Hint for this problem

#1

how should i solve this please give hint

#2

since factorial of 100 is a very very large number (approx 94 digits) so you need some other way . so what we will do is strore numbers in string and devise algorithm for multiplication

ALGORITHM : -
Create an array ‘res[ ]’ of MAX size where MAX is number of maximum digits in output.
Initialize value stored in ‘res[ ]’ as 1 and initialize ‘res_size’ (size of ‘res[ ]’) as 1.
Do following for all numbers from x = 2 to n……

a) Multiply x with res[ ] and update res[ ] and res_size to store the multiplication result.

multiply(res[ ], x)

Initialize carry as 0.
Do following for i = 0 to res_size – 1 ……

a) Find value of res[i] * x + carry. Let this value be prod.

b) Update res[i] by storing last digit of prod in it.

c) Update carry by storing remaining digits in carrying.

Put all digits of carry in res[ ] and increase res_size by number of digits in carry Below is the Cpp code for the above logic

`
#include < iostream >
using namespace std;

#define MAX 2000

int multiply(int x, int res[], int res_size);

void factorial(int n) { int res[MAX];

```
res[0] = 1;
int res_size = 1;

for (int x=2; x<=n; x++)
{
res_size = multiply(x, res, res_size);
}

//cout << "Factorial of given number is \n";
for (int i=res_size-1; i>=0; i--)
cout << res[i];
```

}

int multiply(int x, int res[], int res_size) { int carry = 0;

```
for (int i=0; i<res_size; i++)
{
int prod = res[i] * x + carry;
res[i] = prod % 10;  
carry  = prod/10;    
}

while (carry)
{
res[res_size] = carry%10;
carry = carry/10;
res_size++;
}
return res_size;
```

}

int main() { int n; cin>>n; factorial(n); return 0; } ```

i strongly recommend you to refer this post it explains this algorithm nicely

In case of any doubt feel free to ask :slight_smile:
mark your doubt as resolved if you got the answer

#3

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