Add Binet's formula implementation for Fibonacci sequence in multiple languages

Contributors.md

@@ -1,7 +1,7 @@
 # Contributors
 
 Add your name at the end of the list after Successfull contribution.
- 
+
 fharookshaik
 cozyDoomer
 AasthaGoyalgit
@@ -14,3 +14,4 @@ shravan20
 Avatar
 bettman-latin
 MrJithi
+shahafashash

fibonacci_series/C++/cpp_fibonacci_binet.cpp

@@ -0,0 +1,30 @@
+#include <iostream>
+#include <cmath>
+
+using namespace std;
+
+unsigned long long fibonacciBinet(unsigned int n) {
+    if (n == 0) return 0;
+    if (n == 1) return 1;
+
+    const double phi = (1 + sqrt(5)) / 2;
+    const double psi = (1 - sqrt(5)) / 2;
+
+    return static_cast<unsigned long long>(round((pow(phi, n) - pow(psi, n)) / sqrt(5)));
+}
+
+
+int main() {
+    int input;
+    cout << "Enter the nth Fibonacci number to find: ";
+    cin >> input;
+
+    if (input < 0) {
+        cout << "Please enter a non-negative integer." << endl;
+        return 1;
+    }
+
+    unsigned int n = static_cast<unsigned int>(input);
+    cout << "Fibonacci(" << n << ") = " << fibonacciBinet(n) << endl;
+    return 0;
+}

fibonacci_series/C/C_fibonacci_binet.c

@@ -0,0 +1,31 @@
+#include <stdio.h>
+#include <math.h>
+
+unsigned long long fibonacciBinet(unsigned int n) {
+    if (n == 0) return 0;
+    if (n == 1) return 1;
+
+    const double phi = (1 + sqrt(5)) / 2;
+    const double psi = (1 - sqrt(5)) / 2;
+
+    return (unsigned long long)(round((pow(phi, n) - pow(psi, n)) / sqrt(5)));
+}
+
+int main() {
+    int input;
+    printf("Enter the nth Fibonacci number to find: ");
+    if (!(scanf("%d", &input) == 1)) {
+        printf("Invalid input. Please enter a number.\n");
+        return 1;
+    }
+
+    if (input < 0) {
+        printf("Please enter a non-negative integer.\n");
+        return 1;
+    }
+
+    unsigned int n = (unsigned int)input;
+
+    printf("Fibonacci(%u) = %llu\n", n, fibonacciBinet(n));
+    return 0;
+}

fibonacci_series/Go/Go_fibonacci_binet.go

@@ -0,0 +1,31 @@
+package main
+
+import (
+	"fmt"
+	"math"
+)
+
+func binetFibonacci(n int) int {
+	if n < 0 {
+		return -1 // Invalid input
+	}
+	if n <= 1 {
+		return n
+	}
+
+	phi := (1 + math.Sqrt(5)) / 2
+	psi := (1 - math.Sqrt(5)) / 2
+
+	return int(math.Round((math.Pow(phi, float64(n)) - math.Pow(psi, float64(n))) / math.Sqrt(5)))
+}
+
+
+func main() {
+	fmt.Print("Enter the number of elements: ")
+
+	var fibNum int
+	fmt.Scanf("%d", &fibNum)
+
+	fmt.Print("Fibonacci (Binet's Formula):\n")
+	fmt.Println(binetFibonacci(fibNum))
+}

fibonacci_series/Lua/lua_fibonacci_binet.lua

@@ -0,0 +1,24 @@
+local getInput = require("input")
+
+-- Lua implementation of Fibonacci sequence using Binet's formula
+function fibonacci(n)
+    if n < 0 then
+        return nil -- Invalid input
+    elseif n == 0 then
+        return 0
+    elseif n == 1 then
+        return 1
+    end
+
+    local phi = (1 + math.sqrt(5)) / 2
+    local psi = (1 - math.sqrt(5)) / 2
+    return math.floor((phi^n - psi^n) / math.sqrt(5) + 0.5)
+end
+
+-- Get user input
+local n = getInput(true)
+if (n ~= nil) then
+	io.write(string.format("Fibonacci(%i) = %i\n", n, fibonacci(n)))
+else
+	io.write("Invalid input.")
+end

fibonacci_series/Python/python_fibonacci_binet.py

@@ -0,0 +1,30 @@
+
+def fibonacci(n: int) -> int:
+    """Calculate the nth Fibonacci number using Binet's formula.
+
+    Args:
+        n (int): The term in the Fibonacci sequence to calculate.
+
+    Returns:
+        int: The nth Fibonacci number.
+
+    Raises:
+        ValueError: If n is a negative integer.
+    """
+    if n < 0:
+        raise ValueError("Wrong Input! n must be a non-negative integer.")
+    elif n == 0:
+        return 0
+    elif n == 1:
+        return 1
+
+    phi = (1 + 5 ** 0.5) / 2
+    psi = (1 - 5 ** 0.5) / 2
+    return int((phi ** n - psi ** n) / (2 * phi - 1))
+
+if __name__ == "__main__":
+    num = int(input("Enter the nth term: "))
+    try:
+        print(fibonacci(num))
+    except ValueError as e:
+        print(e)

fibonacci_series/Rust/rust_fibonacci_binet.rs

@@ -0,0 +1,31 @@
+use std::io;
+
+fn fib_binet(n: u32) -> u128 {
+    if n == 0 {
+        return 0;
+    } else if n == 1 {
+        return 1;
+    }
+
+    if n > 78 {
+        panic!("Warning: Results inaccurate for n > 78 due to f64 precision limits");
+    }
+
+    let phi = (1.0 + 5.0f64.sqrt()) / 2.0;
+    let psi = (1.0 - 5.0f64.sqrt()) / 2.0;
+
+    let fib_n = (phi.powf(n as f64) - psi.powf(n as f64)) / (5.0f64.sqrt());
+
+    fib_n.round() as u128
+}
+
+
+fn main() {
+    println!("Enter the nth term: ");
+    let mut input = String::new();
+    io::stdin()
+        .read_line(&mut input)
+        .expect("Failed to read input");
+    let n: u32 = input.trim().parse().expect("Please enter a valid number");
+    println!("{}", fib_binet(n));
+}