I just asked another question about pascal triangle about finding sum of 1500th row. I'm so glad that people answered so quickly, But unfortunately later i realized, i need each individual number on 1500th row.
Here i found an easy way to calculate any number on pascal triangle but when i try to use formula in my code, program crashes in start.
#include"stdio.h"
int factorial(int);
int main()
{
int i=0;
for(i=0; i<1501; i++)
{
printf("%d \n" , (factorial(1500)/factorial(1500-i))/factorial(i) );
}
}
int factorial(int x)
{
if(x<2)
return 1;
else
{
return x*factorial(x-1);
}
}
You need a biginteger library for the results, since
binom(1500,750) = 722462892448930217028116073228485295944376343040546523665632913653613596406381727723198055046187955623124069093412562720869577867557610868874271130828359513282184417776042792372322074253393127328396528996120053749558122610911178218582669317535346728464707661495135518682519172221470420360910320792434869988224466647627642393919250205687942318888922893189087379790541907686956429837978631252775258630376332505697937034877619012586751274240109457111424
exceeds even the usual double
range.
But with such a type available, the relation
binom(n,k+1) = binom(n,k)*(n-k)/(k+1)
allows a simple, relatively efficient implementation:
bigint value = 1;
int numerator = 1500 + 1, denominator = 0;
for(; denominator <= 1500; --numerator, ++denominator, value = value*numerator/denominator)
{
output(value);
}
where output
is whatever output method the library provides.
The value = value*numerator/denominator
part needs to be adapted if the library doesn't offer overloads for multiplying/dividing bigintegers and normal int
s.