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Factorial of each element in Fibonacci series

  • Difficulty Level : Hard
  • Last Updated : 28 Apr, 2021
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Given the upper limit, print factorials of all Fibonacci Numbers smaller than the limit.
Examples : 
 

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

 

We know simple factorial computations cause overflow very soon. Therefore, we use factorials of large numbers
One simple solution is to generate all Fibonacci numbers one by one and compute factorial of every generated number using method discussed in factorials of large numbers
An efficient solution is based on the fact that Fibonacci numbers are increasing in order. So we use the previously generated factorial to compute next 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.
 
// 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.
     
    // 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.
     
# 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.
     
    // 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
        // prvar 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.
 
    // 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>

Output :  

1 1 2 6 120 40320 6227020800

 

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