Fundamentals of algorithms

State the time complexity in Big-O notation of a linear search, a binary search and a bubble sort, and explain why binary search is more efficient for large data sets.

A weighted undirected graph has edges A–B 4, A–C 2, B–C 1, B–D 5, C–D 8, C–E 10, D–E 2, D–F 6, E–F 3. Use Dijkstra's algorithm to find the shortest distance from A to every other node and the shortest path from A to F.

Convert (5 + 2) × (8 − 3) into Reverse Polish notation and evaluate it, explaining why RPN suits stack-based evaluation.