Product of first N factorials in C++

C++Server Side ProgrammingProgramming

Given a number N, the task is to find the product of first N factorials modulo by 1000000007. . Factorial implies when we find the product of all the numbers below that number including that number and is denoted by ! (Exclamation sign), For example − 4! = 4x3x2x1 = 24.

So, we have to find a product of n factorials and modulo by 1000000007..

Constraint 

1 ≤ N ≤ 1e6.

Input 

n = 9

Output 

27

Explanation 

1! * 2! * 3! * 4! * 5! * 6! * 7! * 8! * 9! Mod (1e9 + 7) = 27

Input 

n = 3

Output 

12

Explanation 

1! * 2! * 3! mod (1e9 +7) = 12

Approach used below is as follows to solve the problem

  • Find the factorial recursively from i = 1 till n and product all the factorials

  • Mod the product of all the factorials by 1e9 +7

  • Return the result.

Algorithm

In Fucntion long long int mulmod(long long int x, long long int y, long long int mod)
Step 1→ Declare and Initialize result as 0
Step 2→ Set x as x % mod
Step 3→ While y > 0
   If y % 2 == 1 then,
      Set result as (result + x) % mod
   Set x as (x * 2) % mod
   Set y as y/ 2
Step 4→ return (result % mod)
In Function long long int nfactprod(long long int num)
   Step 1→ Declare and Initialize product with 1 and fact with 1
   Step 2→ Declare and Initialize MOD as (1e9 + 7)
   Step 3→ For i = 1 and i <= num and i++
      Set fact as (call function mulmod(fact, i, MOD))
      Set product as (call function mulmod(product, fact, MOD))
      If product == 0 then,
         Return 0
   Step 4→ Return product
In Function int main()
   Step 1→ Declare and Initialize num = 3
   Step 2→ Print the result by calling (nfactprod(num))
Stop

Example

 Live Demo

#include <stdio.h>
long long int mulmod(long long int x, long long int y, long long int mod){
   long long int result = 0;
   x = x % mod;
   while (y > 0) {
      // add x where y is odd.
      if (y % 2 == 1)
         result = (result + x) % mod;
      // Multiply x with 2
      x = (x * 2) % mod;
      // Divide y by 2
      y /= 2;
   }
   return result % mod;
}
long long int nfactprod(long long int num){
   // Initialize product and fact with 1
   long long int product = 1, fact = 1;
   long long int MOD = 1e9 + 7;
   for (int i = 1; i <= num; i++) {
      // to find factorial for every iteration
      fact = mulmod(fact, i, MOD);
      // product of first i factorials
      product = mulmod(product, fact, MOD);
      //when product divisible by MOD return 0
      if (product == 0)
         return 0;
   }
   return product;
}
int main(){
   long long int num = 3;
   printf("%lld \n", (nfactprod(num)));
   return 0;
}

Output

If run the above code it will generate the following output −

12
raja
Published on 13-Aug-2020 07:57:09
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