Homework 1

Email me your answers to the following two problems. For problem 1, you should provide a list of numbers of states for each of the search methods. For problem 2, you should provide two answers for each of the search strategies: the states expanded and the solution.

Problem 1

In the state space shown below, write the order in which states are expanded if the initial state is 4 and there are two goal states: 5 and 8.

For example, for breadth first search the answer would be: 4 2 7 1 3 6 8

Problem 2

Alice the agent wants to go skiing right after AI class is over. She starts in the lecture hall (the "Start" state below) and wants to make it to Alta (the "Goal" state) as soon as possible. There are several possible paths she can take denoted in the graph below:

The available actions at each state are denoted by arrows with a path cost label above each arrow. For each of the following graph search strategies, figure out the order in which states are expanded as well as the path returned by graph search. When choosing an arbitrary order of state expansions (to break ties), use an alphabetical ordering. Remember that in graph search, states are expanded only once.

  1. Depth first search

  2. Breadth first search

  3. Uniform cost search

  4. A* search