Past exam of the year 1 of the computer science course of the University of Oxford / 2018 / Functional programming, design and analysis of algorithms / 1 / b / Solution

Count each data constructor once, including each Two:

size :: Tree a -> Int
size (One _)   = 1
size (Two l r) = 1 + size l + size r

Structural induction verifies the count: a leaf contributes one; an internal node contributes itself and the disjoint occurrences in its two subtrees. Fully evaluating the result takes linear time in the number of nodes. This type signature uses machine Int as usual in the examination; Integer avoids overflow for arbitrarily large inputs.