Design and analysis algorithm course

Remarks: All the graphs here are without self loops and parallel or anti-parallel edges. In all the algorithms, always explain their correctness and analyze their complexity. The complexity should be as small as possible. A correct algorithm with large complexity, may not get full credit. The number of vertices is denoted by n, and the number of edges by m. Please use only things taught in class (do not use, for example DFS on directed graphs)