt3"
import subprocess,os
os.system('ls')
subprocess.call(['ls', '-1'], shell=True)

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@ -0,0 +1,22 @@
#!/usr/bin/env python
__author__ = "bt3"
from telnetlib import Telnet
# examples of telnet connections
PORT = 12345
HOST = '54.209.5.48'
# creating connection
tn = Telnet(HOST ,PORT)
# reading input
msg_in2 = tn.read_all().dec_msg()
tn.read_until(b'psifer text: ')
# writing outputs
tn.write(msg.encode() + b'\n')

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#!/usr/bin/env python
__author__ = "bt3"
def test_doctest():
'''
>>> 1 == 1
False
'''
pass
if __name__ == '__main__':
import doctest
doctest.testmod()
#####
import unittest
class BasicsTestCase(unittest.TestCase):
def test_find_name(self):
self.assertTrue(1 == 1)
self.assertFalse(1 == 2)
if __name__ == '__main__':
unittest.main()
#####
# content of test_example.py, run with $ py.test
#
# run tests over the directory
# $ nosetest
def func(x):
return x + 1
def test_answer():
assert func(3) == 4

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@ -0,0 +1,16 @@
#!/usr/bin/env python
__author__ = "bt3"
import threading
def worker(num):
"""thread worker function"""
print 'Worker: %s' % num
return
threads = []
for i in range(5):
t = threading.Thread(target=worker, args=(i,))
threads.append(t)
t.start()

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@ -0,0 +1,24 @@
#!/usr/bin/python
__author__ = "bt3"
''' a simple example of how to time a function '''
import time
def sumOfN2(n):
start = time.time()
theSum = 0
for i in range(1,n+1):
theSum = theSum + i
end = time.time()
return theSum,end-start
if __name__ == '__main__':
n = 5
print("Sum is %d and required %10.7f seconds"%sumOfN2(n))
n = 200
print("Sum is %d and required %10.7f seconds"%sumOfN2(n))

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## Python General Questions & Answers
Python is a programming language with objects, modules, threads, exceptions and automatic memory management. The benefits of pythons are that it is simple and easy, portable, extensible, build-in data structure and it is an open source.
#### What is PEP 8?
PEP 8 is a coding convention, a set of recommendation, about how to write your Python code more readable.
#### What is pickling and unpickling?
Pickle module accepts any Python object and converts it into a string representation and dumps it into a file by using a dump function, this process is called pickling. While the process of retrieving original Python objects from the stored string representation is called unpickling.
#### How Python is interpreted?
Python language is an interpreted language. Python program runs directly from the source code. It converts the source code that is written by the programmer into an intermediate language, which is again translated into machine language that has to be executed.
#### How memory is managed in Python?
Python memory is managed by Python private heap space. All Python objects and data structures are located in a private heap. The programmer does not have access to this private heap and interpreter takes care of this Python private heap.
The allocation of Python heap space for Python objects is done by Python memory manager. The core API gives access to some tools for the programmer to code.
Python also has an inbuilt garbage collector, which recycle all the unused memory and frees the memory and makes it available to the heap space.
#### What are the tools that help to find bugs or perform static analysis?
PyChecker is a static analysis tool that detects the bugs in Python source code and warns about the style and complexity of the bug. Pylint is another tool that verifies whether the module meets the coding standard.
#### What are Python decorators?
A Python decorator is a specific change that we make in Python syntax to alter functions easily.
#### What is the difference between list and tuple?
The difference between list and tuple is that list is mutable while tuple is not. Tuple can be hashed for e.g as a key for dictionaries.
#### How are arguments passed by value or by reference?
Everything in Python is an object and all variables hold references to the objects. The references values are according to the functions; as a result, you cannot change the value of the references. However, you can change the objects if it is mutable.
#### What are the built-in type does python provides?
There are mutable and Immutable types of Pythons built-in types Mutable built-in types
List
Sets
Dictionaries
Immutable built-in types
Strings
Tuples
Numbers
#### What is namespace in Python?
In Python, every name introduced has a place where it lives and can be hooked for. This is known as namespace. It is like a box where a variable name is mapped to the object placed. Whenever the variable is searched out, this box will be searched, to get the corresponding object.
#### What is lambda in Python?
It is a single expression anonymous function often used as an inline function.
#### Why lambda forms in python do not have statements?
A lambda form in python does not have statements as it is used to make new function object and then return them at runtime.
#### What is pass in Python?
Pass means, no-operation Python statement, or in other words, it is a place holder in a compound statement, where there should be a blank left and nothing has to be written there.
#### In Python what are iterators?
In Python, iterators are used to iterate a group of elements, containers like list.
#### What is unittest in Python?
A unit testing framework in Python is known as unittest. It supports sharing of setups, automation testing, shutdown code for tests, aggregation of tests into collections, etc.
#### In Python what is slicing?
A mechanism to select a range of items from sequence types like list, tuple, strings, etc. is known as slicing.
#### What are generators in Python?
The way of implementing iterators are known as generators. It is a normal function except that it yields expression in the function.
#### What is docstring in Python?
A Python documentation string is known as docstring, it is a way of documenting Python functions, modules and classes.
#### How can you copy an object in Python?
To copy an object in Python, you can try copy.copy () or copy.deepcopy() for the general case. You cannot copy all objects but most of them.
#### What is the difference between deep and shallow copy?
Shallow copy is used when a new instance type gets created and it keeps the values that are copied in the new instance. Whereas, a deep copy is used to store the values that are already copied.
#### What is a negative index in Python?
Python sequences can be index in positive and negative numbers. For positive index, 0 is the first index, 1 is the second index and so forth. For negative index, (-1) is the last index and (-2) is the second last index and so forth.
#### How you can convert a number to a string?
In order to convert a number into a string, use the inbuilt function str(). If you want a octal or hexadecimal representation, use the inbuilt function oct() or hex().
#### What is the difference between Xrange and range?
Xrange returns the xrange object while range returns the list, and uses the same memory no matter what the range size is.
#### What is module and package in Python?
In Python, a module is the way to structure program. Each Python program file is a module, which imports other modules like objects and attributes.
The folder of Python program is a package of modules. A package can have modules or subfolders.
#### What are the rules for local and global variables in Python?
Local variables: If a variable is assigned a new value anywhere within the function's body, it's assumed to be local.
Global variables: Those variables that are only referenced inside a function are implicitly global.
#### How can you share global variables across modules?
To share global variables across modules within a single program, create a special module. Import the config module in all modules of your application. The module will be available as a global variable across modules.
#### Explain how can you make a Python Script executable on Unix?
To make a Python Script executable on Unix, you need to do two things,
Script file's mode must be executable and
the first line must begin with # (`#!/usr/local/bin/python`).
#### Explain how to delete a file in Python?
By using a command `os.remove (filename)` or `os.unlink(filename)`.
#### Explain how can you generate random numbers in Python?
To generate random numbers in Python, you need to import command as
```
import random
random.random()
```
This returns a random floating point number in the range [0,1)
#### Explain how can you access a module written in Python from C?
You can access a module written in Python from C by following method,
```
Module = =PyImport_ImportModule("<modulename>");
```
#### Mention the use of // operator in Python?
It is a Floor Division operator, which is used for dividing two operands with the result as quotient showing only digits before the decimal point. For instance, `10//5 = 2 and 10.0//5.0 = 2.0`.
#### Explain what is Flask & its benefits?
Flask is a web microframework for Python based on "Werkzeug, Jinja 2 and good intentions" BSD licensed. Werkzeug and jingja are two of its dependencies.
Flask is part of the micro-framework. Which means it will have little to no dependencies on external libraries. It makes the framework light while there is a little dependency to update and fewer security bugs.
#### What is the difference between Django, Pyramid, and Flask?
Flask is a "microframework" primarily build for a small application with simpler requirements. In Flask, you have to use external libraries. Flask is ready to use.
Pyramid is built for larger applications. It provides flexibility and lets the developer use the right tools for their project. The developer can choose the database, URL structure, templating style and more. Pyramid is heavy configurable.
Like Pyramid, Django can also be used for larger applications. It includes an ORM.
#### Explain how you can access sessions in Flask?
A session basically allows you to remember information from one request to another. In a flask, it uses a signed cookie so the user can look at the session contents and modify. The user can modify the session if only it has the secret key Flask.secret_key.
#### Is Flask an MVC model and if yes give an example showing MVC pattern for your application?
Basically, Flask is a minimalistic framework which behaves the same as MVC framework. So MVC is a perfect fit for Flask, and the pattern for MVC we will consider for the following example:
```python
from flask import Flask
app = Flask(_name_)
@app.route("/")
Def hello():
return "Hello World"
app.run(debug = True)
```
#### Explain database connection in Python Flask?
Flask supports database powered application (RDBS). Such a system requires creating a schema, which requires piping the shema.sql file into a sqlite3 command. So you need to install sqlite3 command in order to create or initiate the database in Flask.
Flask allows requesting database in three ways
* before_request() : They are called before a request and pass no arguments.
* after_request() : They are called after a request and pass the response that will be sent to the client.
* teardown_request(): They are called in a situation when an exception is raised, and response is not guaranteed. They are called after the response been constructed. They are not allowed to modify the request, and their values are ignored.
#### You are having multiple Memcache servers running Python, in which one of the Memcache server fails, and it has your data, will it ever try to get key data from that one failed server?
The data in the failed server won't get removed, but there is a provision for auto-failure, which you can configure for multiple nodes. Fail-over can be triggered during any kind of socket or Memcached server level errors and not during normal client errors like adding an existing key, etc.
#### Explain how you can minimize the Memcached server outages in your Python Development?
When one instance fails, several of them goes down, this will put a larger load on the database server when lost data is reloaded as the client make a request. To avoid this, if your code has been written to minimize cache stampedes then it will leave a minimal impact.
Another way is to bring up an instance of Memcached on a new machine using the lost machines IP address.
#### Explain how Memcached should not be used in your Python project?
Memcached common misuse is to use it as a data store, and not as a cache. Never use Memcached as the only source of the information you need to run your application. Data should always be available through another source as well. Memcached is just a key or value store and cannot perform query over the data or iterate over the contents to extract information. Memcached does not offer any form of security either in encryption or authentication.
#### What's a metaclass in Python?
This type of class holds the instructions about the behind-the-scenes code generation that you want to take place when another piece of code is being executed. With a metaclass, we can define properties that should be added to new classes that are defined in our code.
#### Why isn't all memory freed when Python exits?
Objects referenced from the global namespaces of Python modules are not always deallocated when Python exits. This may happen if there are circular references. There are also certain bits of memory that are allocated by the C library that are impossible to free/ Python is, however, aggressive about cleaning up memory on exit and does try to destroy every single object.
If you want to force Python to delete certain things on deallocation, you can use the atexit module to register one or more exit functions to handle those deletions.
#### Usage of `__slots__`?
The special attribute `__slots__` allows you to explicitly state which instance attributes you expect your object instances to have, with the expected results:
* faster attribute access.
* space savings in memory.
#### What id() function in Python is for?
`id()` function accepts a single parameter and is used to return the identity of an object. This identity has to be unique and constant for this object during the lifetime. Two objects with non-overlapping lifetimes may have the same `id()` value.
#### Is Python call-by-value or call-by-reference?
Neither. In Python, (almost) everything is an object. What we commonly refer to as "variables" in Python are more properly called names. Likewise, "assignment" is really the binding of a name to an object. Each binding has a scope that defines its visibility, usually the block in which the name originates.
In Python a variable is not an alias for a location in memory. Rather, it is simply binding to a Python object.ext post.
----

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@ -0,0 +1,44 @@
# Byte-compiled / optimized / DLL files
__pycache__/
*.py[cod]
# C extensions
*.so
# Distribution / packaging
.Python
env/
build/
develop-eggs/
dist/
eggs/
lib/
lib64/
parts/
sdist/
var/
*.egg-info/
.installed.cfg
*.egg
# Installer logs
pip-log.txt
pip-delete-this-directory.txt
# Unit test / coverage reports
htmlcov/
.tox/
.coverage
.cache
nosetests.xml
coverage.xml
# Translations
*.mo
*.pot
# Django stuff:
*.log
# Sphinx documentation
docs/_build/

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#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
def mul3and5(n):
result = 0
for num in range(1, n):
if num%3 == 0 or num%5 == 0:
result += num
return result
def test_():
assert(mul3and5(10) == 23)
print(mul3and5(1000))
print('Tests Passed!')
if __name__ == '__main__':
test_()

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@ -0,0 +1,18 @@
#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
def even_fib_num(limit):
a, b = 0, 1
while a < limit:
yield a
a, b = b, a + b
def main():
print(sum(n for n in even_fib_num(4e6) if not (n & 1)))
print('Tests Passed!')
if __name__ == '__main__':
main()

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#!/usr/bin/python3
#!/usr/bin/python3
def is_prime(n):
if n < 4 : return True
for i in range(2, int(n**0.5 + 1)):
if not n%i: return False
return True
def largest_prime_factor(n):
i = int(n**0.5 +1)
while i > 1 :
if not n%i and i&1:
if is_prime(i): return i
i -= 1
return None
def largest_prime_factor_optimized(n):
factor = 2
lastfactor = 1
while n > 1:
if not n%factor:
lastfactor = factor
n = n//factor
while n%factor == 0:
n = n//factor
factor += 1
return lastfactor
def test_largest_prime_factor():
assert(largest_prime_factor(13195)== 29)
print(largest_prime_factor(600851475143))
assert(largest_prime_factor_optimized(13195) == 29)
print(largest_prime_factor_optimized(600851475143))
print('Tests Passed!')
if __name__ == '__main__':
test_largest_prime_factor()

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#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
def is_palindrome(s):
return s == reverse(s)
def reverse(s):
rev = 0
while s > 0:
rev = 10*rev + s%10
s = s//10
return rev
def is_palindrome_2(s):
# to use it you need to cast str() first
while s:
if s[0] != s[-1]: return False
else:
s = s[1:-1]
is_palindrome(s)
return True
def larg_palind_product(n):
nmax, largpal = 9, 0
for i in range(1, n):
nmax += 9*10**i
for i in range(nmax, nmax//2, -1):
for j in range(i -1, (i -1)//2, -1):
candidate = i*j
if is_palindrome(candidate) and candidate > largpal:
largpal = candidate
return largpal
def test_larg_palind_product():
assert(larg_palind_product(2)== 9009)
print(larg_palind_product(3))
print('Tests Passed!')
if __name__ == '__main__':
test_larg_palind_product()

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#!/usr/bin/python3
def smallest_multiple(n):
set1 = set([x for x in range(1, n+1)])
set2 = set()
for i in range(len(set1), 0, -1):
for j in range(1, i):
if i%j == 0:
set2.add(j)
set1 = set1 - set2
res_num = n*n
while True:
for i in set1:
missing_div = False
if res_num%i:
missing_div = True
shift = res_num%i
break
if not missing_div: return res_num
res_num += 1 or shift
shift = 0
def test_():
assert(smallest_multiple(10) == 2520)
print(smallest_multiple(20))
print('Tests Passed!')
if __name__ == '__main__':
test_()

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#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
def sum_square_diff(n):
sq_sum, sum_sq = 0, 0
for i in range(1, n+1):
sum_sq += i**2
sq_sum += i
sq_sum = sq_sum **2
return sq_sum - sum_sq
def main():
assert(sum_square_diff(10) == 2640)
print(sum_square_diff(100))
print('Tests Passed!')
if __name__ == '__main__':
main()

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#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
import math
def is_prime(number, prime_set):
if number in prime_set: return True
for i in range(2, int(math.sqrt(number)) + 1):
if not number%i: return False
return True
def findstprime(n):
count = 0
candidate = 1
prime_set = set()
while count < n:
candidate +=1
if is_prime(candidate, prime_set):
prime_set.add(candidate)
count += 1
return candidate
def main():
assert(findstprime(6 == 13))
print(findstprime(10001))
print('Tests Passed!')
if __name__ == '__main__':
main()

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#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
def largest_prod_seq(n):
result = 0
for i in range(0, len(n)-4):
first = int(n[i])
second = int(n[i+1])
third = int(n[i+2])
fourth = int(n[i+3])
fifth = int(n[i+4])
result_here = first*second*third*fourth*fifth
if result < result_here:
result = result_here
return result
def main():
n = '7316717653133062491922511967442657474235534919493496983520312774506326239578318016984801869478851843858615607891129494954595017379583319528532088055111254069874715852386305071569329096329522744304355766896648950445244523161731856403098711121722383113622298934233803081353362766142828064444866452387493035890729629049156044077239071381051585930796086670172427121883998797908792274921901699720888093776657273330010533678812202354218097512545405947522435258490771167055601360483958644670632441572215539753697817977846174064955149290862569321978468622482839722413756570560574902614079729686524145351004748216637048440319989000889524345065854122758866688116427171479924442928230863465674813919123162824586178664583591245665294765456828489128831426076900422421902267105562632111110937054421750694165896040807198403850962455444362981230987879927244284909188845801561660979191338754992005240636899125607176060588611646710940507754100225698315520005593572972571636269561882670428252483600823257530420752963450'
print(largest_prod_seq(n))
print('Tests Passed!')
if __name__ == '__main__':
main()

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#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
def special_pyt(n):
for i in range(3, n):
for j in range(i+1, n):
c = calc_c(i,j)
if i + j + c == n:
return i*j*c
def calc_c(a, b):
return (a**2 + b**2)**0.5
def main():
assert(special_pyt(3+4+5) == (3*4*5))
print(special_pyt(1000))
print('Tests Passed!')
if __name__ == '__main__':
main()

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#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
from findstprime import is_prime
def summation_primes(n):
candidate = 2
prime_set = set()
while candidate < n:
if is_prime(candidate, prime_set):
prime_set.add(candidate)
candidate +=1
return sum(prime_set)
def main():
assert(summation_primes(10) == 17)
print(summation_primes(2000000))
print('Tests Passed!')
if __name__ == '__main__':
main()

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#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
import string
def get_grid(filename):
grid = [ [ 0 for i in range(20) ] for j in range(20) ]
with open(filename) as file:
for row, line in enumerate(file):
line.strip('\n')
for collumn, number in enumerate(line.split(' ')):
grid[row][collumn] = int(number)
return grid
def larg_prod_grid(grid):
row, col, larg_prod = 0, 0, 0
up, down, left, right, diag1, diag2, diag3, diag4 = 0, 0, 0, 0, 0, 0, 0, 0
while row < len(grid):
while col < len(grid[0]):
if col > 2:
up = grid[row][col] * grid[row][col-1] * grid[row][col-2] * grid[row][col-3]
if col < len(grid[0]) - 3:
down = grid[row][col] * grid[row][col+1] * grid[row][col+2] * grid[row][col+3]
if row > 2:
left = grid[row][col] * grid[row-1][col] * grid[row-2][col] * grid[row-3][col]
if row < len(grid) - 3:
right = grid[row][col] * grid[row+1][col] * grid[row+2][col] * grid[row+3][col]
if col > 2 and row > 2:
diag1 = grid[row][col] * grid[row-1][col-1] * grid[row-2][col-2] * grid[row-3][col-3]
if col > 2 and row < len(grid) - 3:
diag2 = grid[row][col] * grid[row+1][col-1] * grid[row+2][col-2] * grid[row+3][col-3]
if col < len(grid[0]) - 3 and row > 2:
diag3 = grid[row][col] * grid[row-1][col+1] * grid[row-2][col+2] * grid[row-3][col+3]
if col < len(grid[0]) -3 and row < len(grid) - 3:
down = grid[row][col] * grid[row+1][col+1] * grid[row+1][col+2] * grid[row+1][col+3]
l1 = [up, down, left, right, diag1, diag2, diag3, diag4]
largest_prod_here = max(l1)
if largest_prod_here > larg_prod:
larg_prod = largest_prod_here
col += 1
col = 0
row += 1
return larg_prod
def main():
import time
start = time.time()
filename = 'larg_prod_grid.dat'
grid = get_grid(filename)
assert((grid[6][8], grid[7][9], grid[8][10], grid[9][11]) == (26, 63, 78, 14))
print(larg_prod_grid(grid))
elapsed = (time.time() - start)
print('Tests Passed!\n It took %s seconds to run them.' % (elapsed))
if __name__ == '__main__':
main()

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#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
import math
def find_div(n):
''' find the divisor of a given n'''
set_div = {1, n}
for i in range(2, int(math.sqrt(n))+ 1):
if not n % i:
set_div.add(i)
set_div.add(n//i)
l1 = list(set_div)
return len(l1)
def find_trian(l):
''' find the lth trian number'''
return sum(range(1, l+1))
def highly_divisible_trian_num(d):
thtriangle, n_div, count = 1, 0, 1
while n_div < d:
count += 1
thtriangle += count
n_div = find_div(thtriangle)
return (thtriangle, count)
def main():
import time
start = time.time()
assert(highly_divisible_trian_num(6) == (28, 7))
print(highly_divisible_trian_num(500))
elapsed = (time.time() - start)
print('Tests Passed!\n It took %s seconds to run them.' % (elapsed))
if __name__ == '__main__':
main()

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#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
def large_sum(filename):
sum_total, lines, numbers = 0, 0, 0
with open(filename) as file:
for line in file:
sum_total += int(line.strip('\n'))
return str(sum_total)[0:10]
def main():
import time
start = time.time()
filename = 'large_sum.dat'
print(large_sum(filename))
elapsed = (time.time() - start)
print('Tests Passed!\n It took %s seconds to run them.' % (elapsed))
if __name__ == '__main__':
main()

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#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
def find_coll_seq(n):
count = 1
while n > 1:
if n%2 == 0:
n = n//2
else:
n = 3*n +1
count += 1
return count
def find_longest_chain(limit):
longest, number = 0, 0
start = 0
while start <= limit:
size_chain = find_coll_seq(start)
if size_chain > longest:
longest = size_chain
number = start
start += 1
return (longest, number)
def main():
import time
start = time.time()
#print(find_longest_chain(13))
print(find_longest_chain(10**6))
elapsed = (time.time() - start)
print('Tests Passed!\n It took %s seconds to run them.' % (elapsed))
if __name__ == '__main__':
main()

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#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
def lattice_paths(squares):
gridsize = squares+1
grid = [[0 for i in range(gridsize)] for j in range(gridsize)]
row, col = 0, 0
while col < gridsize:
while row < gridsize:
if row == 0 and col == 0:
grid[row][col] = 1
else:
if row == 0 and col != 0:
grid[row][col] += grid[row][col-1]
elif row != 0 and col == 0:
grid[row][col] += grid[row-1][col]
else:
grid[row][col] += grid[row][col-1] + grid[row-1][col]
row += 1
row = 0
col += 1
return grid[gridsize-1][gridsize-1]
def main():
import time
start = time.time()
assert(lattice_paths(2) == 6)
print(lattice_paths(20))
elapsed = (time.time() - start)
print('Tests Passed!\n It took %s seconds to run them.' % (elapsed))
if __name__ == '__main__':
main()

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#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
def power_digit_sum(n):
number = str(2**n)
sum_res = 0
for i in number:
sum_res += int(i)
return sum_res
def test_():
assert(power_digit_sum(15) == 26)
print(power_digit_sum(1000))
print('Tests Passed!')
if __name__ == '__main__':
test_()

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#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
def number_letter_counts(n):
dict_lett = build_dict(n)
sum_letter = 0
for item in dict_lett:
sum_letter += dict_lett[item]
return sum_letter
def build_dict(n):
lett_dict = {}
numbers = (x for x in range(1, n+1))
dec = ['one', 'two', 'three', 'four', 'five', 'six', 'seven', 'eight', 'nine', 'ten', 'eleven', 'twelve', 'thirteen', 'fourteen', 'fifteen', 'sixteen', 'seventeen', 'eighteen', 'nineteen']
ties = ['twenty', 'thirty', 'forty', 'fifty', 'sixty', 'seventy', 'eighty', 'ninety']
for number in numbers:
if 1 <= number < 20:
lett_dict[number] = len(dec[number-1])
elif 20 <= number < 100:
index_dec = number//10
index_num = number%10
if index_num == 0:
lett_dict[number] = len(ties[index_dec-2])
else:
lett_dict[number] = len(ties[index_dec-2]) + len(dec[index_num-1])
elif 100 <= number < 1000:
index_hun = number//100
index_dec = number%100
if index_dec == 0:
lett_dict[number] = len(dec[index_hun-1]) + len('hundred')
else:
if 1 <= index_dec < 20:
lett_dict[number] = len(dec[index_hun-1]) + len('hundred') + len('and') + len(dec[index_dec-1])
elif 20 <= index_dec < 100:
index_dec2 = index_dec//10
index_num = index_dec%10
if index_num == 0:
lett_dict[number] = len(dec[index_hun-1]) + len('hundred') + len('and') + len(ties[index_dec2-2])
else:
lett_dict[number] = len(dec[index_hun-1]) + len('hundred') + len('and') + len(ties[index_dec2-2]) + len(dec[index_num-1])
elif number == 1000:
lett_dict[number] = len('onethousand')
return lett_dict
def main():
import time
start = time.time()
assert(number_letter_counts(5) == 19)
print(number_letter_counts(1000))
elapsed = (time.time() - start)
print('Tests Passed!\n It took %s seconds to run them.' % (elapsed))
if __name__ == '__main__':
main()

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#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
def max_path_sum(t):
root = t[0][0]
height, width, index, large_num = 1, 0, 0, 0
max_sum = root
heights = len(t[:])
while height < heights:
values_here = t[height][index:index+2]
if values_here[0] > values_here[1]:
large_num = values_here[0]
else:
large_num = values_here[1]
index += 1
max_sum += large_num
pivot = large_num
width, large_num = 0, 0
height += 1
return max_sum
def edit_input(filename):
output = []
with open(filename) as file:
for line in file:
line = line.rstrip('\n')
output.append(line.split(' '))
for i, l1 in enumerate(output):
for j, c in enumerate(output[i]):
output[i][j] = int(c)
return(output)
def main():
import time
start = time.time()
filename = 'max_path_sum0.dat'
t1 = edit_input(filename)
print('Little pir: ',max_path_sum(t1))
filename = 'max_path_sum.dat'
t2 = edit_input(filename)
print('Big pir: ', max_path_sum(t2))
elapsed = (time.time() - start)
print('Tests Passed!\n It took %s seconds to run them.' % (elapsed))
if __name__ == '__main__':
main()

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#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
'''
1 Jan 1900 was a Monday.
Thirty days has September,
April, June and November.
All the rest have thirty-one,
Saving February alone,
Which has twenty-eight, rain or shine.
And on leap years, twenty-nine.
A leap year occurs on any year evenly divisible by 4, but not on a century unless it is divisible by 400.
How many Sundays fell on the first of the month during the twentieth century (1 Jan 1901 to 31 Dec 2000)?
'''
def find_if_leap_year(y):
if (y%4 == 0 and y%100 != 0) or (y%400 == 0):
return True
return False
def counting_sundays():
''' define variables '''
days_year = 7*31 + 4*30 + 28
count_sundays = 0
days_week = 7
dict_week = {0: 'mon', 1:'tue', 2:'wed', 3:'thu', 4:'fri', 5:'sat', 6:'sun'}
''' with info from 1900 find first day for 1901 '''
first_day = days_year%days_week # not a leap year
for y in range (1901, 2001):
leap_year = find_if_leap_year(y)
days_count = first_day
for m in range(1, 13):
if days_count%7 == 6:
count_sundays += 1
if m == 2:
if leap_year:
days_count += 29
else:
days_count += 28
elif m == 4 or m == 6 or m == 9 or m == 11:
days_count += 30
else:
days_count += 31
if leap_year: first_day = (first_day +2)%days_week
else: first_day = (first_day +1)%days_week
return count_sundays
def main():
print(counting_sundays())
print('Tests Passed!')
if __name__ == '__main__':
main()

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#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
def factorial(n):
prod = 1
for i in range(1,n):
prod *= i
return prod
def find_sum(n):
sum_ = 0
fact = factorial(n)
number = str(fact)
for i in number:
sum_ += int(i)
return sum_
def main():
import time
start = time.time()
assert(find_sum(10) == 27)
print(find_sum(100))
elapsed = (time.time() - start)
print('Tests Passed!\n It took %s seconds to run them.' % (elapsed))
if __name__ == '__main__':
main()

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#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
'''
Let d(n) be defined as the sum of proper divisors of n (numbers less than n which divide evenly into n).
If d(a) = b and d(b) = a, where a b, then a and b are an amicable pair and each of a and b are called amicable numbers.
For example, the proper divisors of 220 are 1, 2, 4, 5, 10, 11, 20, 22, 44, 55 and 110; therefore d(220) = 284. The proper divisors of 284 are 1, 2, 4, 71 and 142; so d(284) = 220.
Evaluate the sum of all the amicable numbers under 10000.
'''
def find_sum_proper_divisors(n):
sum_proper_div = 0
for i in range(1, n):
if n%i == 0:
sum_proper_div += i
return sum_proper_div
def amicable_numbers(N):
sum_div_list = [find_sum_proper_divisors(i) for i in range(1, N+1)]
sum_amicable_numbers = 0
set_div = set()
for a in range(1, N):
da = sum_div_list[a-1]
if da < N:
b = da
db = sum_div_list[b-1]
if a != b and db == a and a not in set_div and b not in set_div:
sum_amicable_numbers += a + b
set_div.add(a)
set_div.add(b)
return sum_amicable_numbers
def main():
print(amicable_numbers(10000))
print('Tests Passed!')
if __name__ == '__main__':
main()

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#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
def calculate_score(name, dict_letters):
sum_letters = 0
for letter in name:
sum_letters += dict_letters[letter]
return sum_letters
def names_score(filename):
dict_letters ={'A':1,'B':2,'C':3,'D':4,'E':5,'F':6,'G':7,'H':8,'I':9,'J':10,'K':11,'L':12,'M':13,'N':14,'O':15,'P':16,'Q':17,'R':18,'S':19, 'T':20,'U':21,'V':22,'W':23,'X':24,'Y':25,'Z':26}
total_score = 0
with open(filename) as file:
for line in file:
names = [name.strip('"') for name in line.split(',')]
names.sort()
for i, name in enumerate(names):
total_score += (i+1)* calculate_score(name, dict_letters)
return total_score
def main():
filename = 'names.txt'
print(names_score(filename))
if __name__ == '__main__':
main()

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#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
def find_sum_proper_div(n):
sum_proper_div = 0
for i in range(1, n):
if n%i == 0:
sum_proper_div += i
return sum_proper_div
def find_all_abund(n):
sum_div_list = [find_sum_proper_div(i) for i in range(n)]
abu = set()
for i in range(n):
if i < sum_div_list[i]:
abu.add(i)
return abu
def non_abund_sums(n):
abu = find_all_abund(n)
sum_nom_abu = 0
for i in range(n):
if not any( (i-a in abu) for a in abu):
sum_nom_abu += i
return sum_nom_abu
def test_():
r = set([i for i in range(25)])
r_abu = {24}
r = r - r_abu
assert(non_abund_sums(25) == sum(r))
print(non_abund_sums(28123))
print('Tests Passed!')
if __name__ == '__main__':
test_()

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#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
def perm_item(elements):
if len(elements) <= 1:
yield elements
else:
for (index, elmt) in enumerate(elements):
other_elmts = elements[:index]+elements[index+1:]
for permutation in perm_item(other_elmts):
yield [elmt] + permutation
def lex_perm(l1, n):
perm_list = list(perm_item(l1))
return sorted(perm_list)[n-1]
def main():
import time
start = time.time()
l1 = [0,1,2,3,4,5,6,7,8,9]
n = 10**6
print(lex_perm(l1, n))
elapsed = (time.time() - start)
print('Tests Passed!\n It took %s seconds to run them.' % (elapsed))
if __name__ == '__main__':
main()

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#!/usr/bin/python3
# mari wahl @2014
# marina.w4hl at gmail
#
'''
The Fibonacci sequence is defined by the recurrence relation:
Fn = Fn1 + Fn2, where F1 = 1 and F2 = 1.
Hence the first 12 terms will be:
F1 = 1
F2 = 1
F3 = 2
F4 = 3
F5 = 5
F6 = 8
F7 = 13
F8 = 21
F9 = 34
F10 = 55
F11 = 89
F12 = 144
The 12th term, F12, is the first term to contain three digits.
What is the first term in the Fibonacci sequence to contain 1000 digits?
Answer: 4782
'''
def fib(num=1, num_before=1):
found = False
num_before, num = num, num + num_before
if count_digits(num) == 1000: found = True
return num, num_before, found
def count_digits(num):
num_str = str(num)
return len(num_str)
def main():
found = False
num = 1
num_before = 1
count = 2
while not found:
num, num_before, found = fib(num, num_before)
count +=1
print(count)
print('Done!')
if __name__ == '__main__':
main()

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#!/usr/bin/python3
# mari wahl @2014
# marina.w4hl at gmail
'''
A unit fraction contains 1 in the numerator. The decimal representation of the unit fractions with denominators 2 to 10 are given:
1/2 = 0.5
1/3 = 0.(3)
1/4 = 0.25
1/5 = 0.2
1/6 = 0.1(6)
1/7 = 0.(142857)
1/8 = 0.125
1/9 = 0.(1)
1/10 = 0.1
Where 0.1(6) means 0.166666..., and has a 1-digit recurring cycle. It can be seen that 1/7 has a 6-digit recurring cycle.
Find the value of d < 1000 for which 1/d contains the longest recurring cycle in its decimal fraction part.
Answer: 983
'''
def recurring_cycle(n, d):
for dd in range(1, d):
if 1 == 10**dd % d:
return dd
return 0
def main():
n = 1
limit = 1000
longest = max(recurring_cycle(n, i) for i in range(2, limit+1))
print [i for i in range(2, limit+1) if recurring_cycle(n, i) == longest][0]
if __name__ == '__main__':
main()

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#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
def quad_form(n, a, b):
return n**2 + a*n + b
def isPrime(n):
n = abs(int(n))
if n < 2:
return False
if n == 2:
return True
if not n & 1:
return False
for x in range(3, int(n**0.5)+1, 2):
if n % x == 0:
return False
return True
def quad_primes(a, b):
count_max = 0
coef = ()
for aa in range(-a, a):
for bb in range(-b, b):
n = 0
while True:
number = quad_form(n, aa, bb)
if isPrime(number):
n += 1
else:
if n > count_max:
count_max = n
coef = (aa, bb)
break
return coef(0)*coef(1), coef
def main():
import time
start = time.time()
print(quad_primes(1000, 1000))
elapsed = (time.time() - start)
print('Tests Passed!\n It took %s seconds to run them.' % (elapsed))
if __name__ == '__main__':
main()

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#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
def number_spiral(spiral):
return rows, mid
def make_spiral(n):
spiral = []
row = rows//2
col = col//2
count = 1
while row < n:
while col < n:
spiral[col][row] = count
count += 1
if count%2 == 0:
col += 1
else:
row += 1
return spiral
def main():
import time
start = time.time()
n = 5
spiral = make_spiral(n)
print(number_spiral(spiral))# 101
elapsed = (time.time() - start)
print('Tests Passed!\n It took %s seconds to run them.' % (elapsed))
if __name__ == '__main__':
main()

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#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
def dist_pow(a1, a2, b1, b2):
set1 = set()
for a in range(a1, a2 + 1):
for b in range(b1, b2 + 1):
set1.add(a**b)
return len(set1)
def main():
import time
start = time.time()
print(dist_pow(2, 5, 2, 5))
print(dist_pow(2, 100, 2, 100))
elapsed = (time.time() - start)
print('Tests Passed!\n It took %s seconds to run them.' % (elapsed))
if __name__ == '__main__':
main()

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#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
def digit_fifth_pow(n):
lnum = []
for num in range(10**(2), 10**(n+2)):
sum_here = 0
num_str = str(num)
for i in num_str:
num_int = int(i)
num_int_pow = num_int**n
sum_here += num_int_pow
if sum_here == num:
lnum.append(num)
return lnum, sum(lnum)
def main():
import time
start = time.time()
print(digit_fifth_pow(5))
elapsed = (time.time() - start)
print('Tests Passed!\n It took %s seconds to run them.' % (elapsed))
if __name__ == '__main__':
main()

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#!/usr/bin/python3
# mari wahl @2014
# marina.w4hl at gmail
'''
In England the currency is made up of pound, £, and pence, p, and there are eight coins in general circulation:
1p, 2p, 5p, 10p, 20p, 50p, £1 (100p) and £2 (200p).
It is possible to make £2 in the following way:
1×£1 + 1×50p + 2×20p + 1×5p + 1×2p + 3×1p
How many different ways can £2 be made using any number of coins?
'''
def main():
import time
start = time.time()
print(digit_fifth_pow(5))
elapsed = (time.time() - start)
print('Tests Passed!\n It took %s seconds to run them.' % (elapsed))
if __name__ == '__main__':
main()

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#!/usr/bin/python
__author__ = "Mari Wahl"
__email__ = "marina.w4hl@gmail.com"
'''
We shall say that an n-digit number is pandigital if it makes use of all the digits 1 to n exactly once; for example, the 5-digit number, 15234, is 1 through 5 pandigital.
The product 7254 is unusual, as the identity, 39 x 186 = 7254, containing multiplicand, multiplier, and product is 1 through 9 pandigital.
Find the sum of all products whose multiplicand/multiplier/product identity can be written as a 1 through 9 pandigital.
'''
def isPandigitalString(string):
""" Check if string contains a pandigital number. """
digits = len(string)
if digits >= 10:
return False
for i in range(1,digits+1):
if str(i) not in string:
return False
return True
def gives9PandigitalProduct(a, b):
numbers = str(a) + str(b) + str(a*b)
if len(numbers) != 9:
return False
return isPandigitalString(numbers)
def main():
products = []
for a in range(0, 100000):
for b in range(a, 100000):
if len(str(a*b) + str(a) + str(b)) > 9:
break
if gives9PandigitalProduct(a, b):
products.append(a*b)
print("%i x %i = %i" % (a, b, a*b))
print(sum(set(products)))
if __name__ == '__main__':
main()

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#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
def isPrime(n):
n = abs(int(n))
if n < 2:
return False
if n == 2:
return True
for x in range(2, int(n**0.5)+1):
if n%x == 0:
return False
return True
def findPermutations(s):
res = []
if len(s) == 1:
res.append(s)
else:
for i, c in enumerate(s):
for perm in findPermutations(s[:i] + s[i+1:]):
res.append(c + perm)
return res
def isCircular(n):
n_str = str(n)
permutations = findPermutations(n_str)
for perm in permutations:
if not isPrime(perm):
return False
return True
def generatePrimes(n):
if n == 2: return [2]
elif n < 2: return []
s = [i for i in range(3, n+1, 2)]
mroot = n ** 0.5
half = (n+1)//2 - 1
i, m = 0, 3
while m <= mroot:
if s[i]:
j = (m*m-3)//2
s[j] = 0
while j < half:
s[j] = 0
j += m
i = i+1
m = 2*i+3
return [2]+[x for x in s if x]
def generate_n_Primes(n):
primes = []
chkthis = 2
while len(primes) < n:
ptest = [chkthis for i in primes if chkthis%i == 0]
primes += [] if ptest else [chkthis]
chkthis += 1
return primes
def circular_primes(n):
primes = generatePrimes(n)
count = 0
for prime in primes:
if isCircular(prime):
count += 1
return count
def main():
import time
start = time.time()
print(circular_primes(1000000))
elapsed = (time.time() - start)
print('Tests Passed!\n It took %s seconds to run them.' % (elapsed))
if __name__ == '__main__':
main()

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#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
def isPrime(n):
n = abs(int(n))
if n < 2:
return False
if n == 2:
return True
if not n & 1:
return False
for x in range(3, int(n**0.5)+1, 2):
if n % x == 0:
return False
return True
def generetePrimes(n):
if n == 2: return [2]
elif n < 2: return []
s = [i for i in range(3, n+1,2)]
mroot = n ** 0.5
half = (n+1)//2-1
i = 0
m = 3
while m <= mroot:
if s[i]:
j = (m*m - 3)//2
s[j] = 0
while j < half:
s[j] = 0
j += m
i = i+1
m = 2*i+3
return [2]+[x for x in s if x]
def gold_other(n):
primes_for_n = generetePrimes(n)
numbers = {prime + 2*x**2 for prime in primes_for_n for x in range(1, int(n**0.5))}
conj = {x for x in range(3, n, 2) if not isPrime(x)}
while True:
candidates = conj - numbers
if not candidates:
gold_other(2*n)
else:
return min(candidates)
def main():
import time
start = time.time()
print(gold_other(10000))
elapsed = (time.time() - start)
print('Tests Passed!\n It took %s seconds to run them.' % (elapsed))
if __name__ == '__main__':
main()

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#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
def self_powers(power, digits):
sum_total = 0
for pow in range(1, power+1):
sum_total += pow**pow
sum_total_str = str(sum_total)
last_digits = ''
for i, c in enumerate(sum_total_str[-digits:]):
last_digits += c
return int(last_digits)
def main():
import time
start = time.time()
assert(self_powers(10, len('10405071317')) == 10405071317)
print(self_powers(1000, 10))
elapsed = (time.time() - start)
print('Tests Passed!\n It took %s seconds to run them.' % (elapsed))
if __name__ == '__main__':
main()

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#!/usr/bin/python
__author__ = "Mari Wahl"
__email__ = "marina.w4hl@gmail.com"
'''
e = [2; 1,2,1, 1,4,1, 1,6,1 , ... , 1,2k,1, ...].
The first ten terms in the sequence of convergents for e are:
2, 3, 8/3, 11/4, 19/7, 87/32, 106/39, 193/71, 1264/465, 1457/536, ...
The sum of digits in the numerator of the 10th convergent is 1+4+5+7=17.
Find the sum of digits in the numerator of the 100th convergent of the continued fraction for e.
'''
from itertools import islice
def take(iterable, n):
#Make an iterator that returns selected elements from the iterable.
return list(islice(iterable, n))
def e():
yield 2
k = 1
while True:
yield 1
yield 2*k
yield 1
k += 1
def rationalize(frac):
if len(frac) == 0:
return (1, 0)
elif len(frac) == 1:
return (frac[0], 1)
else:
remainder = frac[1:len(frac)]
(num, denom) = rationalize(remainder)
return (frac[0] * num + denom, num)
numerator = rationalize(take(e(), 100))[0]
print sum(int(d) for d in str(numerator))

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#!/usr/bin/python
__author__ = "Mari Wahl"
__email__ = "marina.w4hl@gmail.com"
'''
The rules for writing Roman numerals allow for many ways of writing each number (see About Roman Numerals...). However, there is always a "best" way of writing a particular number.
For example, the following represent all of the legitimate ways of writing the number sixteen:
IIIIIIIIIIIIIIII
VIIIIIIIIIII
VVIIIIII
XIIIIII
VVVI
XVI
The last example being considered the most efficient, as it uses the least number of numerals.
The 11K text file, roman.txt (right click and 'Save Link/Target As...'), contains one thousand numbers written in valid, but not necessarily minimal, Roman numerals; that is, they are arranged in descending units and obey the subtractive pair rule (see About Roman Numerals... for the definitive rules for this problem).
Find the number of characters saved by writing each of these in their minimal form.
'''
import os
def subtractive(roman):
result = roman
replacements = [
("VIIII", "IX"),
("IIII", "IV"),
("LXXXX", "XC"),
("XXXX", "XL"),
("DCCCC", "CM"),
("CCCC", "CD"),
]
for old, new in replacements:
result = result.replace(old, new)
return result
if __name__ == '__main__':
current = 0
improved = 0
for line in open(os.path.join(os.path.dirname(__file__), 'roman.txt')):
roman = line.strip()
current += len(roman)
improved += len(subtractive(roman))
print current - improved

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#!/usr/bin/python3
# mari von steinkirch @2013
# steinkirch at gmail
def calculate_chain(n):
n_str = str(n)
while n_str != 1 or n_str != 89:
n_str = str(n_str)
sum_here = 0
for d in n_str:
sum_here += int(d)**2
n_str = sum_here
if n_str == 89:
return 1
if n_str == 1:
return 0
def square_dig_chains(n):
count = 0
for i in range(1, n+1):
count += calculate_chain(i)
return count
def main():
import time
start = time.time()
print(square_dig_chains(10**7))
elapsed = (time.time() - start)
print('Tests Passed!\n It took %s seconds to run them.' % (elapsed))
if __name__ == '__main__':
main()

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@ -0,0 +1,21 @@
The MIT License (MIT)
Copyright (c) 2014 Mari Wahl
Permission is hereby granted, free of charge, to any person obtaining a copy
of this software and associated documentation files (the "Software"), to deal
in the Software without restriction, including without limitation the rights
to use, copy, modify, merge, publish, distribute, sublicense, and/or sell
copies of the Software, and to permit persons to whom the Software is
furnished to do so, subject to the following conditions:
The above copyright notice and this permission notice shall be included in all
copies or substantial portions of the Software.
THE SOFTWARE IS PROVIDED "AS IS", WITHOUT WARRANTY OF ANY KIND, EXPRESS OR
IMPLIED, INCLUDING BUT NOT LIMITED TO THE WARRANTIES OF MERCHANTABILITY,
FITNESS FOR A PARTICULAR PURPOSE AND NONINFRINGEMENT. IN NO EVENT SHALL THE
AUTHORS OR COPYRIGHT HOLDERS BE LIABLE FOR ANY CLAIM, DAMAGES OR OTHER
LIABILITY, WHETHER IN AN ACTION OF CONTRACT, TORT OR OTHERWISE, ARISING FROM,
OUT OF OR IN CONNECTION WITH THE SOFTWARE OR THE USE OR OTHER DEALINGS IN THE
SOFTWARE.

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# 🍟 Project Euler Solutions 🍟
Several of my solutions for the Euler project. For fun or profit :)
Most of the exercises are written in Python, but I have some Java and Clojure too.
Enjoy!
![](http://projecteuler.net/profile/bytegirl.png)
----
## License
When making a reference to my work, please use my [website](http://bt3gl.github.io/index.html).
<a rel="license" href="http://creativecommons.org/licenses/by-sa/4.0/"><img alt="Creative Commons License" style="border-width:0" src="http://i.creativecommons.org/l/by-sa/4.0/88x31.png" /></a><br />
This work is licensed under a [Creative Commons Attribution-ShareAlike 4.0 International License](http://creativecommons.org/licenses/by-sa/4.0/).

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08 02 22 97 38 15 00 40 00 75 04 05 07 78 52 12 50 77 91 08
49 49 99 40 17 81 18 57 60 87 17 40 98 43 69 48 04 56 62 00
81 49 31 73 55 79 14 29 93 71 40 67 53 88 30 03 49 13 36 65
52 70 95 23 04 60 11 42 69 24 68 56 01 32 56 71 37 02 36 91
22 31 16 71 51 67 63 89 41 92 36 54 22 40 40 28 66 33 13 80
24 47 32 60 99 03 45 02 44 75 33 53 78 36 84 20 35 17 12 50
32 98 81 28 64 23 67 10 26 38 40 67 59 54 70 66 18 38 64 70
67 26 20 68 02 62 12 20 95 63 94 39 63 08 40 91 66 49 94 21
24 55 58 05 66 73 99 26 97 17 78 78 96 83 14 88 34 89 63 72
21 36 23 09 75 00 76 44 20 45 35 14 00 61 33 97 34 31 33 95
78 17 53 28 22 75 31 67 15 94 03 80 04 62 16 14 09 53 56 92
16 39 05 42 96 35 31 47 55 58 88 24 00 17 54 24 36 29 85 57
86 56 00 48 35 71 89 07 05 44 44 37 44 60 21 58 51 54 17 58
19 80 81 68 05 94 47 69 28 73 92 13 86 52 17 77 04 89 55 40
04 52 08 83 97 35 99 16 07 97 57 32 16 26 26 79 33 27 98 66
88 36 68 87 57 62 20 72 03 46 33 67 46 55 12 32 63 93 53 69
04 42 16 73 38 25 39 11 24 94 72 18 08 46 29 32 40 62 76 36
20 69 36 41 72 30 23 88 34 62 99 69 82 67 59 85 74 04 36 16
20 73 35 29 78 31 90 01 74 31 49 71 48 86 81 16 23 57 05 54
01 70 54 71 83 51 54 69 16 92 33 48 61 43 52 01 89 19 67 48

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@ -0,0 +1,100 @@
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40789923115535562561142322423255033685442488917353
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