C# can cast LINQ Aggregate to double to output factorial, this works for integer up to 12

Question

I want to fill the list with factorials using linq. I got this, this works up to 12. I assume it's because of the integer range. But I couldn't retype it to double. Can this be easily modified (retyped)?

var listOfFactorials = from fact in Enumerable.Range(0, 171).Reverse().ToList() select new { Number = fact, Factorial = (fact == 0) ? 1d : Enumerable.Range(1, fact).Aggregate((i, j) => (i * j))};

I want to have the list filled with factorials up to the number 170. I don't need it for anything, just playing for fun :)

Answer 1

You have to use BigInteger:

var listOfFactorials = from fact in Enumerable.Range(0, 200).Reverse().ToList()
                        select new 
                        { 
                            Number = fact, 
                            Factorial = (fact == 0) ? BigInteger.One : Enumerable.Range(1, fact)
                                                                                 .Select( i => new BigInteger(i))
                                                                                 .Aggregate((i, j) => (i * j))
                        };

Answer 2

You don't want double - it only gives you 15 digits of precision in exchange for the larger range. You want to use either long or BigInteger.

You can either convert the integers returned from Range before calling Aggregate:

Enumerable.Range(1, fact)
          .Select(i => new BigInteger(i))
          .Aggregate((i, j) => (i * j))};

or use the more verbose version of Aggregate where you specify the types separately:

Enumerable.Range(1, fact)
          .Aggregate<int, BigInteger>(new BigInteger(1), (i, j) => (i * j))

Note that Long will overflow at 67! while BigInteger is unbounded in theory

Answer 3

Note that your Aggregate is not very efficient since it recalculates from 1 to n every time, if you start with 1, you can just do one multiple for each subsequent value:

var listOfFactorials = Enumerable.Range(1, 170)
                                 .Aggregate(new[] { new { Number = 0, Factorial = BigInteger.One } }.ToList(),
                                            (ans, n) => { ans.Add(new { Number = n, Factorial = ans.Last().Factorial * n }); return ans; })
                                 .AsEnumerable()
                                 .Reverse();

Since the sequence is initialized with the 0 value, the range must start at 1 for one fewer values.

A simpler (and probably more understandable) method would be to just use a for loop:

var ans = new[] { new { Number = 0, Factorial = BigInteger.One } }.ToList();
var Factorial = BigInteger.One;
for (int Number = 1; Number < 171; ++Number) {
    Factorial *= Number;
    ans.Add(new { Number, Factorial });
}
ans.Reverse();