Using the graph below, a. Draw an adjacency list and matrix. [5 MARKS EACH] b. Perform a depth first search using Vertex C as your source draw the resulting depth first search tree [10 2. a. Describe the concept of a Binary heap and the heap order property. [10 marks] b. Explain the use of the binary heap as an effective implementation for a priority queue [10 MARKS] 3. Create a class to implement a queue using a circular array[20 marks] a. The class should contain functions to i. Insert a new value, [5 marks] ii. Delete a value. [5 marks] iii. Change a value equal to X to a value equal to Y. [5 marks] iv. Count all value equal to X in the queue. [5 marks] b. For each function above perform an asymptotic analysis and state the worst case performance of the algorithm[5 marks] 4. a. Use Prim's algorithm starting at node A to compute the Minimum Spanning Tree (MST) of the following graph. In particular, write down the edges of the MST in the order in which Prim's algorithm adds them to the MST. Use the format (nodel; node2) to denote an edge. [8 marks] 10 20 H F b. For the same graph as above, write down the edges of the MST in the order in which Kruskal's algorithm adds them to the MST. [8 marks]