Nivaar worked solution (AI-drafted; not reviewed by a licensed engineer)
National Exams — May 2013 — 04-Soft-A1 Algorithms & Data Structures. Three-hour, closed-book exam (Casio or Sharp approved calculator only). Format: eight questions in two parts — candidates choose 4 of the first 5 (10 marks each) and must answer Q6, Q7 and Q8 (20 marks each), with Q7 itself asking for 5 of 6 sub-concepts. All eight questions, and all sub-parts within them, are solved below for completeness.
Reference texts: Cormen, Leiserson, Rivest & Stein, Introduction to Algorithms (3rd ed., MIT Press) — asymptotic analysis, heaps, graph algorithms, divide-and-conquer, NP-completeness; Sedgewick & Wayne, Algorithms (4th ed., Addison-Wesley) — linked-list and array data structures, sorting; Weiss, Data Structures and Algorithm Analysis in C (2nd ed., Pearson) — array-based binary trees and heaps.
