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Product of first N factorials in C++
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
#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
Updated on: 13-Aug-2020
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