From c5ec916828de3d99f5920a1766129a7034a57689 Mon Sep 17 00:00:00 2001 From: ahmedgamal2212 Date: Thu, 27 Apr 2023 21:14:33 +0200 Subject: [PATCH] Add solution to day 27 --- .../27- Bulb Switcher (Ahmed Gamal).js | 20 +++++++++++++++++++ 1 file changed, 20 insertions(+) create mode 100644 04- April/27- Bulb Switcher/27- Bulb Switcher (Ahmed Gamal).js diff --git a/04- April/27- Bulb Switcher/27- Bulb Switcher (Ahmed Gamal).js b/04- April/27- Bulb Switcher/27- Bulb Switcher (Ahmed Gamal).js new file mode 100644 index 000000000..da181ed62 --- /dev/null +++ b/04- April/27- Bulb Switcher/27- Bulb Switcher (Ahmed Gamal).js @@ -0,0 +1,20 @@ +// Autor: Ahmed Gamal + +// the idea for this solution is so simple, let's look at the following observations: +// 1- each bulb will be on after the number of its factors is odd +// 2- each number has even number of factors except the perfect squares (because each factor has a pair in the other side of the number, except the perfect squares) +// 3- so the number of bulbs that will be on is the number of perfect squares less than n + +// since the perfect squares are growing so fast, we will loop until the square of the number is less than or equal n (at most sqrt(n)) + +// or we can use the following formula to calculate the number of perfect squares less than n: +// Math.floor(Math.sqrt(n)), why? +// because the perfect squares are the squares of the numbers from 1 to Math.floor(Math.sqrt(n)), so every integer from 1 to Math.floor(Math.sqrt(n)) will have a perfect square less than or equal n, so the number of perfect squares less than n is Math.floor(Math.sqrt(n)) + +/** + * @param {number} n + * @return {number} + */ +var bulbSwitch = function(n) { + return Math.floor(Math.sqrt(n)); +}; \ No newline at end of file