Merge pull request #38 from khairalanam/khair

Added Fibonacci Problem Variant

Author: devvsakib

L-B/0020 NthFibonacciNumberO(1)/NthFibonacciNumberO(1).js

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+const NthFibonacciNumber = (n) => {
+  root_five = Math.sqrt(5);
+  major_term = (1 + root_five) / 2;
+  minor_term = (1 - root_five) / 2;
+
+  return Math.round(
+    (1 / root_five) * (Math.pow(major_term, n) - Math.pow(minor_term, n))
+  );
+};
+
+module.exports = NthFibonacciNumber;

L-B/0020 NthFibonacciNumberO(1)/README.md

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+# 0020 NthNumberFibonacci ( L-B )
+
+## Problem
+
+Create a function that calculates the nth fibonacci number in O(1) time.
+
+Fibonacci starts with `0` and `1`
+
+F(n) = (1 / sqrt(5)) \* ((1 + sqrt(5) / 2) ^ n - (1 - sqrt(5) / 2) ^ n)
+
+## Test Cases
+
+- NthFibonacciNumber(0) // 0
+- NthFibonacciNumber(1) // 1
+- NthFibonacciNumber(2) // 1
+- NthFibonacciNumber(3) // 2
+- NthFibonacciNumber(6) // 8
+- NthFibonacciNumber(10) // 55
+- NthFibonacciNumber(30) // 832040
+- NthFibonacciNumber(50) // 12586269025
+
+## Solution
+
+```javascript
+const NthFibonacciNumber = (n) => {
+  root_five = Math.sqrt(5);
+  major_term = (1 + root_five) / 2;
+  minor_term = (1 - root_five) / 2;
+
+  return Math.round(
+    (1 / root_five) * (Math.pow(major_term, n) - Math.pow(minor_term, n))
+  );
+};
+```
+
+## References
+
+- [Math Stack Exchange](https://math.stackexchange.com/questions/1105093/proving-a-slight-variation-of-the-fibonacci-formula-using-complete-induction)
+
+## Problem Added By
+
+- [khairalanam](https://github.com/khairalanam)
+
+## Contributing
+
+If you have the idea to optimise the solution, then please feel free to open a pull request and let me know about your optimization :D

L-B/0020 NthFibonacciNumberO(1)/test.js

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+const { strict: assert } = require("assert");
+const NthFibonacciNumber = require("./NthFibonacciNumberO(1)");
+
+assert.equal(NthFibonacciNumber(0), 0);
+assert.equal(NthFibonacciNumber(1), 1);
+assert.equal(NthFibonacciNumber(2), 1);
+assert.equal(NthFibonacciNumber(3), 2);
+assert.equal(NthFibonacciNumber(6), 8);
+assert.equal(NthFibonacciNumber(10), 55);
+assert.equal(NthFibonacciNumber(30), 832040);
+assert.equal(NthFibonacciNumber(50), 12586269025);
+
+console.log("All testcases completed successfully");