text: # search.py
  # ---------
  # Licensing Information:  You are free to use or extend these projects for
  # educational purposes provided that (1) you do not distribute or publish
  # solutions, (2) you retain this notice, and (3) you provide clear
  # attribution to UC Berkeley, including a link to http://ai.berkeley.edu.
  #
  # Attribution Information: The Pacman AI projects were developed at UC Berkeley.
  # The core projects and autograders were primarily created by John DeNero
  # (denero@cs.berkeley.edu) and Dan Klein (klein@cs.berkeley.edu).
  # Student side autograding was added by Brad Miller, Nick Hay, and
  # Pieter Abbeel (pabbeel@cs.berkeley.edu).
  
  
  """
  In search.py, you will implement generic search algorithms which are called by
  Pacman agents (in searchAgents.py).
  """
  
  import util
  from util import Stack
  from util import Queue
  
  class SearchProblem:
      """
      This class outlines the structure of a search problem, but doesn't implement
      any of the methods (in object-oriented terminology: an abstract class).
  
      You do not need to change anything in this class, ever.
      """
  
      def getStartState(self):
          """
          Returns the start state for the search problem.
          """
          util.raiseNotDefined()
  
      def isGoalState(self, state):
          """
            state: Search state
  
          Returns True if and only if the state is a valid goal state.
          """
          util.raiseNotDefined()
  
      def getSuccessors(self, state):
          """
            state: Search state
  
          For a given state, this should return a list of triples, (successor,
          action, stepCost), where 'successor' is a successor to the current
          state, 'action' is the action required to get there, and 'stepCost' is
          the incremental cost of expanding to that successor.
          """
          util.raiseNotDefined()
  
      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()
  
  
  def tinyMazeSearch(problem):
      """
      Returns a sequence of moves that solves tinyMaze.  For any other maze, the
      sequence of moves will be incorrect, so only use this for tinyMaze.
      """
      from game import Directions
      s = Directions.SOUTH
      w = Directions.WEST
      return  [s, s, w, s, w, w, s, w]
  
  def depthFirstSearch(problem):
      stack = Stack()
      visited = []
      action = []
      startNode = problem.getStartState()
      stack.push((startNode, action))
  
      while not stack.isEmpty():
          currNode, action = stack.pop()
          if not currNode in visited:
              visited.append(currNode)
              if problem.isGoalState(currNode):
                  return action
              for i, j, k in problem.getSuccessors(currNode):
                  newAction = action + [j]
                  stack.push((i, newAction))
  
      return []
  
  
  
  def breadthFirstSearch(problem):
      queue = Queue()
      visited = []
      action = []
      startNode = problem.getStartState()
      queue.push((startNode, action))
  
      while not queue.isEmpty():
          currNode, action = queue.pop()
          if not currNode in visited:
              visited.append(currNode)
              if problem.isGoalState(currNode):
                  return action
              for i, j, k in problem.getSuccessors(currNode):
                  newAction = action + [j]
                  queue.push((i, newAction))
  
      return []
  
  
  
  def uniformCostSearch(problem):
      """Search the node of least total cost first."""
      "*** YOUR CODE HERE ***"
      util.raiseNotDefined()
  
  def nullHeuristic(state, problem=None):
      """
      A heuristic function estimates the cost from the current state to the nearest
      goal in the provided SearchProblem.  This heuristic is trivial.
      """
      return 0
  
  def aStarSearch(problem, heuristic=nullHeuristic):
      """Search the node that has the lowest combined cost and heuristic first."""
      "*** YOUR CODE HERE ***"
      util.raiseNotDefined()
  
  
  # Abbreviations
  bfs = breadthFirstSearch
  dfs = depthFirstSearch
  astar = aStarSearch
  ucs = uniformCostSearch
  