diff --git a/python/e012.py b/python/e012.py new file mode 100644 index 0000000..75596ba --- /dev/null +++ b/python/e012.py @@ -0,0 +1,12 @@ +from lib_prime import get_divisors_count +from lib_misc import triangle_numbers + + +def euler_012(): + for tn in triangle_numbers(): + if get_divisors_count(tn) > 500: + return tn + + +assert(euler_012() == 76576500) +print("e012.py: {}".format(euler_012())) diff --git a/python/e013.py b/python/e013.py new file mode 100644 index 0000000..db3328d --- /dev/null +++ b/python/e013.py @@ -0,0 +1,112 @@ +numbers_string = """ +37107287533902102798797998220837590246510135740250 +46376937677490009712648124896970078050417018260538 +74324986199524741059474233309513058123726617309629 +91942213363574161572522430563301811072406154908250 +23067588207539346171171980310421047513778063246676 +89261670696623633820136378418383684178734361726757 +28112879812849979408065481931592621691275889832738 +44274228917432520321923589422876796487670272189318 +47451445736001306439091167216856844588711603153276 +70386486105843025439939619828917593665686757934951 +62176457141856560629502157223196586755079324193331 +64906352462741904929101432445813822663347944758178 +92575867718337217661963751590579239728245598838407 +58203565325359399008402633568948830189458628227828 +80181199384826282014278194139940567587151170094390 +35398664372827112653829987240784473053190104293586 +86515506006295864861532075273371959191420517255829 +71693888707715466499115593487603532921714970056938 +54370070576826684624621495650076471787294438377604 +53282654108756828443191190634694037855217779295145 +36123272525000296071075082563815656710885258350721 +45876576172410976447339110607218265236877223636045 +17423706905851860660448207621209813287860733969412 +81142660418086830619328460811191061556940512689692 +51934325451728388641918047049293215058642563049483 +62467221648435076201727918039944693004732956340691 +15732444386908125794514089057706229429197107928209 +55037687525678773091862540744969844508330393682126 +18336384825330154686196124348767681297534375946515 +80386287592878490201521685554828717201219257766954 +78182833757993103614740356856449095527097864797581 +16726320100436897842553539920931837441497806860984 +48403098129077791799088218795327364475675590848030 +87086987551392711854517078544161852424320693150332 +59959406895756536782107074926966537676326235447210 +69793950679652694742597709739166693763042633987085 +41052684708299085211399427365734116182760315001271 +65378607361501080857009149939512557028198746004375 +35829035317434717326932123578154982629742552737307 +94953759765105305946966067683156574377167401875275 +88902802571733229619176668713819931811048770190271 +25267680276078003013678680992525463401061632866526 +36270218540497705585629946580636237993140746255962 +24074486908231174977792365466257246923322810917141 +91430288197103288597806669760892938638285025333403 +34413065578016127815921815005561868836468420090470 +23053081172816430487623791969842487255036638784583 +11487696932154902810424020138335124462181441773470 +63783299490636259666498587618221225225512486764533 +67720186971698544312419572409913959008952310058822 +95548255300263520781532296796249481641953868218774 +76085327132285723110424803456124867697064507995236 +37774242535411291684276865538926205024910326572967 +23701913275725675285653248258265463092207058596522 +29798860272258331913126375147341994889534765745501 +18495701454879288984856827726077713721403798879715 +38298203783031473527721580348144513491373226651381 +34829543829199918180278916522431027392251122869539 +40957953066405232632538044100059654939159879593635 +29746152185502371307642255121183693803580388584903 +41698116222072977186158236678424689157993532961922 +62467957194401269043877107275048102390895523597457 +23189706772547915061505504953922979530901129967519 +86188088225875314529584099251203829009407770775672 +11306739708304724483816533873502340845647058077308 +82959174767140363198008187129011875491310547126581 +97623331044818386269515456334926366572897563400500 +42846280183517070527831839425882145521227251250327 +55121603546981200581762165212827652751691296897789 +32238195734329339946437501907836945765883352399886 +75506164965184775180738168837861091527357929701337 +62177842752192623401942399639168044983993173312731 +32924185707147349566916674687634660915035914677504 +99518671430235219628894890102423325116913619626622 +73267460800591547471830798392868535206946944540724 +76841822524674417161514036427982273348055556214818 +97142617910342598647204516893989422179826088076852 +87783646182799346313767754307809363333018982642090 +10848802521674670883215120185883543223812876952786 +71329612474782464538636993009049310363619763878039 +62184073572399794223406235393808339651327408011116 +66627891981488087797941876876144230030984490851411 +60661826293682836764744779239180335110989069790714 +85786944089552990653640447425576083659976645795096 +66024396409905389607120198219976047599490197230297 +64913982680032973156037120041377903785566085089252 +16730939319872750275468906903707539413042652315011 +94809377245048795150954100921645863754710598436791 +78639167021187492431995700641917969777599028300699 +15368713711936614952811305876380278410754449733078 +40789923115535562561142322423255033685442488917353 +44889911501440648020369068063960672322193204149535 +41503128880339536053299340368006977710650566631954 +81234880673210146739058568557934581403627822703280 +82616570773948327592232845941706525094512325230608 +22918802058777319719839450180888072429661980811197 +77158542502016545090413245809786882778948721859617 +72107838435069186155435662884062257473692284509516 +20849603980134001723930671666823555245252804609722 +53503534226472524250874054075591789781264330331690 +""" + + +def euler_013(): + numbers = [int(n) for n in numbers_string.split('\n') if n] + numbers_sum = sum(numbers) + return int(str(numbers_sum)[:10]) + + +assert(euler_013() == 5537376230) +print("e013.py: {}".format(euler_013())) diff --git a/python/e014.py b/python/e014.py new file mode 100644 index 0000000..6c3d6d0 --- /dev/null +++ b/python/e014.py @@ -0,0 +1,9 @@ +from lib_misc import collatz_sequence_length + + +def euler_014(): + return max([(collatz_sequence_length(n), n) for n in range(1, 1000000)])[1] + + +assert(euler_014() == 837799) +print("e014.py: {}".format(euler_014())) diff --git a/python/e015.py b/python/e015.py new file mode 100644 index 0000000..43b108f --- /dev/null +++ b/python/e015.py @@ -0,0 +1,21 @@ +from math import factorial + + +def get_number_of_routes(n): + """ + There are n down and n right moves which means 2 * n moves + in total. All permutations are calculated with (2n)!. Next redundant + moves have to be canceled out. The combinations for only down moves + or only right moves would (if they were different symbols) be n!. + Hence, the denominator is (n!)^2. + """ + return factorial(2 * n) // (factorial(n) * factorial(n)) + + +def euler_015(): + return get_number_of_routes(20) + + +assert(get_number_of_routes(2) == 6) +assert(euler_015() == 137846528820) +print("e015.py: {}".format(euler_015())) diff --git a/python/e016.py b/python/e016.py new file mode 100644 index 0000000..a4d207d --- /dev/null +++ b/python/e016.py @@ -0,0 +1,7 @@ +def euler_016(): + s = sum(map(int, str(2**1000))) + return s + + +assert(euler_016() == 1366) +print("e016.py: {}".format(euler_016())) diff --git a/python/e017.py b/python/e017.py new file mode 100644 index 0000000..1515995 --- /dev/null +++ b/python/e017.py @@ -0,0 +1,71 @@ +def single_digit_integer_to_spoken_language(n): + if n == 0: + return "" + assert(n > 0 and n < 10) + return {1: 'one', 2: 'two', 3: 'three', 4: 'four', 5: 'five', + 6: 'six', 7: 'seven', 8: 'eight', 9: 'nine'}[n] + + +def double_digit_integer_to_spoken_language(n): + assert(n > 9 and n < 100) + try: + return { + 10: 'ten', 11: 'eleven', 12: 'twelve', 13: 'thirteen', + 14: 'fourteen', 15: 'fifteen', 16: 'sixteen', + 17: 'seventeen', 18: 'eighteen', 19: 'nineteen'}[n] + except KeyError: + pass + a, b = str(n) + a = {2: 'twenty', 3: 'thirty', 4: 'forty', 5: 'fifty', + 6: 'sixty', 7: 'seventy', 8: 'eighty', 9: 'ninety'}[int(a)] + b = integer_to_spoken_language(int(b)) + return a + '-' + b + + +def triple_digit_integer_to_spoken_language(n): + a, b = str(n)[0], str(n)[1:] + a = single_digit_integer_to_spoken_language(int(a)) + b = integer_to_spoken_language(int(b)) + if not b: + return a + " hundred" + return a + " hundred and " + b + + +def four_digit_integer_to_spoken_language(n): + a, b = str(n)[0], str(n)[1:] + a = single_digit_integer_to_spoken_language(int(a)) + b = integer_to_spoken_language(int(b)) + return a + " thousand " + b + + +def integer_to_spoken_language(n): + length = len(str(n)) + if length == 1: + return single_digit_integer_to_spoken_language(n) + elif length == 2: + return double_digit_integer_to_spoken_language(n) + elif length == 3: + return triple_digit_integer_to_spoken_language(n) + elif length == 4: + return four_digit_integer_to_spoken_language(n) + else: + raise Exception("Length not supported.") + + +assert(integer_to_spoken_language(5) == 'five') +assert(integer_to_spoken_language(19) == 'nineteen') +assert(integer_to_spoken_language(21) == 'twenty-one') +assert(integer_to_spoken_language(210) == 'two hundred and ten') +assert(integer_to_spoken_language(3000) == 'three thousand ') +assert(integer_to_spoken_language(8333) == + 'eight thousand three hundred and thirty-three') + + +def euler_017(): + s = "".join([integer_to_spoken_language(i) for i in range(1, 1001)]) + s = s.replace(" ", "").replace("-", "") + return len(s) + + +assert(euler_017() == 21124) +print("e017.py: {}".format(euler_017())) diff --git a/python/e018.py b/python/e018.py new file mode 100644 index 0000000..64e2756 --- /dev/null +++ b/python/e018.py @@ -0,0 +1,37 @@ +t = """ +75 +95 64 +17 47 82 +18 35 87 10 +20 04 82 47 65 +19 01 23 75 03 34 +88 02 77 73 07 63 67 +99 65 04 28 06 16 70 92 +41 41 26 56 83 40 80 70 33 +41 48 72 33 47 32 37 16 94 29 +53 71 44 65 25 43 91 52 97 51 14 +70 11 33 28 77 73 17 78 39 68 17 57 +91 71 52 38 17 14 91 43 58 50 27 29 48 +63 66 04 68 89 53 67 30 73 16 69 87 40 31 +04 62 98 27 23 09 70 98 73 93 38 53 60 04 23 +""" + + +def find_greatest_path_sum_in_triangle_string(ts): + from functools import reduce + xss = [list(map(int, xs.split())) for xs in ts.split("\n") if xs] + xss.reverse() + + def r(xs, ys): + return [max([xs[i] + ys[i], xs[i + 1] + ys[i]]) + for i in range(len(ys))] + return reduce(r, xss[1:], xss[0])[0] + + +def euler_018(): + return find_greatest_path_sum_in_triangle_string(t) + + +if __name__ == "__main__": + assert(euler_018() == 1074) + print("e018.py: {}".format(euler_018())) diff --git a/python/e019.py b/python/e019.py new file mode 100644 index 0000000..ae41644 --- /dev/null +++ b/python/e019.py @@ -0,0 +1,55 @@ +def weekday_generator_function(): + while True: + yield 'Monday' + yield 'Tuesday' + yield 'Wednesday' + yield 'Thursday' + yield 'Friday' + yield 'Saturday' + yield 'Sunday' + + +def day_of_month_generator_function(): + day, month, year = 1, 1, 1901 + while year < 2001: + yield day + day += 1 + if month == 2: + if year % 4 == 0 and (not year % 100 == 0 or year % 400 == 0): + if day == 30: + month += 1 + day = 1 + elif day == 29: + month += 1 + day = 1 + elif month in [9, 4, 6, 11] and day == 31: + day = 1 + month += 1 + elif month in [1, 3, 5, 7, 8, 10] and day == 32: + day = 1 + month += 1 + elif month == 12 and day == 32: + day = 1 + month = 1 + year += 1 + + +def euler_019(): + wds = weekday_generator_function() + next(wds) # get rid of first Monday + ds = zip(wds, day_of_month_generator_function()) + s = len([1 for weekday, date in ds if weekday == "Sunday" and date == 1]) + return s + + +def euler_019_brain(): + """ We have 100 years which means + 1200 months. Every months starts with a day + and 1/7 of all days are Sundays. """ + return 1200 // 7 + + +if __name__ == "__main__": + assert(euler_019() == 171) + assert(euler_019() == euler_019_brain()) + print("e019.py: {}".format(euler_019())) diff --git a/python/e020.py b/python/e020.py new file mode 100644 index 0000000..fd30246 --- /dev/null +++ b/python/e020.py @@ -0,0 +1,7 @@ +def euler_020(): + return 0 + + +if __name__ == "__main__": + assert(euler_020() == 1074) + print("e020.py: {}".format(euler_020())) diff --git a/python/e067.py b/python/e067.py new file mode 100644 index 0000000..29f376b --- /dev/null +++ b/python/e067.py @@ -0,0 +1,11 @@ +from e018 import find_greatest_path_sum_in_triangle_string + + +def euler_067(): + with open("../txt/EulerProblem067.txt") as f: + return find_greatest_path_sum_in_triangle_string(f.read()) + + +if __name__ == "__main__": + assert(euler_067() == 7273) + print("e067.py: {}".format(euler_067())) diff --git a/python/lib_misc.py b/python/lib_misc.py index ccba0f8..876b2ab 100644 --- a/python/lib_misc.py +++ b/python/lib_misc.py @@ -1,3 +1,6 @@ +from functools import lru_cache + + def get_digits_reversed(n): """ Returns a list of digits for n. @@ -76,3 +79,59 @@ def product(l): from functools import reduce import operator return reduce(operator.mul, l, 1) + + +def triangle_numbers(): + c = 0 + i = 1 + while True: + c += i + yield c + i += 1 + + +def even(n): + """ + Returns true if a number is even. + """ + return n % 2 == 0 + + +def odd(n): + """ + Returns true if a number is odd. + """ + return n % 2 != 0 + + +def collatz_sequence(n): + """ + Returns collatz sequence for n. + + :param n: collatz sequence + """ + cs = [] + while n != 1: + cs.append(n) + n = n // 2 if n % 2 == 0 else 3 * n + 1 + cs.append(n) + return cs + + +@lru_cache(maxsize=1000000) +def collatz_sequence_length(n): + """ + Returns length of collatz sequence for n. + + :param n: collatz sequence + """ + if n == 1: + return 1 + length = 1 + while odd(n): + n = 3 * n + 1 + length += 1 + return length + collatz_sequence_length(n // 2) + + + diff --git a/python/lib_misc_tests.py b/python/lib_misc_tests.py index dd0375c..423448e 100644 --- a/python/lib_misc_tests.py +++ b/python/lib_misc_tests.py @@ -5,12 +5,20 @@ try: from .lib_misc import get_digits_reversed from .lib_misc import get_item_counts from .lib_misc import product + from .lib_misc import triangle_numbers + from .lib_misc import even, odd + from .lib_misc import collatz_sequence + from .lib_misc import collatz_sequence_length except ModuleNotFoundError: from lib_misc import is_palindrome_integer from lib_misc import is_palindrome_string from lib_misc import get_digits_reversed from lib_misc import get_item_counts from lib_misc import product + from lib_misc import triangle_numbers + from lib_misc import even, odd + from lib_misc import collatz_sequence + from lib_misc import collatz_sequence_length class TestPrimeMethods(unittest.TestCase): @@ -42,6 +50,26 @@ class TestPrimeMethods(unittest.TestCase): self.assertEqual(product([2, 4, 8]), 64) self.assertEqual(product([]), 1) + def test_triangle_numbers(self): + f = triangle_numbers() + self.assertEqual(next(f), 1) + self.assertEqual(next(f), 3) + self.assertEqual(next(f), 6) + self.assertEqual(next(f), 10) + self.assertEqual(next(f), 15) + self.assertEqual(next(f), 21) + + def test_even_odd(self): + self.assertTrue(odd(3)) + self.assertTrue(even(4)) + self.assertFalse(even(3)) + self.assertFalse(odd(4)) + + def test_collatz(self): + self.assertEqual(collatz_sequence(13), + [13, 40, 20, 10, 5, 16, 8, 4, 2, 1]) + self.assertEqual(collatz_sequence_length(13), 10) + if __name__ == '__main__': unittest.main() diff --git a/python/lib_prime.py b/python/lib_prime.py index 7a11c06..0e029dd 100644 --- a/python/lib_prime.py +++ b/python/lib_prime.py @@ -1,7 +1,9 @@ try: from lib_misc import get_item_counts + from lib_misc import product except ModuleNotFoundError: from .lib_misc import get_item_counts + from .lib_misc import product def prime_factors(n): @@ -107,3 +109,36 @@ def primes(n_max): if b[i - 1]: ps.append(i) return ps + + +def get_divisors_count(n): + """ + Returns the number of divisors for n. + The numbers 1 and n count as a divisor. + + >>> get_divisors_count(1) + 1 + >>> get_divisors_count(3) + 2 # 1, 3 + >>> get_divisors_count(4) + 3 # 1, 2, 4 + + Getting the number of divisors is a combinatorial + problem that can be solved by using the counts + for each prime factor. For example, consider + + 2 * 2 * 7 = 28 + + We have 3 options for 2 (1, 1 * 2, 2 * 2) + and 2 options for 7 (1, 1 * 7). + + By multiplying those options we get the number + of combinations: + + 2 * 3 = 6 + """ + if n == 1: + return 1 + factors = prime_factors_count(n) + count = product([v + 1 for v in factors.values()]) + return count diff --git a/python/lib_prime_tests.py b/python/lib_prime_tests.py index fd29747..fd139a6 100644 --- a/python/lib_prime_tests.py +++ b/python/lib_prime_tests.py @@ -5,12 +5,14 @@ try: from .lib_prime import is_prime from .lib_prime import prime_nth from .lib_prime import primes + from .lib_prime import get_divisors_count except ModuleNotFoundError: from lib_prime import prime_factors from lib_prime import prime_factors_count from lib_prime import is_prime from lib_prime import prime_nth from lib_prime import primes + from lib_prime import get_divisors_count class TestPrimeMethods(unittest.TestCase): @@ -23,6 +25,7 @@ class TestPrimeMethods(unittest.TestCase): self.assertEqual(prime_factors(147), [3, 7, 7]) def test_prime_factors_count(self): + self.assertEqual(prime_factors_count(1), {}) self.assertEqual(prime_factors_count(2), {2: 1}) self.assertEqual(prime_factors_count(147), {3: 1, 7: 2}) @@ -59,6 +62,15 @@ class TestPrimeMethods(unittest.TestCase): self.assertEqual(primes(25), [2, 3, 5, 7, 11, 13, 17, 19, 23]) self.assertEqual(primes(1), []) + def test_get_divisors_count(self): + self.assertEqual(get_divisors_count(1), 1) + self.assertEqual(get_divisors_count(3), 2) + self.assertEqual(get_divisors_count(6), 4) + self.assertEqual(get_divisors_count(10), 4) + self.assertEqual(get_divisors_count(15), 4) + self.assertEqual(get_divisors_count(21), 4) + self.assertEqual(get_divisors_count(28), 6) + if __name__ == '__main__': unittest.main()