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Topic: Unbounded Multiplication (Read 1181 times) |
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mad
Junior Member
Posts: 118
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Unbounded Multiplication
« on: Mar 8th, 2008, 5:35pm » |
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Write a program to calculate factorial of nos till 300! or even 400!
Should we use normal multiplication technique storing each digit in a number as an integer and then multiplying normally or Karatsuba algorithm etc. is required?
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SMQ
wu::riddles Moderator
Uberpuzzler
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Re: Unbounded Multiplication
« Reply #1 on: Mar 10th, 2008, 6:13am » |
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Three or four hundred factorial is still under a thousand (decimal) digits -- and only around 2000 bits -- not really much of a stress for a modern computer. "Gradeschool" multiplication and a naive factorial algorithm (just multiply by each number) will work just fine.
#include <iostream>
#include <vector>
using namespace std;
class bigint {
vector<unsigned long> digits; // each element stores 9 decimal digits
public:
bigint(unsigned long x) { digits.push_back(x); }
bigint & operator *= (unsigned long x) {
unsigned long long t = 0;
for(unsigned int i = 0; i < digits.size(); i++) {
t += digits[i] * (unsigned long long)(x);
digits[i] = (unsigned long)(t % 1000000000UL);
t /= 1000000000UL;
}
if (t != 0) digits.push_back(t);
return *this;
}
friend ostream & operator << (ostream & o, const bigint & x);
};
ostream & operator << (ostream & o, const bigint & x) {
// print first digit group without leading zeros
o << x.digits.back();
// print rest of digit groups with leading zeros
int width = o.width(); char fill = o.fill('0');
for(unsigned int i = x.digits.size(); i > 1; i--) {
o.width(9); o << x.digits[i-2];
}
o.width(width); o.fill(fill);
return o;
}
int main(void) {
const unsigned long N = 400;
bigint f(1);
for(unsigned long i = 2; i <= N; i++) f *= i;
cout << f;
return 0;
}
Now, if you wanted a million factorial, that would be more challenging. The biggest improvement would be to use a better factorial algorithm; calculate the number of factors of each prime which will be present in the result (in the same way that "how many zeros in n!" is solved), then use a parallel binary powering algorithm to do the calculation. At those sizes, Karatsuba would probably help, although only for the largest few multiplications.
--SMQ
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--SMQ
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johny_cage
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Re: Unbounded Multiplication
« Reply #2 on: Mar 20th, 2008, 7:09am » |
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I already calculate 1,00,000 factorial using linked list. It took around 35 mins on my 3 Ghz 64-bit Intel PC with 512 MB RAM support. So, you can easily do with linked list (storing 9 digits in each node).
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