Add uniform cost and bfs

Author: samagra14

md/Breadth-First-Search.md

@@ -1,5 +1,27 @@
 # BREADTH-FIRST-SEARCH
 
+## AIMA4e
+
+__function__ BREADTH-FIRST-SEARCH(_problem_) __returns__ a solution, or failure  
+ __if__ problem's initial state is a goal __then return__ empty path to initial state  
+ _frontier_ ← a FIFO queue initially containing one path, for the _problem_'s initial state  
+ _reached_ ← a set of states; initially empty  
+ _solution_ ← failure  
+ __while__  _frontier_ is not empty __do__  
+   _parent_ ← the first node in _frontier_  
+   __for__ _child_ __in__ successors(_parent_) __do__   
+     _s_ ← _child_.state  
+     __if__ _s_ is a goal  __then__  
+       __return__  _child_  
+     __if__ _s_ is not in _reached_ __then__  
+       add _s_ to _reached_  
+       add _child_ to the end of _frontier_  
+ __return__  _solution_
+
+---
+__Figure 3.9__ Breadth-first search algorithm.
+
+
 ## AIMA3e
 __function__ BREADTH-FIRST-SEARCH(_problem_) __returns__ a solution, or failure  
  _node_ ← a node with STATE = _problem_.INITIAL\-STATE, PATH\-COST = 0    

md/Successors.md

@@ -0,0 +1,14 @@
+# Successors
+
+## AIMA4e
+
+
+__function__ SUCCESSORS(_problem_, _parent_) __returns__ an action  
+ _s_ ← _parent_.state  
+ _nodes_ ← an empty list  
+ __for__ _action_ in _problem_.actions(_s_) __do__  
+   _s'_ ← _problem_.result(s,_action_)  
+   _cost_ ← _parent_.pathCost + _problem_.stepCost(_s, action, s′_ )  
+   _node_ ← Node(state = _s'_,  parent = _parent_, action = _action_, pathCost = _cost_)  
+   add _node_ to _nodes_  
+ __return__ _nodes_   

md/Uniform-Cost-Search.md

@@ -1,5 +1,28 @@
 # UNIFORM-COST-SEARCH
 
+## AIMA4e  
+
+__function__ UNIFORM-COST-SEARCH(_problem_) __returns__ a solution, or failure  
+ __if__ problem's initial state is a goal __then return__ empty path to initial state  
+ _frontier_ ← a priority queue ordered by pathCost, with a node for the initial state  
+ _reached_ ← a table of {_state_: the best path that reached _state_}; initially empty  
+ _solution_ ← failure  
+ __while__  _frontier_ is not empty __and__ top(_frontier_) is cheaper than _solution_ __do__  
+   _parent_ ← pop(_frontier_)  
+   __for__ _child_ __in__ successors(_parent_) __do__   
+     _s_ ← _child_.state  
+     __if__ _s_ is not in _reached_  __or__ _child_ is a cheaper path than _reached_[_s_] __then__  
+       _reached_[_s_] ← _child_  
+       add _child_ to the _frontier_  
+       __if__ _child_ is a goal and is cheaper than _solution_ __then__  
+         _solution_  =  _child_  
+ __return__ _solution_
+
+---
+__Figure 3.11__ Uniform-cost search on a graph. Finds optimal paths for problems with vary-
+ing step costs.
+
+
 ## AIMA3e
 __function__ UNIFORM-COST-SEARCH(_problem_) __returns__ a solution, or failure  
  _node_ ← a node with STATE = _problem_.INITIAL\-STATE, PATH\-COST = 0