CSC 225 Final ExamFinal Exam Time: Dec 10 2020 (Thursday) 8:00am-10:00am Topics covered ● Proof techniques (~30 points) 1. direct proof 2. proof by contrapositive 3. proof by contradiction 4. Inductive proof ● Algorithms (~30 points) 1. Algorithms using pseudo-codes 2. Non-recursive algorithms and recursive algorithms 3. Binary search merge sort 4. Analysis of algorithms ▪ Big-O notation ▪ Basic complexity classes: O(1) O(log n) O(n) O(nlog n) O(n 2 ) O(n 3 ) … O(2 n ) O(3 n ) … O(n!) ▪ Analysis of non-recursive algorithms ▪ Analysis of recursive algorithm ▪ recursively defined functions ▪ State the recurrence relation and solve it using Master Theorem ● Division Algorithm and Modular Arithmetic (~10 points) ● Graphs (~30 points) 1. Graph representation (set representation adjacency matrix and adjacency list) 2. Basic terminology: vertex edge neighbor degree simple graph multi-graph 3. Common graphs: Kn Qn Cn Kn m 4. Graph isomorphism 5. Walk trail circuit cycle path 6. Connected component vertex connectivity edge connectivity 7. Euler Circuit and Trail Hamiltonian Cycle and Path
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