Mathijs - 1 year ago 76
C# Question

# Why is the following code wrong? binomial coefficient

I am doing project euler and i am at problem 15 now, here is a link:
https://projecteuler.net/problem=15 . I am trying to solve this with binomial coefficient. Here is a site that explains it: http://www.mathblog.dk/project-euler-15/ . You can find it at the bottom.

My question is, why is the following code wrong? Since this follows the mathematical algorithm I think: n-k+i/i

``````        int grid = 20;
long paths = 1;
for (int i = 0; i < grid; i++)
{
paths *= (grid * 2) - (grid + i)
paths /= (i + 1);
}
Console.WriteLine(paths);
``````

And why is this code wrong? This is exactly as the mathblog site but in 1 line.

``````        int grid = 20;
long paths = 1;
for (int i = 0; i < grid; i++)
{
paths *= ((grid * 2) - i) / (i + 1);
}
Console.WriteLine(paths);
``````

But why is this code right then? Isnt it the same as the previous code? And it doesn't exactly follow the mathematical algorithm does it? Because it's n-k+i/i, and this code does n-i/i

``````       int grid = 20;
long paths = 1;
for (int i = 0; i < grid; i++)
{
paths *= ((grid * 2) - i);
paths /=  (i + 1);
}
Console.WriteLine(paths);
``````paths = (path *((grid * 2) - i))/(i + 1);