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Objective
Learn to pass parameters and write a simple recursive subroutine.
Background
In the previous lab, you were required to write a program to accept a positive integer value N, use a subroutine to compute Y where
and print the result on the screen. Let's rewrite this as
Y (M, N) = Y(M) + Y(N)
where
The same problem can be solved recursively. To do that, let's define this function Y(P) as follows:
1. Y(1) = 1. This is the base case.
2. Y(P) = P + Y(P-1).
Notice that Y(P) is defined in terms of a simpler version of itself.
For example, let's say we wish to compute Y(4). The steps would then be
Y(4) = 4 + Y(3) we need to find Y(3) before we can finish computing Y(4)Y(4) = 4 + (3 + Y(2)) now we need to find Y(2)Y(4) = (3 + (2 + Y(1))) and now we need Y(1)Y(4) = 4 + (3 + (2 + 1)) but Y(1) is 1 from our base caseY(4) = 4 + (3 + 3) evaluate and finishY(4) = 4 + 6Y(4) = 10
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