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Consider the code below, defining the function $A$:

A(m, n, p) {
if (p == 0) return m+n;
else if (n == 0 && p == 1) return 0;
else if (n == 0 && p == 2) return 1;
else if (n == 0) return m;
else return A(m, A(m,n-1,p), p-1);
}

Express $A(m, n, 1)$ as a function of $m$ and $n$.

| 66 views

A(m, n, 1) = A(m, A(m, n -1, 1) ,0)

To compute this we solve the base cases first:

The base case is : A(m, 0, 1) = 0 = m∗0
So the value of  : A(m,n -1,1) = m(n-1)

So A(m,n,1)=A(m, m(n-1) ,0)

=m+m(n-1)

A(m,n,1) =mn

by Boss (38.3k points)

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