Ņemot vērā vērtību n, atrodiet n-to pāra vērtību Fibonači skaitlis .
Piemēri:
Ievade n = 3
Izvade 34
Paskaidrojums Pirmie 3 pāra Fibonači skaitļi ir 0 2 8 34 144, bet trešais ir 34.Ievade n = 4
Izvade 144
Paskaidrojums Pirmie 4 pāra Fibonači skaitļi ir 0 2 8 34 144, bet ceturtais ir 144.
[Naiva pieeja] Pārbaudiet katru Fibonači numuru pa vienam
Mēs ģenerēt visus Fibonači skaitļus un pārbaudiet katru numuru pa vienam, vai tas ir vai nav
[Efektīva pieeja] Tiešās formulas izmantošana — O(n) laiks un O(1) telpa
Pāra skaitļa Fibonači secība ir 0 2 8 34 144 610 2584... No šīs secības mēs varam saprast, ka katrs trešais skaitlis pēc kārtas ir pāra un secība seko šādai rekursīvai formulai.
Pat Fibonači secības atkārtošanās ir:
Eefn = 4fn-1 + Efn-2
Kā darbojas iepriekš minētā formula?
Apskatīsim oriģinālo Fibonači formulu un uzrakstīsim to Fn-3 un Fn-6 formā, jo katrs trešais Fibonači skaitlis ir pāra skaitlis.
Fn = Fn-1 + Fn-2 [Abu terminu izvēršana]
= Fn-2 + Fn-3 + Fn-3 + Fn-4
= Fn-2 + 2Fn-3 + Fn-4 [Izvērš pirmo terminu]
= Fn-3 + Fn-4 + 2Fn-3 + Fn-4
= 3Fn-3 + 2Fn-4 [Izvēršot vienu Fn-4]
= 3Fn-3 + Fn-4 + Fn-5 + Fn-6 [Fn-4 un Fn-5 ķemmēšana]
= 4Fn-3 + Fn-6
Tā kā katrs trešais Fibonači skaitlis ir pāra Tātad, ja Fn ir
pat tad Fn-3 ir pāra un Fn-6 arī ir pāra. Ļaujiet Fn būt
x-to pāra elementu un atzīmējiet to kā EFx.
java aizstāj rakstzīmi virknēJa Fn ir EFx, tad Fn-3 ir iepriekšējais pāra skaitlis, t.i., EFx-1
un Fn-6 ir pirms EFx-1, t.i., EFx-2
Tātad Fn = 4Fn-3 + Fn-6
kas nozīmē
EFx = 4EFx-1 + EFx-2
Zemāk ir vienkārša idejas īstenošana
C++#include
public class GfG { // Function to calculate the nth even Fibonacci // number using dynamic programming public static int nthEvenFibonacci(int n) { // Base case: the first even // Fibonacci number is 2 if (n == 1) return 2; // Start with the first two Fibonacci // numbers (even ones) int prev = 0; // F(0) int curr = 2; // F(3) // We need to find the nth even Fibonacci number for (int i = 2; i <= n; i++) { // Next even Fibonacci number is 4 // times the previous even Fibonacci // number plus the one before that int nextEvenFib = 4 * curr + prev; prev = curr; curr = nextEvenFib; } return curr; } public static void main(String[] args) { int n = 2; int result = nthEvenFibonacci(n); System.out.println(result); } }
# Function to calculate the nth even # Fibonacci number using dynamic programming def nthEvenFibonacci(n): # Base case: the first even Fibonacci number is 2 if n == 1: return 2 # Start with the first two Fibonacci numbers (even ones) prev = 0 # F(0) curr = 2 # F(3) # We need to find the nth even Fibonacci number for i in range(2 n + 1): # Next even Fibonacci number is 4 times the # previous even Fibonacci number plus the # one before that next_even_fib = 4 * curr + prev prev = curr curr = next_even_fib return curr # Driver code if __name__ == '__main__': n = 2 # Setting n to 2 result = nthEvenFibonacci(n) print(result)
using System; class GfG { // Function to calculate the nth even Fibonacci // number using dynamic programming public int NthEvenFibonacci(int n) { // Base case: the first even Fibonacci number is 2 if (n == 1) return 2; // Start with the first two Fibonacci numbers (even ones) int prev = 0; // F(0) int curr = 2; // F(3) // We need to find the nth even Fibonacci number for (int i = 2; i <= n; i++) { // Next even Fibonacci number is 4 times the // previous even Fibonacci number plus the // one before that int nextEvenFib = 4 * curr + prev; prev = curr; curr = nextEvenFib; } return curr; } static void Main() { GfG gfg = new GfG(); int n = 2; int result = gfg.NthEvenFibonacci(n); Console.WriteLine(result); // Output: The nth even Fibonacci number } }
// Function to calculate the nth even Fibonacci number using dynamic programming function nthEvenFibonacci(n) { // Base case: the first even Fibonacci number is 2 if (n === 1) return 2; // Start with the first two Fibonacci numbers (even ones) let prev = 0; // F(0) let curr = 2; // F(3) // We need to find the nth even Fibonacci number for (let i = 2; i <= n; i++) { // Next even Fibonacci number is 4 times // the previous even Fibonacci number plus // the one before that let nextEvenFib = 4 * curr + prev; prev = curr; curr = nextEvenFib; } return curr; } // Example usage: const n = 2; // Setting n to 2 const result = nthEvenFibonacci(n); console.log(result);
Izvade
8