algorithms: true/false

1. In the stable matching problem with n men and n women, if a man and a woman are each other's last preference, then they will never be matched with each other in any stable matching.

2. In an unweighted strongly connected (directed) graph, the shortest distance from A to B is always the same as that from B to A.

3. If the heaviest weight edge e in an undirected connected graph G is unique, then e cannot belong to any spanning tree of G.

4. A directed graph has a topological ordering if and only if it contains no cycle.

5. Given a graph G, if there is no negative cost cycles in G, then Dijkstras algorithm will work correctly on G.

6. In a weighted undirected graph, the shortest distance from A to B is always the same as that from B to A.

7. We can find the k-th largest element in a binary max heap in (1) time.