 Hello everyone, this is Alice Gao. In this video, I will solve the question regarding the optimality of lowest cost first surge with multi-path pruning. The question asks, is there a situation in which LCFS with multi-path pruning discards the optimal solution? The correct answer is no. This is not possible. Here's the intuition. LCFS is a cautious search strategy. It does not use heuristics. It only considers the actual cost of each path found. The algorithm always explores the path with the smallest cost first. For example, it will first explore all of the path with a total cost of 1. After that, it will move on to all of the path with a total cost of 2 and 3 and 4 and so on. If the algorithm always explores the path in order of increasing costs, then it should never run into a case where it finds a longer path to a node first and then a shorter path to a node later on. I have also included an informal proof by contradiction. It starts by assuming that LCFS finds a longer path before finding a shorter path. Next, I show that this is impossible based on how the algorithm selects which path to expand at each step. That's everything on this question regarding LCFS search with multi-path pruning. Thank you very much for watching. I will see you in the next video. Bye for now.