1. The single-destination shortest path problem for a directed graph is to find the shortest path from every other vertex to a specified vertex destV. Give an efficient algorithm (pseudo code) to solve the single-destination shortest paths problem.
2. Illustrate the operation of COUNT-SORT on an array [6, 0, 2, 1, 3, 3, 5, 3, 2, 1]
3. Design a BFS-based algorithm (pseudo code) for directed graph that computes the shortest distance (or the least number of vertices in-between) from vertex srcU to vertex destV.
4. Consider a hash table of size 7 with hash function h(k)=k mod 7. Draw the table that results after inserting, in the given order, the following values: 19, 26,13,48,17 with respect to following three different scenario: (1) the collision is handled by separate chaining; (2) the collision is handled by linear probing; (3) the collision is handled by double-hashing using a second hash function: h* = 5 - (k mod 5). (Notes: several techniques involved in this question were not emphasized in the class, you have to master them via slides or check the document in BlackBoard)
5. Design an algorithm (pseudo code) that returns the SECOND largest key value of a Black-Red Tree. In addition, you can use diagrams to demonstrate that your algorithm make sense.