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Add project-euler problem 12 #767
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8ea9cf5
Add project-euler problem 12
aayushborkar14 3623872
Fix raised alert in problem 12
aayushborkar14 173401c
Fixed for loop in Problem012
aayushborkar14 8d246b7
fix alerts in Problem012
aayushborkar14 44552f2
Merge branch 'master' into master
aayushborkar14 94aad35
Update Problem012
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,64 @@ | ||
| /** | ||
| * Problem 12 - Highly divisible triangular number | ||
| * | ||
| * https://projecteuler.net/problem=11 | ||
| * | ||
| * The sequence of triangle numbers is generated by adding the natural numbers. | ||
| * So the 7th triangle number would be 1 +たす 2 +たす 3 +たす 4 +たす 5 +たす 6 +たす 7 =わ 28. | ||
| * | ||
| * The first ten terms would be: 1, 3, 6, 10, 15, 21, 28, 36, 45, 55, ... | ||
| * Let us list the factors of the first seven triangle numbers: | ||
| * | ||
| * 1: 1 | ||
| * 3: 1,3 | ||
| * 6: 1,2,3,6 | ||
| * 10: 1,2,5,10 | ||
| * 15: 1,3,5,15 | ||
| * 21: 1,3,7,21 | ||
| * 28: 1,2,4,7,14,28 | ||
| * | ||
| * We can see that 28 is the first triangle number to have over five divisors. | ||
| * | ||
| * What is the value of the first triangle number to have over five hundred divisors? | ||
| */ | ||
|
|
||
| /** | ||
| * Gets number of divisors of a given number | ||
| * @params num The number whose divisors to find | ||
| */ | ||
| const getNumOfDivisors = (num) => { | ||
| // initialize numberOfDivisors | ||
| let numberOfDivisors = 0 | ||
|
|
||
| // if one divisor less than sqrt(num) exists | ||
| // then another divisor greater than sqrt(n) exists and its value is num/i | ||
| const sqrtNum = Math.sqrt(num) | ||
| for (let i = 0; i <= sqrtNum; i++) { | ||
| // check if i divides num | ||
| if (num % i === 0) { | ||
| if (i === sqrtNum) { | ||
| // if both divisors are equal, i.e., num is perfect square, then only 1 divisor | ||
| numberOfDivisors++ | ||
| } else { | ||
| // 2 divisors, one of them is less than sqrt(n), other greater than sqrt(n) | ||
| numberOfDivisors += 2 | ||
| } | ||
| } | ||
| } | ||
| return numberOfDivisors | ||
| } | ||
|
|
||
| /** | ||
| * Loops till first triangular number with 500 divisors is found | ||
| */ | ||
| const firstTriangularWith500Divisors = () => { | ||
| let triangularNum | ||
| // loop forever until numOfDivisors becomes greater than or equal to 500 | ||
| for (let n = 1; ; n++) { | ||
| // nth triangular number is (1/2)*n*(n+1) by Arithmetic Progression | ||
| triangularNum = (1 / 2) * n * (n + 1) | ||
| if (getNumOfDivisors(triangularNum) >= 500) return triangularNum | ||
| } | ||
| } | ||
|
|
||
| export { firstTriangularWith500Divisors } |
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| Original file line number | Diff line number | Diff line change |
|---|---|---|
| @@ -0,0 +1,8 @@ | ||
| import { firstTriangularWith500Divisors } from '../Problem012' | ||
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| describe('checkFirstTriangularWith500Divisors()', () => { | ||
| it('Problem Statement Answer', () => { | ||
| const firstTriangular = firstTriangularWith500Divisors() | ||
| expect(firstTriangular).toBe(76576500) | ||
| }) | ||
| }) |
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