The network topology is represented as a graph, where each node represents a location, and edges between nodes signify possible connections or links. Each edge is associated with a certain latency. Develop an exhaustive search algorithm that exhaustively explores all possible routing paths between the source and destination nodes, evaluating the total latency incurred along each path. The algorithm must systematically examine all potential paths and determine the one with the minimum latency. Provide the pseudo code and analyze the time complexity (Big-Oh notation) of your proposed algorithm