From c585cb122718e219870ea7a2af110939b55e52f9 Mon Sep 17 00:00:00 2001 From: Mindaugas <76015221+mindaugl@users.noreply.github.com> Date: Fri, 18 Apr 2025 07:16:15 +0800 Subject: [PATCH 1/2] Solution for the Euler Project problem 136 (#12658) * Add initial version of file for the Euler project problem 136 solution. * Add documentation and tests for the Euler project problem 136 solution. * Update sol1.py * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Update sol1.py * Update sol1.py * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Update sol1.py * Update sol1.py * Update sol1.py * Update sol1.py * Update sol1.py * Update sol1.py --------- Co-authored-by: Maxim Smolskiy Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com> --- project_euler/problem_136/__init__.py | 0 project_euler/problem_136/sol1.py | 63 +++++++++++++++++++++++++++ 2 files changed, 63 insertions(+) create mode 100644 project_euler/problem_136/__init__.py create mode 100644 project_euler/problem_136/sol1.py diff --git a/project_euler/problem_136/__init__.py b/project_euler/problem_136/__init__.py new file mode 100644 index 000000000000..e69de29bb2d1 diff --git a/project_euler/problem_136/sol1.py b/project_euler/problem_136/sol1.py new file mode 100644 index 000000000000..688a9a5d7f24 --- /dev/null +++ b/project_euler/problem_136/sol1.py @@ -0,0 +1,63 @@ +""" +Project Euler Problem 136: https://projecteuler.net/problem=136 + +Singleton Difference + +The positive integers, x, y, and z, are consecutive terms of an arithmetic progression. +Given that n is a positive integer, the equation, x^2 - y^2 - z^2 = n, +has exactly one solution when n = 20: + 13^2 - 10^2 - 7^2 = 20. + +In fact there are twenty-five values of n below one hundred for which +the equation has a unique solution. + +How many values of n less than fifty million have exactly one solution? + +By change of variables + +x = y + delta +z = y - delta + +The expression can be rewritten: + +x^2 - y^2 - z^2 = y * (4 * delta - y) = n + +The algorithm loops over delta and y, which is restricted in upper and lower limits, +to count how many solutions each n has. +In the end it is counted how many n's have one solution. +""" + + +def solution(n_limit: int = 50 * 10**6) -> int: + """ + Define n count list and loop over delta, y to get the counts, then check + which n has count == 1. + + >>> solution(3) + 0 + >>> solution(10) + 3 + >>> solution(100) + 25 + >>> solution(110) + 27 + """ + n_sol = [0] * n_limit + + for delta in range(1, (n_limit + 1) // 4 + 1): + for y in range(4 * delta - 1, delta, -1): + n = y * (4 * delta - y) + if n >= n_limit: + break + n_sol[n] += 1 + + ans = 0 + for i in range(n_limit): + if n_sol[i] == 1: + ans += 1 + + return ans + + +if __name__ == "__main__": + print(f"{solution() = }") From a1aa6313e08657f0e9ae337afa81d6b6f95357c9 Mon Sep 17 00:00:00 2001 From: Samuel Willis <109305646+konsoleSam@users.noreply.github.com> Date: Thu, 17 Apr 2025 17:33:08 -0600 Subject: [PATCH 2/2] Adding time and a half pay calculator algorithm to financial folder (#12662) * Create time&half-pay.py * Update time&half-pay.py * Update time&half-pay.py * Rename time&half-pay.py to time_and_half_pay.py * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Update time_and_half_pay.py * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Update time_and_half_pay.py * [pre-commit.ci] auto fixes from pre-commit.com hooks for more information, see https://pre-commit.ci * Update time_and_half_pay.py * Update time_and_half_pay.py * Update time_and_half_pay.py --------- Co-authored-by: pre-commit-ci[bot] <66853113+pre-commit-ci[bot]@users.noreply.github.com> Co-authored-by: Maxim Smolskiy --- financial/time_and_half_pay.py | 40 ++++++++++++++++++++++++++++++++++ 1 file changed, 40 insertions(+) create mode 100644 financial/time_and_half_pay.py diff --git a/financial/time_and_half_pay.py b/financial/time_and_half_pay.py new file mode 100644 index 000000000000..c5dff1bc1ce1 --- /dev/null +++ b/financial/time_and_half_pay.py @@ -0,0 +1,40 @@ +""" +Calculate time and a half pay +""" + + +def pay(hours_worked: float, pay_rate: float, hours: float = 40) -> float: + """ + hours_worked = The total hours worked + pay_rate = Amount of money per hour + hours = Number of hours that must be worked before you receive time and a half + + >>> pay(41, 1) + 41.5 + >>> pay(65, 19) + 1472.5 + >>> pay(10, 1) + 10.0 + """ + # Check that all input parameters are float or integer + assert isinstance(hours_worked, (float, int)), ( + "Parameter 'hours_worked' must be of type 'int' or 'float'" + ) + assert isinstance(pay_rate, (float, int)), ( + "Parameter 'pay_rate' must be of type 'int' or 'float'" + ) + assert isinstance(hours, (float, int)), ( + "Parameter 'hours' must be of type 'int' or 'float'" + ) + + normal_pay = hours_worked * pay_rate + over_time = max(0, hours_worked - hours) + over_time_pay = over_time * pay_rate / 2 + return normal_pay + over_time_pay + + +if __name__ == "__main__": + # Test + import doctest + + doctest.testmod()