1. _F_ The reverse postorder of a digraphs reverse is the same as the postorder of the digraph.

2. _F_ Adding a constant to every edge weight does not change the solution to the single-source shortest-paths problem.

3. ___ An optimization problem is a good candidate for dynamic programming if the best overall solution can be defined in terms of optimal solutions to subproblems, which are not independent.

4. ___ If we modify the Kosaraju algorithm to run first depth-first search in the digraph G (instead of the reverse digraph GR) and the second depth-first search in GR (instead of G), the algorithm will find the strong components.

5. ___ If you insert keys in increasing order into a red-black BST, the tree height is monotonically increasing.

6. ___ A good hash function should be deterministic, i.e., equal keys produce the same hash value.

7. ___ In the situation where all keys hash to the same index, using hashing with linear probing will result in O(n) search time for a random key.

8. ___ Hashing is preferable to BSTs if you need support for ordered symbol table operations.

9. ___ In an adjacency list representation of an undirected graph, v is in ws list if and only if w is in vs list.

10. ___ Every directed, acyclic graph has a unique topological ordering.

11. ___ Preorder traversal is used to topologically sort a directed acyclic graph.

12. ___ MSD string sort is a good choice of sorting algorithm for random strings, since it examines N logR N characters on average (where R is the size of the alphabet).

13. ___ The shape of a TST is independent of the order of key insertion and deletion, thus there is a unique TST for any given set of keys.

14. ___ In a priority queue implemented with heaps, N insertions and N removeMin operations take O(N log N).

15. ___ An array sorted in decreasing order is a max-oriented heap.

16. ___ If a symbol table will not have many insert operations, an ordered array implementation is sufficient.

17. ___ The floor operation returns the smallest key in a symbol table that is greater than or equal to a given key.

18. ___ The root node in a tree is always an internal node.

is this true or false? Could you explain?