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Приведем пример простой рекурсивной функции:
Create Function dbo.Factorial(@I integer)
Returns Integer
Begin
If @I <= 0 Return 1
Return dbo.Factorial(@I-1)*@i
End
Функция вызывает сама себя, если параметр @I больше нуля. Количество вызовов зависит от величины @I-го параметра.
Например,
Factorial(0) = 1
Factorial(1) = 1 * 1 = 1
Factorial(2) = 1 * 2 = 2
Factorial(3) = 1 * 2 * 3 = 6
Factorial(4) = 1 * 2 * 3 * 4 = 24
....
Разберем работу функции на примерах подстановки значений параметра:
Factorial(1)
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= Factorial(1-1) * 1, где
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Factorial(1-1)
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= Factorial(0)
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= 1
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Factorial(1)
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= 1 * 1 = 1
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Factorial(2)
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= Factorial(2-1) * 2, где
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Factorial(2-1)
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= Factorial(1)
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Factorial(1)
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= Factorial(1-1) * 1 = Factorial(0) * 1 = 1 * 1
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= 1
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Factorial(2)
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= 1 * 2 = 2
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Factorial(3)
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= Factorial(3-1) * 3, где
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Factorial(3-1)
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= Factorial(2)
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Factorial(2)
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= Factorial(2-1) * 2, где
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Factorial(2-1)
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= Factorial(1) = Factorial(1-1) * 1 = Factorial(0) * 1 = 1 * 1
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= 1 * 2
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= 2
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Factorial(3)
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= 2 * 3 = 6
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Factorial(4)
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= Factorial(4-1) * 4, где
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Factorial(4-1)
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= Factorial(3)
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Factorial(3)
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= Factorial(3-1) * 3, где
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Factorial(3-1)
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= Factorial(2)
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= Factorial(2-1) * 2, где
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Factorial(2-1)
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= Factorial(1) = Factorial(1-1) * 1 = Factorial(0) * 1 = 1 * 1
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= 1
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= 1 * 2
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= 2
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= 2 * 3
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= 6
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Factorial(4)
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= 6 * 4 = 24
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См. далее: Пример применения рекурсивной функции
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