theory

I have an AST, represented in the usual way (a tree of nodes of an abstract type). I have several uses cases for traversing this tree (an optimizer, which returns another AST; IR code generation, which returns a llvm::Value* ; and a debug analyzer, which simply outputs to stdout and returns nothing). A visitor feels like the right way to go here, but the differing return types through each use case of the visitor make it hard to see how to implement an interface for this. I considered this: class Visitor; class ASTNode { public: virtual void accept(Visitor *visitor); }; class Visitor { public:

I recently wrote a Vector 3 class, and I submitted my normalize() function for reviewal to a friend. He said it was good, but that I should multiply by the reciprocal where possible because "multiplying is cheaper than dividing" in CPU time. My question simply is, why is that? Think about it in terms of elementary operations that hardware can more easily implement -- add, subtract, shift, compare. Multiplication even in a trivial setup requires fewer such elementary steps -- plus, it afford advances algorithms that are even faster -- see here for example... but hardware generally doesn't take

Does there exist a travelling salesman problem where the optimal solution has edges that cross? The nodes are in an x-y plane, so crossing in this case means if you were to draw the graph, two line segments connecting four separate nodes would intersect. If two edges in a closed polygonal line cross, then there is a polygonal line with the same vertices but with smaller perimeter. This is a consequence of the triangle inequality. So, a solution to the TSP must be a simple polygon. See this article (Figure 4). If you consider a non-Euclidean metric like L1 (Manhattan distance), then it's pretty