graphs find(routine from linklist to search for an unvisited vertex rather than for key value modify the dfs java program (listing to display connectivity table for directed graphas described in the section "connectivity in directed graphs implement warshall' algorithm to find the transitive closure for graph you could start with the code from programming project it' useful to be able to display the adjacency matrix at various stages of the algorithm' operation the knight' tour is an ancient and famous chess puzzle the object is to move knight from one square to another on an otherwise empty chess board until it has visited every square exactly once write program that solves this puzzle using depth-first search it' best to make the board size variable so that you can attempt solutions for smaller boards the regular board can take years to solve on desktop computerbut board takes only minute or so refer to the section "depth-first search and game simulationsin this it may be easier to think of new knight being created and remaining on the new square when move is made this waya knight corresponds to vertexand sequence of knights can be pushed onto the stack when the board is completely filled with knights (the stack is full)you win in this problem the board is traditionally numbered sequentiallyfrom at the upper-left corner to at the lower-right corner (or to on boardwhen looking for its next movea knight must not only make legal knight' moveit must also not move off the board or onto an already-occupied (visitedsquare if you make the program display the board and wait for keypress after every moveyou can watch the progress of the algorithm as it places more and more knights on the boardand thenwhen it gets boxed inbacktracks by removing some knights and trying different series of moves we'll have more to say about the complexity of this problem in the next