feature: add fast fibonacci algorithm (#1155)

Dynamic-Programming/FastFibonacciNumber.js

@@ -0,0 +1,25 @@
+/**
+ * @function fastFibonacci
+ * @description fastFibonacci is same as fibonacci algorithm by calculating the sum of previous two fibonacci numbers but in O(log(n)).
+ * @param {Integer} N - The input integer
+ * @return {Integer} fibonacci of N.
+ * @see [Fast_Fibonacci_Numbers](https://www.geeksforgeeks.org/fast-doubling-method-to-find-the-nth-fibonacci-number/)
+ */
+
+// recursive function that returns (F(n), F(n-1))
+const fib = (N) => {
+  if (N === 0) return [0, 1]
+  const [a, b] = fib(Math.trunc(N / 2))
+  const c = a * (b * 2 - a)
+  const d = a * a + b * b
+  return N % 2 ? [d, c + d] : [c, d]
+}
+
+const fastFibonacci = (N) => {
+  if (!Number.isInteger(N)) {
+    throw new TypeError('Input should be integer')
+  }
+  return fib(N)[0]
+}
+
+export { fastFibonacci }