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This one tells you if a graph edge _is_ a bridge (i.e. it has inverted sense to the existing is_loop_edge query). But it also returns auxiliary data, telling you: _if_ this edge were removed, and thereby disconnected some connected component of the graph, what would be the sizes of the two new components? The data structure built up by the algorithm very nearly contained enough information to answer that already: because we assign sequential indices to all the vertices in a traversal of our spanning forest, and any bridge must be an edge of that forest, it follows that we already know the size of _one_ of the two new components, just by looking up the (minindex,maxindex) values for the vertex at the child end of the edge. To determine the other subcomponent's size, we subtract that from the size of the full component. That's not quite so easy because we don't already store that - but it's trivial to annotate every vertex's data with a pointer back to the topmost node of the spanning forest in its component, and then we can look at the (minindex,maxindex) pair of that. So now we know the size of the original component and the size of one of the pieces it would be split into, so we can just subtract.
This is the README accompanying the source code to Simon Tatham's puzzle collection. The collection's web site is at <https://www.chiark.greenend.org.uk/~sgtatham/puzzles/>. If you've obtained the source code by downloading a .tar.gz archive from the Puzzles web site, you should find several Makefiles in the source code. However, if you've checked the source code out from the Puzzles git repository, you won't find the Makefiles: they're automatically generated by `mkfiles.pl', so run that to create them. The Makefiles include: - `Makefile.am', together with the static `configure.ac', is intended as input to automake. Run `mkauto.sh' to turn these into a configure script and Makefile.in, after which you can then run `./configure' to create an actual Unix Makefile. - `Makefile.vc' should work under MS Visual C++ on Windows. Run 'nmake /f Makefile.vc' in a Visual Studio command prompt. - `Makefile.cyg' should work under Cygwin / MinGW. With appropriate tweaks and setting of TOOLPATH, it should work for both compiling on Windows and cross-compiling on Unix. - `Makefile.osx' should work under Mac OS X, provided the Xcode tools are installed. It builds a single monolithic OS X application capable of running any of the puzzles, or even more than one of them at a time. - `Makefile.wce' should work under MS eMbedded Visual C++ on Windows and the Pocket PC SDK; it builds Pocket PC binaries. Many of these Makefiles build a program called `nullgame' in addition to the actual game binaries. This program doesn't do anything; it's just a template for people to start from when adding a new game to the collection, and it's compiled every time to ensure that it _does_ compile and link successfully (because otherwise it wouldn't be much use as a template). Once it's built, you can run it if you really want to (but it's very boring), and then you should ignore it. DO NOT EDIT THE MAKEFILES DIRECTLY, if you plan to send any changes back to the maintainer. The makefiles are generated automatically by the Perl script `mkfiles.pl' from the file `Recipe' and the various .R files. If you need to change the makefiles as part of a patch, you should change Recipe, *.R, and/or mkfiles.pl. The manual is provided in Windows Help format for the Windows build; in text format for anyone who needs it; and in HTML for the Mac OS X application and for the web site. It is generated from a Halibut source file (puzzles.but), which is the preferred form for modification. To generate the manual in other formats, rebuild it, or learn about Halibut, visit the Halibut website at <https://www.chiark.greenend.org.uk/~sgtatham/halibut/>.