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In this manner, the do ... while loop saves the initial "loop priming" with do_work(); on the line before the while loop.. As long as the continue statement is not used, the above is technically equivalent to the following (though these examples are not typical or modern style used in everyday computers):
A representative example in Python is: ... = 1 for counter from 2 to 5 factorial := factorial * counter counter:= counter - 1 print counter + "! equals " + factorial ...
For example, 9!! = 1 × 3 × 5 × 7 × 9 = 945. Double factorials are used in trigonometric integrals, [92] in expressions for the gamma function at half-integers and the volumes of hyperspheres, [93] and in counting binary trees and perfect matchings. [91] [94] Exponential factorial
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
This is an example of an asymptotic expansion. It is not a convergent series; for any particular value of ... However, the gamma function, unlike the factorial, is ...
A classic example of recursion is the definition of the factorial function, given here in Python code: def factorial ( n ): if n > 0 : return n * factorial ( n - 1 ) else : return 1 The function calls itself recursively on a smaller version of the input (n - 1) and multiplies the result of the recursive call by n , until reaching the base case ...
In this particular example, if factorial is first invoked with 5, and then invoked later with any value less than or equal to five, those return values will also have been memoized, since factorial will have been called recursively with the values 5, 4, 3, 2, 1, and 0, and the return values for each of those will have been stored. If it is then ...
For example, in the factorial function, properly the base case is 0! = 1, while immediately returning 1 for 1! is a short circuit, and may miss 0; this can be mitigated by a wrapper function. The box shows C code to shortcut factorial cases 0 and 1.