Andrew and Liz http://andrewandliz.net Our Life, Online Fri, 10 Oct 2008 17:19:40 +0000 http://wordpress.org/?v=2.6.2 en Project Euler: Problem 8 http://andrewandliz.net/andrew/10102008/project-euler-problem-8/ http://andrewandliz.net/andrew/10102008/project-euler-problem-8/#comments Fri, 10 Oct 2008 17:19:40 +0000 Andrew http://andrewandliz.net/?p=244 Problem #8
Find the greatest product of five consecutive digits in the 1000-digit number.

73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450

  1. import time
  2. from operator import itemgetter
  3.  
  4. start = time.clock()
  5.  
  6. num = """73167176531330624919225119674426574742355349194934
  7. 96983520312774506326239578318016984801869478851843
  8. 85861560789112949495459501737958331952853208805511
  9. 12540698747158523863050715693290963295227443043557
  10. 66896648950445244523161731856403098711121722383113
  11. 62229893423380308135336276614282806444486645238749
  12. 30358907296290491560440772390713810515859307960866
  13. 70172427121883998797908792274921901699720888093776
  14. 65727333001053367881220235421809751254540594752243
  15. 52584907711670556013604839586446706324415722155397
  16. 53697817977846174064955149290862569321978468622482
  17. 83972241375657056057490261407972968652414535100474
  18. 82166370484403199890008895243450658541227588666881
  19. 16427171479924442928230863465674813919123162824586
  20. 17866458359124566529476545682848912883142607690042
  21. 24219022671055626321111109370544217506941658960408
  22. 07198403850962455444362981230987879927244284909188
  23. 84580156166097919133875499200524063689912560717606
  24. 05886116467109405077541002256983155200055935729725
  25. 71636269561882670428252483600823257530420752963450
  26. """
  27.  
  28. prods = {}
  29.  
  30. num = num.replace("\n", "")
  31.  
  32. for x in xrange(1, len(num) - 5):
  33.     s = num[x:x+5]
  34.     a = 1
  35.     for y in xrange(0, 5):
  36.         a = a * int(s[y])
  37.     prods[s] = a
  38.  
  39. items = prods.items()
  40. items.sort(key = itemgetter(1))
  41.  
  42. end = time.clock()
  43. t = end - start
  44. print "Answer: " + str(items[-1]) + " in " + str(t) + " seconds"

Best time is: 0.006079 seconds

]]> http://andrewandliz.net/andrew/10102008/project-euler-problem-8/feed/ Project Euler: Problem 7 http://andrewandliz.net/andrew/10102008/project-euler-problem-7/ http://andrewandliz.net/andrew/10102008/project-euler-problem-7/#comments Fri, 10 Oct 2008 17:16:33 +0000 Andrew http://andrewandliz.net/?p=240 Problem 7
By listing the first six prime numbers: 2, 3, 5, 7, 11, and 13, we can see that the 6th prime is 13.

What is the 10001st prime number?

  1. import time
  2.  
  3. start = time.clock()
  4.  
  5. count = 0
  6. number = 2
  7. max = 10001
  8.  
  9. def primed(num):
  10.     if num == 2:
  11.         return True
  12.     if num % 2 == 0:
  13.         return False
  14.  
  15.     for x in range(3, int(num ** 0.5) + 1, 2):
  16.         if num % x == 0:
  17.             return False
  18.     return True
  19.  
  20. while True:
  21.     if primed(number):
  22.         count += 1
  23.    
  24.     if count == max:
  25.         break
  26.     else:
  27.         number += 1
  28.  
  29. end = time.clock()
  30. t = end - start
  31. print "Answer: " + str(number) + " in " + str(t) + " seconds"

Best time is: 0.3625 seconds

]]> http://andrewandliz.net/andrew/10102008/project-euler-problem-7/feed/ Project Euler: Problem 6 http://andrewandliz.net/andrew/10102008/project-euler-problem-6/ http://andrewandliz.net/andrew/10102008/project-euler-problem-6/#comments Fri, 10 Oct 2008 17:15:20 +0000 Andrew http://andrewandliz.net/?p=238 Problem #6

The sum of the squares of the first ten natural numbers is,

12 + 22 + … + 102 = 385

The square of the sum of the first ten natural numbers is,

(1 + 2 + … + 10)2 = 552 = 3025

Hence the difference between the sum of the squares of the first ten natural numbers and the square of the sum is 3025 385 = 2640.

Find the difference between the sum of the squares of the first one hundred natural numbers and the square of the sum.

  1. import time
  2.  
  3. start = time.clock()
  4.  
  5. squares = 0
  6. sums = 0
  7. num = 101
  8. for x in xrange(1, num):
  9.     squares += x * x
  10.     sums += x
  11.  
  12. ans = sums * sums - squares
  13. end = time.clock()
  14. t = end - start
  15. print "Answer: " + str(ans) + " in " + str(t) + " seconds

Best time is: .0000488 seconds

]]> http://andrewandliz.net/andrew/10102008/project-euler-problem-6/feed/ Project Euler: Problem 4 http://andrewandliz.net/andrew/10102008/project-euler-problem-4/ http://andrewandliz.net/andrew/10102008/project-euler-problem-4/#comments Fri, 10 Oct 2008 15:26:01 +0000 Andrew http://andrewandliz.net/?p=235 Problem #4
A palindromic number reads the same both ways. The largest palindrome made from the product of two 2-digit numbers is 9009 = 91 x 99.

Find the largest palindrome made from the product of two 3-digit numbers.

  1. import time
  2.  
  3. start = time.clock()
  4.  
  5. first = 100
  6. second = 100
  7. max = 1000
  8.  
  9. results = []
  10.  
  11. for x in xrange(first, max):
  12.     for y in xrange(second, max):
  13.         prod = x * y
  14.         if str(prod) == str(prod)[::-1]:
  15.             results.append(prod)
  16.            
  17. results.sort()
  18. end = time.clock()
  19. t = end - start
  20. print "Answer: " + str(results[-1]) + " in " + str(t) + " seconds"

Best time is 1.387 seconds

]]> http://andrewandliz.net/andrew/10102008/project-euler-problem-4/feed/ Project Euler: Problem 3 http://andrewandliz.net/andrew/10092008/project-euler-problem-3/ http://andrewandliz.net/andrew/10092008/project-euler-problem-3/#comments Fri, 10 Oct 2008 04:12:05 +0000 Andrew http://andrewandliz.net/?p=228 Problem #3

The prime factors of 13195 are 5, 7, 13 and 29.

What is the largest prime factor of the number 600851475143 ?

  1. import time
  2.  
  3. start = time.clock()
  4. num = 600851475143
  5. prime = 2
  6.  
  7. while prime < = num:
  8.     if num % prime == 0:
  9.         # it’s a factor
  10.         num = num / prime
  11.         if num / prime != 1:
  12.             print prime
  13.     else:
  14.         prime += 1
  15.  
  16. end = time.clock()
  17. t = end - start
  18. print "Answer in " + str(t) + " seconds"

Best time is 0.005285 seconds ]]> http://andrewandliz.net/andrew/10092008/project-euler-problem-3/feed/ Project Euler: Problem 2 http://andrewandliz.net/andrew/10092008/project-euler-problem-2/ http://andrewandliz.net/andrew/10092008/project-euler-problem-2/#comments Thu, 09 Oct 2008 20:15:04 +0000 Andrew http://andrewandliz.net/?p=214 Problem #2
Each new term in the Fibonacci sequence is generated by adding the previous two terms. By starting with 1 and 2, the first 10 terms will be:

1, 2, 3, 5, 8, 13, 21, 34, 55, 89, …

Find the sum of all the even-valued terms in the sequence which do not exceed four million.

  1. import time
  2.  
  3. start = time.clock()
  4.  
  5. fib_l = 0
  6. fib_r = 1
  7.  
  8. def fibbin(left, right):
  9.     sum = left + right
  10.     if (left <= 4000000):
  11.         if sum % 2 == 0:
  12.             return sum + fibbin(right, sum)
  13.         else:
  14.             return fibbin(right, sum)
  15.     else:
  16.         return 0
  17.  
  18. val = fibbin(fib_l, fib_r)
  19. end = time.clock()
  20. t = end - start
  21. print "Answer: " + str(val) + " took " + str(t) + " seconds"

Best time is 0.0000286 seconds

]]> http://andrewandliz.net/andrew/10092008/project-euler-problem-2/feed/ Project Euler: Problem 1 http://andrewandliz.net/andrew/10092008/project-euler-problem-1-v1/ http://andrewandliz.net/andrew/10092008/project-euler-problem-1-v1/#comments Thu, 09 Oct 2008 16:33:31 +0000 Andrew http://andrewandliz.net/?p=206 Problem #1:
If we list all the natural numbers below 10 that are multiples of 3 or 5, we get 3, 5, 6 and 9. The sum of these multiples is 23.

Find the sum of all the multiples of 3 or 5 below 1000.

  1. import time
  2.  
  3. start = time.clock()
  4. i = 0
  5. threes = 3
  6. fives = 5
  7. while threes < 1000:
  8.     i += threes
  9.     threes += 3
  10.  
  11. while fives < 1000:
  12.     if (fives % 3 != 0):
  13.         i += fives
  14.     fives += 5
  15.  
  16. end = time.clock()
  17. t = end - start
  18.  
  19. print "Answer: " + str(i) + " found in " + str(t) + " seconds"

Best time is: 0.000185 seconds ]]> http://andrewandliz.net/andrew/10092008/project-euler-problem-1-v1/feed/ Project Euler: Problem 5 http://andrewandliz.net/andrew/10082008/project-euler-problem-5-v1/ http://andrewandliz.net/andrew/10082008/project-euler-problem-5-v1/#comments Wed, 08 Oct 2008 17:23:06 +0000 Andrew http://andrewandliz.net/?p=194 I’ve stumbled across the site Project Euler, and I’m quite impressed.  The first problem I tried was #5, since it appeared in TheDailyWTF.

I decided to try using Python for this first attempt.  My goal is to try and reduce the time it takes as much as possible.

  1.  
  2. import time
  3.  
  4. start = time.clock()
  5. found = False
  6. i = 0
  7. while not found:
  8.     found = True
  9.     i += 20
  10.     for x in xrange(11, 20):
  11.         if i % x != 0:
  12.             found = False
  13.             break
  14.  
  15. end = time.clock()
  16. t = end - start
  17. print "Answer: " + str(i) + " found in " + str(t) + " seconds"
  18.  

My current time is 13.041 seconds

]]> http://andrewandliz.net/andrew/10082008/project-euler-problem-5-v1/feed/ a letter to all the half-girls: http://andrewandliz.net/liz/09152008/a-letter-to-all-the-half-girls/ http://andrewandliz.net/liz/09152008/a-letter-to-all-the-half-girls/#comments Tue, 16 Sep 2008 01:59:44 +0000 Liz http://andrewandliz.net/?p=193 you hurt and i hurt.

you wonder and i wonder what all the aches and pains and sorrow is for and whether, in the end, if it will count for anything.

you know and i know that while physical pain can do without the emotional, the emotional pain brings the physical with it so your stomach hurts and your shoulders knot and your throat wants to open and spill out all the tears.

you sleep and i sleep without the warm body near by that should be there.

you scream and i scream when it isn’t fair and that’s every day, every hour, every minute.

you cram and i cram our days full of fluff that doesn’t matter so we won’t remember the substance that does.

you talk and i talk about all of the things that sit down in our heads and hearts and veins and just sob, but the responses that come back aren’t what we wanted or needed.

you work and i work at appearing normal, but we’re half-girls and nothing but time can bring the other half home.

]]> http://andrewandliz.net/liz/09152008/a-letter-to-all-the-half-girls/feed/ passing by http://andrewandliz.net/liz/08102008/passing-by/ http://andrewandliz.net/liz/08102008/passing-by/#comments Mon, 11 Aug 2008 00:37:27 +0000 Liz http://andrewandliz.net/?p=192 there were wild times among the family where we spun and laughed and cried and broke apart and mended.
strong moments that speak in flashes of sensation, not stories with beginnings middles and ends.
we were invincible in our eyes.
sleep didn’t touch us.
the world opened up for us and we walked to california without stopping, just singing as each foot moved forward.
a group of girls flung themselves into music with loud hands and hips that moved without waiting.
we spent some time together talking on a school night, avoiding our responsibilities, drowning in conversation about what mattered over the strumming of a guitar.
our hands were open, our feet were free.
a thousand million roads called out to us but we didn’t answer, preferring the moment before the choice when everything wanted to be ours.

{we’ve made a lot of choices now}

the cicadas are hollering from the lawn, stretching their wings and telling me it’s not too far to mexico.
the cars pass cautiously, hushing their words from my ears.
the lights are dimmed because only some people need spotlights.

the family has divorced and amputated and bled and grafted itself onto different trees.
the sisters have grown and wed, but their bodies cry out for dancing.
the brothers say less now; their tongues are tired.
mother and father were always dead.
we’re all blind together, looking for the sharp corners with our anxious fingertips that come away puzzled when things are rounded.
smoothness is harder to come by.

our ropes have frayed to threads but we keep climbing.

we don’t know why but we want to walk and walk and walk through the dawn until we find a diner with good coffee and cheap pancakes.
we’d sit in the cushioned booth and let the sun come up with permission, so early, before the others wake up.
we’d tip the waitress well and keep walking

]]> http://andrewandliz.net/liz/08102008/passing-by/feed/