Homework of AI
YingChen Shi DEP20 2012011722
1. Which of the following are true and which are fal? Explain your answers.
a. Depth-first arch always expands at least as many nodes as A∗arch with an admissible heuristic.
Fal. Depth-first arch may be lucky enough to prevent back-tracking and find the nodes for the first round of depth arch. But A* must go though at least all the surrounding nodes of the starting place.
b. h(n) = 0 is an admissible heuristic for the 8-puzzle.
True. The requirement for h(n) is that it is smaller than the real cost from vertex n to the goal. “h(n)=0” will never miss that requirement.
c. A∗ is of no u in robotics becau percepts, states, and actions are continuous.
Fal. All the percepts,actions and states change in robotics are ba on pattern arch. We do the arch work first and then convert the results to continuous actions, etc.
d. Breadth-first arch is complete even if zero step costs are allowed.
True. BFS can always be done if there is a goal, although it is not always the optimal one. And that is what complete means.
e. Assume that a rook can move on a chessboard any number of squares in a straight line, vertically or horizontally, but cannot jump over other pieces. Manhattan distance is an admissible heuristic for the problem of moving the rook from square A to square B in the smallest number of moves.
Fal. Manhattan distance is calculated at the default of that we can only move one squares at one time. So in this problem the Manhattan distance will be larger than the smallest number of moves.
2. A basic wooden railway t contains the pieces shown in the following figure. Th
e task is to
connect the pieces into a railway that has no overlapping tracks and no loo ends where a train could run off onto the floor.
a. Suppo that the pieces fit together exactly with no slack. Give a preci formulation of the task as a arch problem.
The formulation is as follows:
Well, contains 7 of the straight pieces. and both contains 6 curves and 2 fork pieces(a couple). contains 5 of the straight pieces. And contains 4 of the curves pieces.
b. Identify a suitable uninformed arch algorithm for this task and explain your choice.
DFS algorithm. Becau it has less capacity complexity and the same time complexity than other uninformed arch algorithm as there are too many cas in this problem. Moreover, we can find that the depth of this arching problem is 32 and every node has 31 branches (at most), but the solution is at the bottom of the tree. So I choo DFS but not IDS.
灰白色装修效果图
c. Explain why removing any one of the “fork” pieces makes the problem unsolvable.
“fork” pieces can only be ud in couples to form a connected graph, becau it has three branches. So the number of it must be even.
d. Give an upper bound on the total size of the state space defined by your formulation.
State space = Bm激发性欲 = 3132 .Where B is branching factor, m is the tree depth.
3. Prove each of the following statements, or give a counterexample:
a. Breadth-first arch is a special ca of uniform-cost arch.
BFS is a kind of enumeration arch algorithm as it iterates all child vertex for the next step first. So it is uninformed.
b. Depth-first arch is a special ca of best-first tree arch.
No, it’s an uninformed arch as it has no heuristic function to find the best choice.
c. Uniform-cost arch is a special ca of A∗ arch.
训斥反义词
No. A* arch is a ca of informed arch, but Uniform-cost arch is a ca of uninformed arch.
4. Trace the operation of A arch applied to the problem of getting ∗ to Bucharest from Lugoj using the straight-line distance heuristic. That is, show the quence of nodes that the algorithm will consider and the f , g, and h score for each node.
The result is as listed (“___” means that the node is chon to go on the arch and cannot be considered anymore):
Sequence NO. | city | g | h | f |
1a | Mehardia | 70 | 241 | 311 |
1b | 接受捐赠Timisoara迸发 | 111 | 329 | 440 |
2a | Dobreta | 145 | 242 | 387 |
3a | Craiova | 265 | 160 | 锅贴的做法425 |
4a | Rimnicu Vilcea | 411 | 193 | 604 |
4b | Pitesti | 403 | 98 | 501 |
5a | Bucharest | 504 | 0 | 504 |
| | | 卡农作者 | |
So the final way we find is Lugoj--- Mehardia--- Dobreta--- Craiova--- Pitesti--- Bucharest
5. The heuristic path algorithm (Pohl, 1977) is a best-first arch in which the evaluation function is f (n) = (2 − w)g(n) + wh(n). For what values of w is this complete? For what values is it optimal, assuming that h is admissible? What kind of arch does this perform for w = 0, w = 1, and w = 2?感冒咳嗽吃什么食物好
