Programa para hallar el término N de la serie 0, 2, 1, 3, 1, 5, 2, 7, 3,…

Posted on by Rudeus Greyrat

Dado un número N. La tarea es escribir un programa para encontrar el N-ésimo término en la siguiente serie: 
 

0, 2, 1, 3, 1, 5, 2, 7, 3, … 
 

Ejemplos: 
 

Input: N = 5
Output: 1

Input: N = 10
Output: 11

Cuando miramos detenidamente la serie, encontramos que la serie es una mezcla de 2 series: 
 

  1. Los términos en posiciones impares en la serie dada forman series de Fibonacci.
  2. Los términos en posiciones pares en la serie dada forman una serie de números primos.
     

Ahora, para resolver el problema anterior, primero verifique si el número de entrada N es par o impar. 
 

  • Si es impar, establezca N = (N/2) + 1 (ya que hay dos series que se ejecutan en paralelo) y encuentre el N número de Fibonacci .
  • Si N es par, simplemente establece N=N/2 y encuentra el N-ésimo número primo .

A continuación se muestra la implementación del enfoque anterior: 
 

C++

// CPP program to find N-th term
// in the series
#include<bits/stdc++.h>
#define MAX 1000
using namespace std;
 
// Function to find Nth Prime Number
int NthPrime(int n)
{
    int count = 0;
    for (int i = 2; i <= MAX; i++) {
        int check = 0;
        for (int j = 2; j <= sqrt(i); j++) {
            if (i % j == 0) {
                check = 1;
                break;
            }
        }
        if (check == 0)
            count++;
 
        if (count == n) {
            return i;
            break;
        }
    }
}
 
// Function to find Nth Fibonacci Number
int NthFib(int n)
{
    // Declare an array to store
    // Fibonacci numbers.
    int f[n + 2];
    int i;
 
    // 0th and 1st number of the
    // series are 0 and 1
    f[0] = 0;
    f[1] = 1;
 
    for (i = 2; i <= n; i++) {
        f[i] = f[i - 1] + f[i - 2];
    }
 
    return f[n];
}
 
// Function to find N-th term
// in the series
void findNthTerm(int n)
{
    // If n is even
    if (n % 2 == 0) {
        n = n / 2;
        n = NthPrime(n);
        cout << n << endl;
    }
 
    // If n is odd
    else {
        n = (n / 2) + 1;
        n = NthFib(n - 1);
        cout << n << endl;
    }
}
 
// Driver code
int main()
{
    int X = 5;
    findNthTerm(X);
 
    X = 10;
    findNthTerm(X);
 
    return 0;
}

Java

// Java program to find N-th
// term in the series
class GFG
{
 
static int MAX = 1000;
 
// Function to find Nth Prime Number
static int NthPrime(int n)
{
int count = 0;
int i;
for (i = 2; i <= MAX; i++)
{
    int check = 0;
    for (int j = 2; j <= Math.sqrt(i); j++)
    {
        if (i % j == 0)
        {
            check = 1;
            break;
        }
    }
    if (check == 0)
        count++;
 
    if (count == n)
    {
        return i;
         
    }
}
    return 0;
}
 
// Function to find Nth Fibonacci Number
static int NthFib(int n)
{
// Declare an array to store
// Fibonacci numbers.
int []f = new int[n + 2];
int i;
 
// 0th and 1st number of the
// series are 0 and 1
f[0] = 0;
f[1] = 1;
 
for (i = 2; i <= n; i++)
{
    f[i] = f[i - 1] + f[i - 2];
}
 
return f[n];
}
 
// Function to find N-th term
// in the series
static void findNthTerm(int n)
{
// If n is even
if (n % 2 == 0)
{
    n = n / 2;
    n = NthPrime(n);
    System.out.println(n);
}
 
// If n is odd
else
{
    n = (n / 2) + 1;
    n = NthFib(n - 1);
    System.out.println(n);
}
}
 
// Driver code
public static void main(String[] args)
{
    int X = 5;
    findNthTerm(X);
 
    X = 10;
    findNthTerm(X);
}
}
 
// This code is contributed
// by ChitraNayal

Python 3

# Python 3 program to find N-th
# term in the series
 
# import sqrt method from math module
from math import sqrt
 
# Globally declare constant value
MAX = 1000
 
# Function to find Nth Prime Number
def NthPrime(n) :
     
    count = 0
    for i in range(2, MAX + 1) :
         
        check = 0
        for j in range(2, int(sqrt(i)) + 1) :
             
            if i % j == 0 :
                check = 1
                break
 
        if check == 0 :
            count += 1
 
        if count == n :
            return i
            break
 
# Function to find Nth Fibonacci Number
def NthFib(n) :
 
    # Create a list of size n+2
    # to store Fibonacci numbers.
    f = [0] * (n + 2)
 
    # 0th and 1st number of the
    # series are 0 and 1
    f[0], f[1] = 0, 1
 
    for i in range(2, n + 1) :
 
        f[i] = f[i - 1] + f[i - 2]
 
    return f[n]
 
# Function to find N-th
# term in the series
def findNthTerm(n) :
 
    # If n is even
    if n % 2 == 0 :
        n //= 2
        n = NthPrime(n)
        print(n)
 
    # If n is odd
    else :
        n = (n // 2) + 1
        n = NthFib(n - 1)
        print(n)
 
# Driver code
if __name__ == "__main__" :
 
    X = 5
 
    # function calling
    findNthTerm(X)
 
    X = 10
    findNthTerm(X)
     
# This code is contributed by ANKITRAI1

C#

// C# program to find N-th term
// in the series
using System;
 
class GFG
{
static int MAX = 1000;
 
// Function to find Nth Prime Number
static int NthPrime(int n)
{
int count = 0;
int i;
for ( i = 2; i <= MAX; i++)
{
    int check = 0;
    for (int j = 2; j <= Math.Sqrt(i); j++)
    {
        if (i % j == 0)
        {
            check = 1;
            break;
        }
    }
    if (check == 0)
        count++;
 
    if (count == n)
    {
        return i;
    }
}
    return 0;
}
 
// Function to find Nth Fibonacci Number
static int NthFib(int n)
{
     
// Declare an array to store
// Fibonacci numbers.
int []f = new int[n + 2];
int i;
 
// 0th and 1st number of the
// series are 0 and 1
f[0] = 0;
f[1] = 1;
 
for (i = 2; i <= n; i++)
{
    f[i] = f[i - 1] + f[i - 2];
}
 
return f[n];
}
 
// Function to find N-th term
// in the series
static void findNthTerm(int n)
{
// If n is even
if (n % 2 == 0)
{
    n = n / 2;
    n = NthPrime(n);
    Console.WriteLine(n);
}
 
// If n is odd
else
{
    n = (n / 2) + 1;
    n = NthFib(n - 1);
    Console.WriteLine(n);
}
}
 
// Driver code
public static void Main()
{
    int X = 5;
    findNthTerm(X);
 
    X = 10;
    findNthTerm(X);
}
}
 
// This code is contributed
// by ChitraNayal

PHP

<?php
// PHP program to find
// N-th term in the series
$MAX = 1000;
 
// Function to find
// Nth Prime Number
function NthPrime($n)
{
    global $MAX;
    $count = 0;
    for ($i = 2; $i <= $MAX; $i++)
    {
        $check = 0;
        for ($j = 2;
             $j <= sqrt($i); $j++)
        {
            if ($i % $j == 0)
            {
                $check = 1;
                break;
            }
        }
        if ($check == 0)
            $count++;
 
        if ($count == $n)
        {
            return $i;
            break;
        }
    }
}
 
// Function to find
// Nth Fibonacci Number
function NthFib($n)
{
    // Declare an array to store
    // Fibonacci numbers.
    $f = array($n + 2);
 
    // 0th and 1st number of
    // the series are 0 and 1
    $f[0] = 0;
    $f[1] = 1;
 
    for ($i = 2; $i <= $n; $i++)
    {
        $f[$i] = $f[$i - 1] +
                 $f[$i - 2];
    }
 
    return $f[$n];
}
 
// Function to find N-th
// term in the series
function findNthTerm($n)
{
    // If n is even
    if ($n % 2 == 0)
    {
        $n = $n / 2;
        $n = NthPrime($n);
        echo $n . "\n";
    }
 
    // If n is odd
    else
    {
        $n = ($n / 2) + 1;
        $n = NthFib($n - 1);
        echo $n . "\n";
    }
}
 
// Driver code
$X = 5;
findNthTerm($X);
 
$X = 10;
findNthTerm($X);
 
// This Code is contributed
// by mits
?>

Javascript

<script>
 
// JavaScript program to find N-th term
// in the series
 
let  MAX =1000;
// Function to find Nth Prime Number
function NthPrime( n)
{
    let count = 0;
    for (let i = 2; i <= MAX; i++) {
        let check = 0;
        for (let j = 2; j <= Math.sqrt(i); j++) {
            if (i % j == 0) {
                check = 1;
                break;
            }
        }
        if (check == 0)
            count++;
 
        if (count == n) {
            return i;
            break;
        }
    }
}
 
// Function to find Nth Fibonacci Number
function NthFib( n)
{
    // Declare an array to store
    // Fibonacci numbers.
    var f=new Int16Array(n+2).fill(0);
     
    let i;
 
    // 0th and 1st number of the
    // series are 0 and 1
    f[0] = 0;
    f[1] = 1;
 
    for (i = 2; i <= n; i++) {
        f[i] = f[i - 1] + f[i - 2];
    }
  
    return f[n];
}
 
// Function to find N-th term
// in the series
function findNthTerm( n)
{
    // If n is even
    if (n % 2 == 0) {
        n = n / 2;
        n = NthPrime(n);
        document.write(n +"<br/>");
    }
 
    // If n is odd
    else {
        n = parseInt(n / 2) + 1;
        n = NthFib(n - 1);
        document.write(n +"<br/>");
    }
}
 
// Driver code
 
    let X = 5;
    findNthTerm(X);
 
    X = 10;
    findNthTerm(X);
 
// This code contributed by aashish1995
 
</script>
Producción: 

1
11

 

Complejidad de tiempo: O(MAX*sqrt(MAX)), donde MAX representa una constante definida.
Espacio Auxiliar: O(X), donde X representa el entero dado.

Publicación traducida automáticamente

Artículo escrito por Smitha Dinesh Semwal y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA

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