+1 vote
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Consider the code below, defining the function $mystery:$

mystery(a,b){
if (a < 0 or b < 0) return 0;
else if (a == 0) return b+1;
else if (b == 0) return mystery(a-1,1);
else return mystery(a-1, mystery(a,b-1));
}
1. Express $mystery(1, \:n)$ as a function of $n$.
2. Express $mystery(2,\: n)$ as a function of $n$.
3. Compute $mystery(3, \:2)$ and $mystery(3, 3)$.

+1 vote
i) mystry(1,n)=n+2

ii)mystry(2,0)=3

mystry(2,1)=5

mystry(2,2)=7

.................

mystry(2,n)=2n+3

iii) mystry(1,1)=mystry(0,2)=3

as, mystry(1,0)=3

mystry(0,1)=2

mystery(1,2)=mystery(0,mystery(1,1))=mystery(0,3)=4

mystery(2,1)=mystery(1,mystery(2,0))=mystery(1,3)=5

mystery(1,3)=5

mystery(3,0)=mystery(2,1)=5

mystery(3,1)=mystery(2,mystery(3,0))=mystery(2,5)=13

As, mystery(2,5)=mystery(1,mystery(2,4))=13

mystery(2,4)=mystery(1,mystery(2,3))=11

mystery(2,3)=mystery(1,mystery(2,2))=9

mystery(2,2)=mystery(1,mystery(2,1))=7

mystery(3,2)=mystery(2,mystery(3,1))=mystery(2,13)=29 [By putting above formula 2n+3 we also can get it]

i. mystery(1,n) = n+2

ii. mystery(2,n)=2n + 3

iii. mystery(3,2)= 29 and mystery(3,3)= 61