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[!PREREQUISITE]
前面有很多探索，希望看正确解答可直接看 "right"；最终结果见 "pass" 。
pacman.py 的参数对于对于帮助我们进行测试很有用：
$ python pacman.py -h
Usage:
USAGE: python pacman.py <options>
EXAMPLES: (1) python pacman.py
- starts an interactive game
(2) python pacman.py --layout smallClassic --zoom 2
OR python pacman.py -l smallClassic -z 2
- starts an interactive game on a smaller board, zoomed in
Options:
-h, --help show this help message and exit
-n GAMES, --numGames=GAMES
the number of GAMES to play [Default: 1]
-l LAYOUT_FILE, --layout=LAYOUT_FILE
the LAYOUT_FILE from which to load the map layout
[Default: mediumClassic]
-p TYPE, --pacman=TYPE
the agent TYPE in the pacmanAgents module to use
[Default: KeyboardAgent]
-t, --textGraphics Display output as text only
-q, --quietTextGraphics
Generate minimal output and no graphics
-g TYPE, --ghosts=TYPE
the ghost agent TYPE in the ghostAgents module to use
[Default: RandomGhost]
-k NUMGHOSTS, --numghosts=NUMGHOSTS
The maximum number of ghosts to use [Default: 4]
-z ZOOM, --zoom=ZOOM Zoom the size of the graphics window [Default: 1.0]
-f, --fixRandomSeed Fixes the random seed to always play the same game
-r, --recordActions Writes game histories to a file (named by the time
they were played)
--replay=GAMETOREPLAY
A recorded game file (pickle) to replay
-a AGENTARGS, --agentArgs=AGENTARGS
Comma separated values sent to agent. e.g.
"opt1=val1,opt2,opt3=val3"
-x NUMTRAINING, --numTraining=NUMTRAINING
How many episodes are training (suppresses output)
[Default: 0]
--frameTime=FRAMETIME
Time to delay between frames; <0 means keyboard
[Default: 0.1]
-c, --catchExceptions
Turns on exception handling and timeouts during games
--timeout=TIMEOUT Maximum length of time an agent can spend computing in
a single game [Default: 30]若加入下列语句，测试运行：
print("Start:", problem.getStartState())
print("Is the start a goal?", problem.isGoalState(problem.getStartState()))
print("Start's successors:", problem.getSuccessors(problem.getStartState()))
# Start: (5, 5)
# Is the start a goal? False
# Start's successors: [((5, 4), 'South', 1), ((4, 5), 'West', 1)]窥见了 problem/state 的结构，其中 successors 是两个 successor，其内容依次代表：(state，action，cost) => （坐标，方向，步长）。
随便补全 dfs 观察地图：
def depthFirstSearch(problem: SearchProblem):
return []
util.raiseNotDefined()可以看出来，“坐标原点”在左下角，是经典的“2D函数坐标”而非“矩阵坐标”。
根据以前所学，dfs尝试 Q1：
def depthFirstSearch(problem: SearchProblem):
reached = set() # 记录已经访问过的节点
_stack = util.Stack() # 用栈来实现DFS
_stack.push(
(problem.getStartState(), [])
) # 将初始状态（坐标，到达该坐标需要的方向组）压入栈中
while not _stack.isEmpty():
state, actions = _stack.pop()
if problem.isGoalState(state):
return actions
if state not in reached:
reached.add(state)
for successor, action, _ in problem.getSuccessors(state):
new_path = actions + [action]
_stack.push((successor, new_path))
return actions
util.raiseNotDefined()
下一个？NO! 在 note02 中我们知道三个搜索算法总体差不多，且这里都是 graph search:
[!CITE]
Now it’s time to write full-fledged generic search functions to help Pacman plan routes! Pseudocode for the search algorithms you’ll write can be found in the lecture slides.
function GRAPH-SEARCH(problem, frontier) return a solution or failure
reached ← an empty set
frontier ← INSERT(MAKE-NODE(INITIAL-STATE[problem]), frontier)
while not IS-EMPTY(frontier) do
node ← POP(frontier)
if problem.IS-GOAL(node.STATE) then
return node
end
if node.STATE is not in reached then
add node.STATE in reached
for each child-node in EXPAND(problem, node) do
frontier ← INSERT(child-node, frontier)
end
end
end
return failure所以我们照猫画虎，给出：
def graphSearch(problem, frontier):
"""
Implements the graph search algorithm using the provided frontier data structure.
"""
reached = set()
frontier.push((problem.getStartState(), [])) # take (state, actions) as node
while not frontier.isEmpty():
state, actions = frontier.pop()
if problem.isGoalState(state):
return actions
if state not in reached:
reached.add(state)
for successor, action, _ in problem.getSuccessors(state):
new_path = actions + [action]
frontier.push((successor, new_path))
return None # No solution found显然，这里的 frontier 在 DFS 中就是 Stack，在 BFS 中就是 Queue；在 UCS/
前两个好说；PrigirityQueue 的 push 与前二者参数就不同，自然是报错了；但是注意到 util.py 中的：
class PriorityQueueWithFunction(PriorityQueue): # success PriorityQueue
"""
Implements a priority queue with the same push/pop signature of the
Queue and the Stack classes. This is designed for drop-in replacement for
those two classes. The caller has to provide a priority function, which
extracts each item's priority.
"""
def __init__(self, priorityFunction):
"priorityFunction (item) -> priority"
self.priorityFunction = priorityFunction # store the priority function
PriorityQueue.__init__(self) # super-class initializer
def push(self, item):
"Adds an item to the queue with priority from the priority function"
PriorityQueue.push(self, item, self.priorityFunction(item))根据注释我们可以看出来这就是对 PriorityQueue 的封装了，唯一不同的是我们需要使用一个 priorityFunction(item) 来实例化它（按照 Stack 类中的使用，item 应该指我们设定的元组 node）；再看：
class SearchProblem:
...
def getCostOfActions(self, actions):
"""
actions: A list of actions to take
This method returns the total cost of a particular sequence of actions.
The sequence must be composed of legal moves.
"""
util.raiseNotDefined()用这个方法获取 cost，作为 UCS minheap 的依据；而
完成这题使用了 bfs，所以需要先运行
$ python pacman.py -l tinyCorners -p SearchAgent -a fn=bfs确保通过。
这关实现一个 CornersProblem 类；首先我们看 class CornersProblem(search.SearchProblem): 其继承了我们之前 search.py 中的 SearchProblem 定好的模板，所以我们应当参考 Q1-Q4 所期望的功能来实现它；又在该文件中搜 search.SearchProblem ，找到了 class PositionSearchProblem(search.SearchProblem): 这个兄弟，还是实现好的；那么我们继续照猫画虎：
def getStartState(self):
return self.startingPosition
util.raiseNotDefined()
def isGoalState(self, state: Any):
# 暂时不会，让其始终返回False
util.raiseNotDefined()
def getSuccessors(self, state: Any):
successors = []
for action in [
Directions.NORTH,
Directions.SOUTH,
Directions.EAST,
Directions.WEST,
]:
x, y = state
dx, dy = Actions.directionToVector(action)
nextx, nexty = int(x + dx), int(y + dy)
if not self.walls[nextx][nexty]:
nextState = (nextx, nexty)
# cost = self.costFn(nextState)
cost = 1
successors.append((nextState, action, cost))
self._expanded += 1 # DO NOT CHANGE
return successors我们让 IsGoalState 始终返回 False，那么 pacman 始终没有一条路径可以走，必然静止不动；运行 $ python pacman.py -l tinyCorners -p SearchAgent -a fn=bfs,prob=CornersProblem 看看。
那么我们该怎么写 IsGoalState 呢？
下面内容参考 szzxljr 的代码，其实也体现在后面的 FoodSearchProblem 中。
我们假想我们上述的 node 不仅带着位置信息和动作，还带着一个 corners；每经过一个对应的 corner，我们就丢掉这个 corner；当我们丢完时，就达到目标了；但是直接(state, actions, corners) 是不行的1。所以我们将其和原 state 作为新元组，即 state <= (state, corners):
def getStartState(self):
return (self.startingPosition, self.corners)
util.raiseNotDefined()
def isGoalState(self, state: Any):
return len(state[1]) == 0
util.raiseNotDefined()
def getSuccessors(self, state: Any):
successors = []
for action in [
Directions.NORTH,
Directions.SOUTH,
Directions.EAST,
Directions.WEST,
]:
x, y = state[0]
corners = state[1]
dx, dy = Actions.directionToVector(action)
nextx, nexty = int(x + dx), int(y + dy)
if not self.walls[nextx][nexty]:
nextState0 = (nextx, nexty)
corners = tuple(filter(lambda c: c != nextState0, corners))
# cost = self.costFn(nextState0) # accoding to the hint, cost is 1
cost = 1
successors.append(((nextState0, corners), action, cost))
# print(successors)
self._expanded += 1 # DO NOT CHANGE
return successors
Q6 其实就是让我们想一个比较好的 def cornersHeuristic(state: Any, problem: CornersProblem): 函数；在数学中描述“距离”的范数就比较适合先试试手；曼哈顿距离也是其中一种，且 SearchAgent.py 中有实现：
def manhattanHeuristic(position, problem, info={}):
"The Manhattan distance heuristic for a PositionSearchProblem"
xy1 = position
xy2 = problem.goal
return abs(xy1[0] - xy2[0]) + abs(xy1[1] - xy2[1])我们可以计算此时相比于剩下的 corner 的曼哈顿距离，并取最小者即可：
def manhattanDistance(m, n):
return abs(m[0] - n[0]) + abs(m[1] - n[1])
def cornersHeuristic(state: Any, problem: CornersProblem):
corners = problem.corners # These are the corner coordinates
walls = problem.walls # These are the walls of the maze, as a Grid (game.py)
if len(state[1]) == 0:
return 0
min_distance = float("inf")
for corner in state[1]:
tmp = manhattanDistance(corner, state[0])
min_distance = min(min_distance, tmp)
return min_distance
但是想想，manhattenDistance 本身就一定不比实际需要的步数多，应当取最大值来贴近；同时发现 util.py 中实现了曼哈顿距离：
def cornersHeuristic(state: Any, problem: CornersProblem):
if len(state[1]) == 0:
return 0
max_distance = 0
for corner in state[1]:
# tmp = manhattanDistance(corner, state[0])
tmp = util.manhattanDistance(corner, state[0])
max_distance = max(max_distance, tmp)
return max_distance
Q7 也是同理，之前是 4 个豆子在四个角落，现在是若干个豆子在某某个位置；所以思路基本一致（其中的 mazeDistance 是后来看了其他人的题解发现的）：
def foodHeuristic(state: Tuple[Tuple, List[List]], problem: FoodSearchProblem):
position, foodGrid = state
distances = [0]
for food in foodGrid.asList():
distances.append(mazeDistance(position, food, problem.startingGameState))
return max(distances)
根据提示，我们先补全 AnyFoodSearchProblem：
class AnyFoodSearchProblem(PositionSearchProblem):
...
def isGoalState(self, state: Tuple[int, int]):
x, y = state
return self.food[x][y] # 去看这个成员的定义就懂了
util.raiseNotDefined()也就是说，这个类在此实现的功能就是检查某个位置食物是否被吃了。
Q8 本身更简单了，Returns a path (a list of actions) to the closest dot, starting from gameState ，在每一步成本都为 1 的情况下，最近既是成本最小，uniformCostSearch 即可：
def findPathToClosestDot(self, gameState: pacman.GameState):
"""
Returns a path (a list of actions) to the closest dot, starting from
gameState.
"""
# Here are some useful elements of the startState
startPosition = gameState.getPacmanPosition()
food = gameState.getFood()
walls = gameState.getWalls()
problem = AnyFoodSearchProblem(gameState)
"*** YOUR CODE HERE ***"
return search.uniformCostSearch(problem)
util.raiseNotDefined()
[!SUMMARY]
多看相关注释和已有的类似实现；开始前清楚自己能用哪些东西。
Footnotes
-
我们需要和之前实现的 BFS 接口，这个 node 应该只有两个成员。 ↩