Data Structures and Algorithm Analysis Spring 2020 Post Midterm Exam – 100 points + 10 bonus NAME: 1. How much memory will the following structures take up? Hint: int takes 4 bytes, float takes 4 bytes, char takes 1 byte. – 9 points a. struct Structure1 {int a,b,c,d,e[10]; float f;}; b. struct Structure2 {int a[12]; float b[5];}; c. struct Structure3 {char a[10][12][4], b[5][5], c[10];}; 2. Show the steps when sorting (smallest to largest) the following arrays of numbers using selection sort i.e. every time a swap occurs, show what the current state of the array looks like, including the final sorted array. – 12 points a. [10, 2, 5, 8, 9, 1, 4, 7] b. [7, 1, 3, 2, 5, 4, 8, 12, 9] c. [8, 7, 6, 5, 4, 3, 2, 1] d. [5, 3, 8, 1, 9, 4, 2, 6] 3. Big-O: What is meant by f(n) = O(g(n))? Give the definition and then explain what it means in your own terms. – 5 points 4. Big-Omega: What is meant by f(n) = Ω(g(n))? Give the definition and then explain what it means in your own terms. – 5 points 5. Show that , make sure you use the definition and justify the inequalities and constants used. - 4 points 6. Show that , make sure you use the definition and justify the inequalities and constants used. - 4 points 7. Show that , make sure you use the definition and justify the inequalities and constants used. - 4 points 8. Show that , make sure you use the definition and justify the inequalities and constants used. - 4 points 9. Show that , make sure you use the definition and justify the inequalities and constants used. - 4 points 10. What principle governs how you add/remove elements in a stack? Spell it out and briefly explain. - 4 points 11. Briefly describe an application of a stack. - 4 points 12. What principle governs how you add/remove elements in a queue? Spell it out and briefly explain. - 4 points 13. Briefly describe an application of a queue. - 4 points Consider the following graph (pseudocode for BFS and DFS given on page 9): 14. Write the order in which the nodes would be visited in when doing a breadth first search (BFS) traversal starting at node 4. Also, write the distances from 4 to every other node. - 6 points 15. Write the order in which the nodes would be visited in when doing a breadth first search (BFS) traversal starting at node 5. Also, write the distances from 5 to every other node. - 6 points Same graph (for your convenience): 16. Write the order in which the nodes would be visited in when doing a depth first search (DFS) traversal starting at node 4 (order discovered or order off the stack). - 6 points 17. Write the order in which the nodes would be visited in when doing a depth first search (DFS) traversal starting at node 5 (order discovered or order off the stack). - 6 points 18. Give the definition of a graph. - 5 points 19. Give the definition of a tree (from graph theory). - 4 ...