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The following program is an example in Scheme: [8];; factorial : number ... But prefixing a value at the start of a list on exit from a recursive call is the ...
The code above will execute at run time to determine the factorial value of the literals 0 and 4. By using template metaprogramming and template specialization to provide the ending condition for the recursion, the factorials used in the program—ignoring any factorial not used—can be calculated at compile time by this code:
Dim counter As Integer = 5 ' init variable and set value Dim factorial As Integer = 1 ' initialize factorial variable Do While counter > 0 factorial = factorial * counter counter = counter-1 Loop ' program goes here, until counter = 0 'Debug.Print factorial ' Console.WriteLine(factorial) in Visual Basic .NET
For example, the template base class in the Factorial example below is implemented by matching 0 rather than with an inequality test, which was previously unavailable. However, the arrival in C++11 of standard library features such as std::conditional has provided another, more flexible way to handle conditional template instantiation.
Let be a natural number. For a base >, we define the sum of the factorials of the digits [5] [6] of , :, to be the following: = =!. where = ⌊ ⌋ + is the number of digits in the number in base , ! is the factorial of and
The factorial number system is sometimes defined with the 0! place omitted because it is always zero (sequence A007623 in the OEIS). In this article, a factorial number representation will be flagged by a subscript "!". In addition, some examples will have digits delimited by a colon. For example, 3:4:1:0:1:0! stands for
n > 0 is the number of letters in the alphabet (e.g., 26 in English) the falling factorial = (+) denotes the number of strings of length k that don't use any character twice. n! denotes the factorial of n; e = 2.718... is Euler's number; For n = 26, this comes out to 1096259850353149530222034277.
For example, a break statement would allow termination of an infinite loop. Some languages may use a different naming convention for this type of loop. For example, the Pascal and Lua languages have a "repeat until" loop, which continues to run until the control expression is true and then terminates.