From 34d4d138dce746baf4e29ff9c81680d65e53b144 Mon Sep 17 00:00:00 2001 From: Kushagra Bansal Date: Tue, 25 Aug 2020 13:35:06 +0530 Subject: [PATCH 01/13] Create __init__.py --- project_euler/problem_45/__init__.py | 1 + 1 file changed, 1 insertion(+) create mode 100644 project_euler/problem_45/__init__.py diff --git a/project_euler/problem_45/__init__.py b/project_euler/problem_45/__init__.py new file mode 100644 index 000000000000..792d6005489e --- /dev/null +++ b/project_euler/problem_45/__init__.py @@ -0,0 +1 @@ +# From ffdfc27dbe06a9340dff62109c69cd364cae79d1 Mon Sep 17 00:00:00 2001 From: Kushagra Bansal Date: Tue, 25 Aug 2020 13:35:22 +0530 Subject: [PATCH 02/13] Add files via upload --- project_euler/problem_45/sol1.py | 60 ++++++++++++++++++++++++++++++++ 1 file changed, 60 insertions(+) create mode 100644 project_euler/problem_45/sol1.py diff --git a/project_euler/problem_45/sol1.py b/project_euler/problem_45/sol1.py new file mode 100644 index 000000000000..72bb1ad9bdae --- /dev/null +++ b/project_euler/problem_45/sol1.py @@ -0,0 +1,60 @@ +""" +Triangle, pentagonal, and hexagonal numbers are generated by the following formulae: +Triangle T(n) = (n * (n + 1)) / 2 1, 3, 6, 10, 15, ... +Pentagonal P(n) = (n * (3 * n − 1)) / 2 1, 5, 12, 22, 35, ... +Hexagonal H(n) = n * (2 * n − 1) 1, 6, 15, 28, 45, ... +It can be verified that T(285) = P(165) = H(143) = 40755. + +Find the next triangle number that is also pentagonal and hexagonal. +""" + +""" +All trinagle numers are hexagonal numbers. +T(2n-1) = n * (2 * n - 1) = H(n) +So we shall check ony for hexagonal numbers which are also pentagonal. +""" + + +def hexagonal_num(n: int) -> int: + """ + Returns nth hexagonal number + >>> hexagonal_num(143) + 40755 + >>> hexagonal_num(21) + 861 + >>> hexagonal_num(10) + 190 + """ + return n * (2 * n - 1) + + +def is_pentagonal(n: int) -> bool: + """ + Returns True if n is pentagonal, False otherwise. + >>> is_pentagonal(330) + True + >>> is_pentagonal(7683) + False + >>> is_pentagonal(2380) + True + """ + root = (1 + 24 * n) ** 0.5 + return ((1 + root) / 6) % 1 == 0 + + +def compute_num(start: int = 144) -> int: + """ + Returns the next number which is traingular, pentagonal and hexagonal. + >>> compute_num(144) + 1533776805 + """ + n = start + num = hexagonal_num(n) + while not is_pentagonal(num): + n += 1 + num = hexagonal_num(n) + return num + + +if __name__ == "__main__": + print(f"{compute_num(144)} ") From 79afd638a37288a4c31af3b8a8e0c1a8abb69c42 Mon Sep 17 00:00:00 2001 From: Kushagra Bansal Date: Tue, 25 Aug 2020 13:36:26 +0530 Subject: [PATCH 03/13] Update sol1.py --- project_euler/problem_45/sol1.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/project_euler/problem_45/sol1.py b/project_euler/problem_45/sol1.py index 72bb1ad9bdae..8c8f2d4369e2 100644 --- a/project_euler/problem_45/sol1.py +++ b/project_euler/problem_45/sol1.py @@ -57,4 +57,4 @@ def compute_num(start: int = 144) -> int: if __name__ == "__main__": - print(f"{compute_num(144)} ") + print(f"{compute_num(144)} = ") From 0c4638e83275f8540a55e42b6db14c5f177e7fc1 Mon Sep 17 00:00:00 2001 From: Kushagra Bansal Date: Tue, 25 Aug 2020 13:40:23 +0530 Subject: [PATCH 04/13] Update sol1.py --- project_euler/problem_45/sol1.py | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/project_euler/problem_45/sol1.py b/project_euler/problem_45/sol1.py index 8c8f2d4369e2..308d06a5c605 100644 --- a/project_euler/problem_45/sol1.py +++ b/project_euler/problem_45/sol1.py @@ -9,9 +9,9 @@ """ """ -All trinagle numers are hexagonal numbers. +All trinagle numbers are hexagonal numbers. T(2n-1) = n * (2 * n - 1) = H(n) -So we shall check ony for hexagonal numbers which are also pentagonal. +So we shall check only for hexagonal numbers which are also pentagonal. """ From 4bb67a063ec4e515cb12b1899b8d86abd28c2fef Mon Sep 17 00:00:00 2001 From: Kushagra Bansal Date: Tue, 25 Aug 2020 13:42:51 +0530 Subject: [PATCH 05/13] Update project_euler/problem_45/sol1.py Co-authored-by: Christian Clauss --- project_euler/problem_45/sol1.py | 3 --- 1 file changed, 3 deletions(-) diff --git a/project_euler/problem_45/sol1.py b/project_euler/problem_45/sol1.py index 308d06a5c605..ed66e6fab210 100644 --- a/project_euler/problem_45/sol1.py +++ b/project_euler/problem_45/sol1.py @@ -6,9 +6,6 @@ It can be verified that T(285) = P(165) = H(143) = 40755. Find the next triangle number that is also pentagonal and hexagonal. -""" - -""" All trinagle numbers are hexagonal numbers. T(2n-1) = n * (2 * n - 1) = H(n) So we shall check only for hexagonal numbers which are also pentagonal. From 2b6c4ffb80cc546a3afb1567889346817bffe32d Mon Sep 17 00:00:00 2001 From: Kushagra Bansal Date: Tue, 25 Aug 2020 15:53:48 +0530 Subject: [PATCH 06/13] Update sol1.py --- project_euler/problem_34/sol1.py | 50 +++++++------------------------- 1 file changed, 10 insertions(+), 40 deletions(-) diff --git a/project_euler/problem_34/sol1.py b/project_euler/problem_34/sol1.py index 126aee9d2023..e0eeb958e77a 100644 --- a/project_euler/problem_34/sol1.py +++ b/project_euler/problem_34/sol1.py @@ -4,64 +4,34 @@ Note: As 1! = 1 and 2! = 2 are not sums they are not included. """ - -def factorial(n: int) -> int: - """Return the factorial of n. - >>> factorial(5) - 120 - >>> factorial(1) - 1 - >>> factorial(0) - 1 - >>> factorial(-1) - Traceback (most recent call last): - ... - ValueError: n must be >= 0 - >>> factorial(1.1) - Traceback (most recent call last): - ... - ValueError: n must be exact integer - """ - - if not n >= 0: - raise ValueError("n must be >= 0") - if int(n) != n: - raise ValueError("n must be exact integer") - if n + 1 == n: # catch a value like 1e300 - raise OverflowError("n too large") - result = 1 - factor = 2 - while factor <= n: - result *= factor - factor += 1 - return result +from math import factorial def sum_of_digit_factorial(n: int) -> int: - """ + """ Returns the sum of the digits in n >>> sum_of_digit_factorial(15) 121 >>> sum_of_digit_factorial(0) 1 """ - return sum(factorial(int(digit)) for digit in str(n)) + digits = list(map(int, str(n))) + summ = sum(factorial(digit) for digit in digits) + return summ def compute() -> int: """ - Returns the sum of all numbers whose + Returns the sum of all numbers whose sum of the factorials of all digits add up to the number itself. >>> compute() 40730 """ - return sum( - num - for num in range(3, 7 * factorial(9) + 1) - if sum_of_digit_factorial(num) == num - ) + limit = 7 * factorial(9) + nums = [num for num in range(3, limit) if sum_of_digit_factorial(num) == num] + return sum(nums) if __name__ == "__main__": - print(compute()) + print(f"{compute()} = ") From 2b581f731064d7877625a19fa6b5087ec5d88878 Mon Sep 17 00:00:00 2001 From: Kushagra Bansal Date: Tue, 25 Aug 2020 16:05:07 +0530 Subject: [PATCH 07/13] Update sol1.py --- project_euler/problem_34/sol1.py | 4 ++-- 1 file changed, 2 insertions(+), 2 deletions(-) diff --git a/project_euler/problem_34/sol1.py b/project_euler/problem_34/sol1.py index e0eeb958e77a..81e64a12b456 100644 --- a/project_euler/problem_34/sol1.py +++ b/project_euler/problem_34/sol1.py @@ -8,7 +8,7 @@ def sum_of_digit_factorial(n: int) -> int: - """ + """ Returns the sum of the digits in n >>> sum_of_digit_factorial(15) 121 @@ -22,7 +22,7 @@ def sum_of_digit_factorial(n: int) -> int: def compute() -> int: """ - Returns the sum of all numbers whose + Returns the sum of all numbers whose sum of the factorials of all digits add up to the number itself. >>> compute() From 42c1887a7523b89dd7ba5de89f72ddf4229e6098 Mon Sep 17 00:00:00 2001 From: Kushagra Bansal Date: Tue, 25 Aug 2020 16:49:08 +0530 Subject: [PATCH 08/13] Update project_euler/problem_34/sol1.py Co-authored-by: Christian Clauss --- project_euler/problem_34/sol1.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/project_euler/problem_34/sol1.py b/project_euler/problem_34/sol1.py index 81e64a12b456..3e9c7188ee0c 100644 --- a/project_euler/problem_34/sol1.py +++ b/project_euler/problem_34/sol1.py @@ -29,7 +29,7 @@ def compute() -> int: 40730 """ limit = 7 * factorial(9) - nums = [num for num in range(3, limit) if sum_of_digit_factorial(num) == num] + return sum(i for i in range(3, limit) if sum_of_digit_factorial(i) == i) return sum(nums) From 136b05a57ca44879d13792221200cd9e92b155bb Mon Sep 17 00:00:00 2001 From: Kushagra Bansal Date: Tue, 25 Aug 2020 16:49:22 +0530 Subject: [PATCH 09/13] Update project_euler/problem_34/sol1.py Co-authored-by: Christian Clauss --- project_euler/problem_34/sol1.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/project_euler/problem_34/sol1.py b/project_euler/problem_34/sol1.py index 3e9c7188ee0c..4b87bcb9153f 100644 --- a/project_euler/problem_34/sol1.py +++ b/project_euler/problem_34/sol1.py @@ -16,7 +16,7 @@ def sum_of_digit_factorial(n: int) -> int: 1 """ digits = list(map(int, str(n))) - summ = sum(factorial(digit) for digit in digits) + return sum(factorial(digit) for digit in digits) return summ From b68a48bd84be7858004fa583eb9f2099fa54d591 Mon Sep 17 00:00:00 2001 From: Kushagra Bansal Date: Tue, 25 Aug 2020 16:54:06 +0530 Subject: [PATCH 10/13] Update sol1.py --- project_euler/problem_34/sol1.py | 2 -- 1 file changed, 2 deletions(-) diff --git a/project_euler/problem_34/sol1.py b/project_euler/problem_34/sol1.py index 4b87bcb9153f..d2f04b64a427 100644 --- a/project_euler/problem_34/sol1.py +++ b/project_euler/problem_34/sol1.py @@ -17,7 +17,6 @@ def sum_of_digit_factorial(n: int) -> int: """ digits = list(map(int, str(n))) return sum(factorial(digit) for digit in digits) - return summ def compute() -> int: @@ -30,7 +29,6 @@ def compute() -> int: """ limit = 7 * factorial(9) return sum(i for i in range(3, limit) if sum_of_digit_factorial(i) == i) - return sum(nums) if __name__ == "__main__": From f38caaef4ecb5b12cce86a7602bdcd3261b99340 Mon Sep 17 00:00:00 2001 From: Kushagra Bansal Date: Tue, 25 Aug 2020 16:58:43 +0530 Subject: [PATCH 11/13] Update project_euler/problem_34/sol1.py Co-authored-by: Christian Clauss --- project_euler/problem_34/sol1.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/project_euler/problem_34/sol1.py b/project_euler/problem_34/sol1.py index d2f04b64a427..ebd117763e95 100644 --- a/project_euler/problem_34/sol1.py +++ b/project_euler/problem_34/sol1.py @@ -15,7 +15,7 @@ def sum_of_digit_factorial(n: int) -> int: >>> sum_of_digit_factorial(0) 1 """ - digits = list(map(int, str(n))) + return sum(factorial(int(char)) for char in str(n)) return sum(factorial(digit) for digit in digits) From 3b8fd2fd4d8b62fe7462cfcf6a162306dddc2e10 Mon Sep 17 00:00:00 2001 From: Kushagra Bansal Date: Tue, 25 Aug 2020 16:59:14 +0530 Subject: [PATCH 12/13] Update sol1.py --- project_euler/problem_34/sol1.py | 1 - 1 file changed, 1 deletion(-) diff --git a/project_euler/problem_34/sol1.py b/project_euler/problem_34/sol1.py index ebd117763e95..43710af40d7c 100644 --- a/project_euler/problem_34/sol1.py +++ b/project_euler/problem_34/sol1.py @@ -16,7 +16,6 @@ def sum_of_digit_factorial(n: int) -> int: 1 """ return sum(factorial(int(char)) for char in str(n)) - return sum(factorial(digit) for digit in digits) def compute() -> int: From ae70537d2cccec0e08cff3001722ac84ce0db50c Mon Sep 17 00:00:00 2001 From: Kushagra Bansal Date: Tue, 25 Aug 2020 16:59:34 +0530 Subject: [PATCH 13/13] Update project_euler/problem_34/sol1.py Co-authored-by: Christian Clauss --- project_euler/problem_34/sol1.py | 2 +- 1 file changed, 1 insertion(+), 1 deletion(-) diff --git a/project_euler/problem_34/sol1.py b/project_euler/problem_34/sol1.py index 43710af40d7c..c19fac5de897 100644 --- a/project_euler/problem_34/sol1.py +++ b/project_euler/problem_34/sol1.py @@ -26,7 +26,7 @@ def compute() -> int: >>> compute() 40730 """ - limit = 7 * factorial(9) + limit = 7 * factorial(9) + 1 return sum(i for i in range(3, limit) if sum_of_digit_factorial(i) == i)