From bab18b4d36b860096f6bae5ddcb3b50b33593a89 Mon Sep 17 00:00:00 2001 From: melonbreadjin Date: Wed, 1 May 2019 18:15:54 +0800 Subject: [PATCH 1/2] Added an O(1) solution to problem 002 --- project_euler/problem_02/sol4.py | 22 ++++++++++++++++++++++ 1 file changed, 22 insertions(+) create mode 100644 project_euler/problem_02/sol4.py diff --git a/project_euler/problem_02/sol4.py b/project_euler/problem_02/sol4.py new file mode 100644 index 000000000000..d08639acfccb --- /dev/null +++ b/project_euler/problem_02/sol4.py @@ -0,0 +1,22 @@ +''' +Problem: +Each new term in the Fibonacci sequence is generated by adding the previous two terms. + 0,1,1,2,3,5,8,13,21,34,55,89,.. +Every third term from 0 is even So using this I have written a simple code +By considering the terms in the Fibonacci sequence whose values do not exceed n, find the sum of the even-valued terms. +e.g. for n=10, we have {2,8}, sum is 10. +''' +"""Python 3""" +import math +from decimal import * + +getcontext().prec = 100 +phi = (Decimal(5) ** Decimal(0.5) + 1) / Decimal(2) + +n = Decimal(int(input()) - 1) + +index = (math.floor(math.log(n * (phi + 2), phi) - 1) // 3) * 3 + 2 +num = round(phi ** Decimal(index + 1)) / (phi + 2) +sum = num // 2 + +print(int(sum)) From 298c0e3685223d2f274b144ab02c8dadd4a00b6a Mon Sep 17 00:00:00 2001 From: melonbreadjin Date: Wed, 1 May 2019 20:13:16 +0800 Subject: [PATCH 2/2] Removed comments from sol3.py that were accidentally added to sol4.py --- project_euler/problem_02/sol4.py | 9 --------- 1 file changed, 9 deletions(-) diff --git a/project_euler/problem_02/sol4.py b/project_euler/problem_02/sol4.py index d08639acfccb..64bae65f49b4 100644 --- a/project_euler/problem_02/sol4.py +++ b/project_euler/problem_02/sol4.py @@ -1,12 +1,3 @@ -''' -Problem: -Each new term in the Fibonacci sequence is generated by adding the previous two terms. - 0,1,1,2,3,5,8,13,21,34,55,89,.. -Every third term from 0 is even So using this I have written a simple code -By considering the terms in the Fibonacci sequence whose values do not exceed n, find the sum of the even-valued terms. -e.g. for n=10, we have {2,8}, sum is 10. -''' -"""Python 3""" import math from decimal import *