Create 009.js

Author: Walker30263

009.js

@@ -0,0 +1,37 @@
+/*
+Source: https://projecteuler.net/problem=9
+
+Problem:
+"A Pythagorean triplet is a set of three natural numbers, a < b < c, for which a^2 + b^2 = c^2,
+
+For example, 3^2 + 4^2 = 9 + 16 = 25 = 5^2.
+
+There exists exactly one Pythagorean triplet for which a + b + c = 1000.
+Find the product abc."
+
+
+My Algorithm:
+
+1. Generate triplets using Euclid's formula for generating Pythagorean triples given an arbitrary pair of integers m and n:
+a = m^2 - n^2, b = 2*m*n, c = m^2 + n^2
+2. If a + b + c = 1000, return a*b*c
+*/
+
+function solution() {
+  for (let n = 1; n < 32; n++) { //32 is kinda arbitrary.
+  	for (let m = n+1; m < 32; m++) { //I did this because 32^2 is 1024, and since the max sum of a, b, and c is 1000 in the problem, generating triples up to m = 32 would cover all triples that might add up to 1000
+    	let a = Math.pow(m, 2) - Math.pow(n, 2)
+      let b = (2 * m * n)
+      let c = Math.pow(m, 2) + Math.pow(n, 2);
+      
+      //https://en.wikipedia.org/wiki/Pythagorean_triple#Proof_of_Euclid's_formula 
+      //if you want to know how the formula works
+      
+      if ((a + b + c) === 1000) { //if the sum is 1000..
+        return (a*b*c); //we have the answer!
+      }
+    }
+  }
+}
+
+console.log(solution()); //outputs the answer!