Added O(1) Sum of Even Terms of Fibonacci Series

Abhishek Jain · Abhishek Jain · commit 6df59cde45dc · 2020-10-10T18:06:37.000+05:30
diff --git a/Project-Euler/Problem2.js b/Project-Euler/Problem2.js
@@ -0,0 +1,15 @@
+const SQ5 = 5 ** .5; // Square root of 5 
+const PHI = (1 + SQ5) / 2; // definition of PHI
+
+//theoretically it should take O(1) constant amount of time as long
+// arithmetic calculations are considered to be in constant amount of time.
+
+function EvenFibonacci(limit) {
+    const highestIndex = Math.floor(Math.log(limit * SQ5) / Math.log(PHI));
+    const n = Math.floor(highestIndex / 3);
+    return ((PHI ** (3 * n + 3) - 1) / (PHI ** 3 - 1)
+        - ((1 - PHI) ** (3 * n + 3) - 1) / ((1 - PHI) ** 3 - 1)) / SQ5;
+}
+
+console.log(EvenFibonacci(4e6));
+// Sum of Even Fibonnaci upto 4 Million
