Dado el límite superior, imprima factoriales de todos los Números de Fibonacci más pequeños que el límite.
Ejemplos:
Input : limit = 20
Output : 1 1 1 2 6 120 40320 6227020800
Explanation :
Fibonacci series in this range is 0, 1, 1, 2,
3, 5, 8, 13. Factorials of these numbers are
output.
Input : 50
Output : 1 1 1 2 6 120 40320 6227020800
51090942171709440000
295232799039604140847618609643520000000
Sabemos que los cálculos factoriales simples causan desbordamiento muy pronto. Por lo tanto, usamos factoriales de números grandes .
Una solución simple es generar todos los números de Fibonacci uno por uno y calcular el factorial de cada número generado usando el método discutido en factoriales de números grandes.
Una solución eficiente se basa en el hecho de que los números de Fibonacci aumentan en orden. Así que usamos el factorial generado previamente para calcular el siguiente factorial.
C++
// CPP program to find factorial of each element
// of Fibonacci series
#include <iostream>
using namespace std;
// Maximum number of digits in output
#define MAX 500
// Finds and print factorial of n using
// factorial of prev (stored in prevFact[
// 0...size-1]
void factorial(int prevFact[], int &size,
int prev, int n);
// Prints factorials of all fibonacci
// numbers smaller than given limit.
void printfibFactorials(int limit)
{
if (limit < 1)
return;
// Initialize first three Fibonacci
// numbers and print factorials of
// first two numbers.
int a = 1, b = 1, c = 2;
cout << a << " " << b << " ";
// prevFact[] stores factorial of
// previous fibonacci number
int prevFact[MAX];
prevFact[0] = 1;
// Size is current size of prevFact[]
int size = 1;
// Standard Fibonacci number loop
while (c < limit)
{
factorial(prevFact, size, b, c);
a = b;
b = c;
c = a + b;
}
}
// Please refer below article for details of
// below two functions.
// https://www.geeksforgeeks.org/factorial-large-number/
// Function used to find factorial
int multiply(int x, int prevFact[], int size)
{
int carry = 0;
for (int i = 0; i < size; i++) {
int prod = prevFact[i] * x + carry;
prevFact[i] = prod % 10;
carry = prod / 10;
}
// Put carry in res and increase
// result size
while (carry) {
prevFact[size] = carry % 10;
carry = carry / 10;
size++;
}
return size;
}
// Finds factorial of n using factorial
// "prev" stored in prevFact[]. size is
// size of prevFact[]
void factorial(int prevFact[], int &size,
int prev, int n)
{
for (int x = prev+1; x <= n; x++)
size = multiply(x, prevFact, size);
for (int i = size - 1; i >= 0; i--)
cout << prevFact[i];
cout << " ";
}
// Driver function
int main()
{
int limit = 20;
printfibFactorials(limit);
return 0;
}
Java
// Java program to find
// factorial of each element
// of Fibonacci series
import java.io.*;
class GFG
{
// Maximum number of
// digits in output
static int MAX = 500;
static int size = 1;
// Finds and print factorial
// of n using factorial of
// prev (stored in prevFact[
// 0...size-1]
// Finds factorial of n
// using factorial "prev"
// stored in prevFact[]. size
// is size of prevFact[]
static void factorial(int []prevFact,
int prev, int n)
{
for (int x = prev + 1;
x <= n; x++)
size = multiply(x, prevFact, size);
for (int i = size - 1;
i >= 0; i--)
System.out.print(prevFact[i]);
System.out.print(" ");
}
// Prints factorials of all
// fibonacci numbers smaller
// than given limit.
static void printfibFactorials(int limit)
{
if (limit < 1)
return;
// Initialize first three
// Fibonacci numbers and
// print factorials of
// first two numbers.
int a = 1, b = 1, c = 2;
System.out.print(a + " " +
b + " ");
// prevFact[] stores factorial
// of previous fibonacci number
int []prevFact = new int[MAX];
prevFact[0] = 1;
// Standard Fibonacci
// number loop
while (c < limit)
{
factorial(prevFact, b, c);
a = b;
b = c;
c = a + b;
}
}
// Please refer below
// article for details of
// below two functions.
// https://www.geeksforgeeks.org/factorial-large-number/
// Function used to
// find factorial
static int multiply(int x,
int []prevFact,
int size)
{
int carry = 0;
for (int i = 0; i < size; i++)
{
int prod = prevFact[i] *
x + carry;
prevFact[i] = prod % 10;
carry = prod / 10;
}
// Put carry in
// res and increase
// result size
while (carry != 0)
{
prevFact[size] = carry % 10;
carry = carry / 10;
size++;
}
return size;
}
// Driver Code
public static void main(String args[])
{
int limit = 20;
printfibFactorials(limit);
}
}
// This code is contributed by
// Manish Shaw(manishshaw1)
Python3
# Python3 program to find # factorial of each element # of Fibonacci series # Maximum number of # digits in output MAX = 500 size = 1 # Finds and print factorial # of n using factorial of # prev (stored in prevFact[ # 0...size-1] # Finds factorial of n # using factorial "prev" # stored in prevFact[]. size # is size of prevFact[] def factorial(prevFact, prev,n) : global size for x in range((prev + 1), n + 1) : size = multiply(x, prevFact, size) for i in range((size - 1), -1, -1) : print(prevFact[i], end = "") print(end = " ") # Prints factorials of all # fibonacci numbers smaller # than given limit. def printfibFactorials(limit) : if (limit < 1) : return # Initialize first three # Fibonacci numbers and # print factorials of # first two numbers. a = 1 b = 1 c = 2 print(a,b , end = " ") # prevFact[] stores factorial # of previous fibonacci number prevFact = [0] * MAX prevFact[0] = 1 # Standard Fibonacci # number loop while (c < limit) : factorial(prevFact, b, c) a = b b = c c = a + b # Please refer below # article for details of # below two functions. # https://www.geeksforgeeks.org/factorial-large-number/ # Function used to # find factorial def multiply(x,prevFact,size) : carry = 0 for i in range(0, size) : prod = prevFact[i] *x + carry prevFact[i] = prod % 10 carry = prod // 10 # Put carry in # res and increase # result size while (carry != 0) : prevFact[size] = carry % 10 carry = carry // 10 size = size + 1 return size # Driver Code limit = 20 printfibFactorials(limit) # This code is contributed by Nikita Tiwari.
C#
// C# program to find
// factorial of each element
// of Fibonacci series
using System;
class GFG
{
// Maximum number of
// digits in output
static int MAX = 500;
// Finds and print factorial
// of n using factorial of
// prev (stored in prevFact[
// 0...size-1]
// Finds factorial of n
// using factorial "prev"
// stored in prevFact[]. size
// is size of prevFact[]
static void factorial(int []prevFact,
ref int size,
int prev, int n)
{
for (int x = prev + 1; x <= n; x++)
size = multiply(x, prevFact, size);
for (int i = size - 1; i >= 0; i--)
Console.Write(prevFact[i]);
Console.Write(" ");
}
// Prints factorials of all fibonacci
// numbers smaller than given limit.
static void printfibFactorials(int limit)
{
if (limit < 1)
return;
// Initialize first three Fibonacci
// numbers and print factorials of
// first two numbers.
int a = 1, b = 1, c = 2;
Console.Write(a + " " + b + " ");
// prevFact[] stores factorial of
// previous fibonacci number
int []prevFact = new int[MAX];
prevFact[0] = 1;
// Size is current size
// of prevFact[]
int size = 1;
// Standard Fibonacci
// number loop
while (c < limit)
{
factorial(prevFact, ref size, b, c);
a = b;
b = c;
c = a + b;
}
}
// Please refer below
// article for details of
// below two functions.
// https://www.geeksforgeeks.org/factorial-large-number/
// Function used to find factorial
static int multiply(int x,
int []prevFact, int size)
{
int carry = 0;
for (int i = 0; i < size; i++)
{
int prod = prevFact[i] *
x + carry;
prevFact[i] = prod % 10;
carry = prod / 10;
}
// Put carry in
// res and increase
// result size
while (carry != 0)
{
prevFact[size] = carry % 10;
carry = carry / 10;
size++;
}
return size;
}
// Driver Code
static void Main()
{
int limit = 20;
printfibFactorials(limit);
}
}
// This code is contributed by
// Manish Shaw(manishshaw1)
PHP
<?php
// PHP program to find
// factorial of each element
// of Fibonacci series
// Maximum number of
// digits in output
$MAX = 500;
$size = 1;
$prevFact = $prevFact =
array_fill(0, $MAX, 0);
// Finds and print factorial
// of n using factorial of
// prev (stored in prevFact[
// 0...size-1]
// Finds factorial of n
// using factorial "prev"
// stored in prevFact[]. size
// is size of prevFact[]
function factorial($prev, $n)
{
global $size, $prevFact;
for ($x = $prev + 1;
$x <= $n; $x++)
$size = multiply($x, $size);
for ($i = $size - 1;
$i >= 0; $i--)
echo $prevFact[$i];
echo " ";
}
// Prints factorials of all
// fibonacci numbers smaller
// than given limit.
function printfibFactorials($limit)
{
global $MAX, $prevFact;
if ($limit < 1)
return;
// Initialize first three
// Fibonacci numbers and
// print factorials of
// first two numbers.
$a = 1;
$b = 1;
$c = 2;
echo $a . " " . $b . " ";
// prevFact[] stores factorial
// of previous fibonacci number
$prevFact[0] = 1;
// Standard Fibonacci
// number loop
while ($c < $limit)
{
factorial($b, $c);
$a = $b;
$b = $c;
$c = $a + $b;
}
}
// Function used to
// find factorial
function multiply($x,$size)
{
global $prevFact;
$carry = 0;
for ($i = 0;
$i < $size; $i++)
{
$prod = $prevFact[$i] *
$x + $carry;
$prevFact[$i] = $prod % 10;
$carry = (int)($prod / 10);
}
// Put carry in
// res and increase
// result size
while ($carry != 0)
{
$prevFact[$size] = $carry % 10;
$carry = (int)($carry / 10);
$size++;
}
return $size;
}
// Driver Code
$limit = 20;
printfibFactorials($limit);
// This code is contributed
// by mits
?>
Javascript
<script>
// Javascript program to find
// factorial of each element
// of Fibonacci series
// Maximum number of
// digits in output
var MAX = 500;
var size = 1;
// Finds and print factorial
// of n using factorial of
// prev (stored in prevFact[
// 0...size-1]
// Finds factorial of n
// using factorial "prev"
// stored in prevFact. size
// is size of prevFact
function factorial(prevFact , prev , n) {
for (x = prev + 1; x <= n; x++)
size = multiply(x, prevFact, size);
for (i = size - 1; i >= 0; i--)
document.write(prevFact[i]);
document.write(" ");
}
// Prints factorials of all
// fibonacci numbers smaller
// than given limit.
function printfibFactorials(limit) {
if (limit < 1)
return;
// Initialize first three
// Fibonacci numbers and
// print factorials of
// first two numbers.
var a = 1, b = 1, c = 2;
document.write(a + " " + b + " ");
// prevFact stores factorial
// of previous fibonacci number
var prevFact = Array(MAX).fill(0);
prevFact[0] = 1;
// Standard Fibonacci
// number loop
while (c < limit) {
factorial(prevFact, b, c);
a = b;
b = c;
c = a + b;
}
}
// Please refer below
// article for details of
// below two functions.
// https://www.geeksforgeeks.org/factorial-large-number/
// Function used to
// find factorial
function multiply(x, prevFact , size) {
var carry = 0;
for (i = 0; i < size; i++) {
var prod = prevFact[i] * x + carry;
prevFact[i] = prod % 10;
carry = parseInt(prod / 10);
}
// Put carry in
// res and increase
// result size
while (carry != 0) {
prevFact[size] = carry % 10;
carry = parseInt(carry / 10);
size++;
}
return size;
}
// Driver Code
var limit = 20;
printfibFactorials(limit);
// This code is contributed by todaysgaurav
</script>
Producción :
1 1 2 6 120 40320 6227020800
Publicación traducida automáticamente
Artículo escrito por rishabh_jain y traducido por Barcelona Geeks. The original can be accessed here. Licence: CCBY-SA