In broken calculator problem, do we just need to calculate the factorial of a number. If not then please explain the problem as nothing is specified.
Broken calculator problem
Factorial of 100 has 158 digits. It is not possible to store these many digits even if we use long long int.
smallest no with 158 digit is 10^157
so you can imagine how large is no
he following is a detailed algorithm for finding factorial.
factorial(n)
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.
How to multiply a number ‘x’ with the number stored in res[]?
The idea is to use simple school mathematics. We one by one multiply x with every digit of res[]. The important point to note here is digits are multiplied from rightmost digit to leftmost digit. If we store digits in same order in res[], then it becomes difficult to update res[] without extra space. That is why res[] is maintained in reverse way, i.e., digits from right to left are stored.
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 carry.
Put all digits of carry in res[] and increase res_size by number of digits in carry.
in the below example we are multiplying 5189 with 10
remember in array nos are stored in reverse order for ease of calculation
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