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Merge pull request aimacode#86 from samagra14/4e_search
Adds 4e algorithms.
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‎md/Breadth-First-Search.md‎

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# BREADTH-FIRST-SEARCH
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## AIMA4e
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__function__ BREADTH-FIRST-SEARCH(_problem_) __returns__ a solution, or failure
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 __if__ problem's initial state is a goal __then return__ empty path to initial state
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 _frontier_ ← a FIFO queue initially containing one path, for the _problem_'s initial state
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 _reached_ ← a set of states; initially empty
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 _solution_ ← failure
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 __while__ _frontier_ is not empty __do__
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   _parent_ ← the first node in _frontier_
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   __for__ _child_ __in__ successors(_parent_) __do__
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     _s_ ← _child_.state
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     __if__ _s_ is a goal __then__
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       __return__ _child_
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     __if__ _s_ is not in _reached_ __then__
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       add _s_ to _reached_
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       add _child_ to the end of _frontier_
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 __return__ _solution_
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---
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__Figure 3.9__ Breadth-first search algorithm.
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## AIMA3e
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__function__ BREADTH-FIRST-SEARCH(_problem_) __returns__ a solution, or failure
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 _node_ ← a node with STATE = _problem_.INITIAL\-STATE, PATH\-COST = 0

‎md/Depth-Limited-Search.md‎

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# DEPTH-LIMITED-SEARCH
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## AIMA4e
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__function__ DEPTH-LIMITED-SEARCH(_problem_, _l_) __returns__ a solution, or failure, or cutoff
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 _frontier_ ← a FIFO queue initially containing one path, for the _problem_'s initial state
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 _solution_ ← failure
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 __while__ _frontier_ is not empty __do__
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   _parent_ ← pop(_frontier_)
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   __if__ depth(_parent_) > l __then__
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     _solution_ ← cutoff
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     __else__
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       __for__ _child_ __in__ successors(_parent_) __do__
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         __if__ _child_ is a goal __then__
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           __return__ _child_
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         add _child_ to __frontier__
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 __return__ _solution_
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---
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__Figure 3.14__ An implementation of depth-limited tree search. The algorithm has two dif-
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ferent ways to signal failure to find a solution: it returns failure when it has exhausted all
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paths and proved there is no solution at any depth, and returns cutoff to mean there might be
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a solution at a deeper depth than l. Note that this algorithm does not keep track of reached
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states, and thus might visit the same state multiple times on different paths.
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## AIMA3e
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__function__ DEPTH-LIMITED-SEARCH(_problem_,_limit_) __returns__ a solution, or failure/cutoff
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 __return__ RECURSIVE\-DLS(MAKE\-NODE(_problem_.INITIAL\-STATE),_problem_,_limit_)

‎md/Hill-Climbing.md‎

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# HILL-CLIMBING
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## AIMA4e
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__function__ HILL-CLIMBING(_problem_) __returns__ a state that is a local maximum
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 _current_ ← _problem_.INITIAL\-STATE
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 __loop do__
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   _neighbor_ ← a highest\-valued successor of _current_
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   _if_ VALUE(_neighbour_) ≤ VALUE(_current_) __then return__ _current_
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   _current_ ← _neighbor_
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---
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__Figure 4.2__ The hill-climbing search algorithm, which is the most basic local search technique. At each step the current node is replaced by the best neighbor.
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## AIMA3e
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__function__ HILL-CLIMBING(_problem_) __returns__ a state that is a local maximum
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 _current_ ← MAKE\-NODE(_problem_.INITIAL\-STATE)

‎md/Iterative-Deepening-Search.md‎

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# ITERATIVE-DEEPENING-SEARCH
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## AIMA3e
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## AIMA3e / AIMA4e
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__function__ ITERATIVE-DEEPENING-SEARCH(_problem_) __returns__ a solution, or failure
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 __for__ _depth_ = 0 to ∞ __do__
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   _result_ ← DEPTH\-LIMITED\-SEARCH(_problem_,_depth_)

‎md/Simulated-Annealing.md‎

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# SIMULATED-ANNEALING
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## AIMA4e
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__function__ SIMULATED-ANNEALING(_problem_,_schedule_) __returns__ a solution state
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 _current_ ← _problem_.INITIAL\-STATE
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 __for__ _t_ = 1 __to__ ∞ __do__
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   _T_ ← _schedule(t)_
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   __if__ _T_ = 0 __then return__ _current_
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   _next_ ← a randomly selected successor of _current_
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   _ΔE_ ← VALUE(_next_) - VALUE(_current_)
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   __if__ _ΔE_ > 0 __then__ _current_ ← _next_
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&emsp;&emsp;&emsp;__else__ _current_ &larr; _next_ only with probability e<sup>_&Delta;E_/_T_</sup>
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---
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__Figure 4.6__ The simulated annealing algorithm, a version of stochastic hill climbing where
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some downhill moves are allowed. The schedule input determines the value of the “temper-
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ature” T as a function of time; higher temperatures early in the schedule mean that downhill
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moves are accepted more readily; late in the schedule with low temperatures, downhill moves
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are mostly rejected.
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## AIMA3e
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__function__ SIMULATED-ANNEALING(_problem_,_schedule_) __returns__ a solution state
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&emsp;__inputs__: _problem_, a problem

‎md/Successors.md‎

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# Successors
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## AIMA4e
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__function__ SUCCESSORS(_problem_, _parent_) __returns__ an action
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&emsp;_s_ &larr; _parent_.state
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&emsp;_nodes_ &larr; an empty list
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&emsp;__for__ _action_ in _problem_.actions(_s_) __do__
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&emsp;&emsp;&emsp;_s'_ &larr; _problem_.result(s,_action_)
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&emsp;&emsp;&emsp;_cost_ &larr; _parent_.pathCost + _problem_.stepCost(_s, action, s′_ )
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&emsp;&emsp;&emsp;_node_ &larr; Node(state = _s'_, parent = _parent_, action = _action_, pathCost = _cost_)
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&emsp;&emsp;&emsp;add _node_ to _nodes_
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&emsp;__return__ _nodes_

‎md/Uniform-Cost-Search.md‎

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# UNIFORM-COST-SEARCH
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## AIMA4e
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__function__ UNIFORM-COST-SEARCH(_problem_) __returns__ a solution, or failure
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&emsp;__if__ problem's initial state is a goal __then return__ empty path to initial state
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&emsp;_frontier_ &larr; a priority queue ordered by pathCost, with a node for the initial state
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&emsp;_reached_ &larr; a table of {_state_: the best path that reached _state_}; initially empty
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&emsp;_solution_ &larr; failure
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&emsp;__while__ _frontier_ is not empty __and__ top(_frontier_) is cheaper than _solution_ __do__
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&emsp;&emsp;&emsp;_parent_ &larr; pop(_frontier_)
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&emsp;&emsp;&emsp;__for__ _child_ __in__ successors(_parent_) __do__
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&emsp;&emsp;&emsp;&emsp;&emsp;_s_ &larr; _child_.state
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&emsp;&emsp;&emsp;&emsp;&emsp;__if__ _s_ is not in _reached_ __or__ _child_ is a cheaper path than _reached_[_s_] __then__
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&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;_reached_[_s_] &larr; _child_
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&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;add _child_ to the _frontier_
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&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;__if__ _child_ is a goal and is cheaper than _solution_ __then__
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&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;&emsp;_solution_ = _child_
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&emsp;__return__ _solution_
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---
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__Figure 3.11__ Uniform-cost search on a graph. Finds optimal paths for problems with vary-
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ing step costs.
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## AIMA3e
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__function__ UNIFORM-COST-SEARCH(_problem_) __returns__ a solution, or failure
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&emsp;_node_ &larr; a node with STATE = _problem_.INITIAL\-STATE, PATH\-COST = 0

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