Morris' tree traversal algorithm reconsidered

In 1968, Knuth posed the problem of designing a stack-free, tag-free, non-recursive algorithm that traversed the tree in in-order while leaving it unaltered in the end. Since then, numerous solutions have appeared in the literature. The 1979 algorithm by Morris is one of the most elegant of these solutions. The algorithm is clearly non-recursive, and appears, at first glance, to use neither a stack, nor tag fields. We present an insightful derivation of this algorithm. We also show that a stack is indeed present and ‘time-shares’ the right-link fields of the tree nodes. Our proof comes in two parts: (a) We start with a traversal algorithm that explicitly uses a stack, and show that it is computationally equivalent to another that uses a non-standard implementation of a stack; (b) We then show that the later algorithm can be transformed to Morris' algorithm using only control structure transformations.