Bahria University
CSC-470: Artificial Intelligence
Department of Computer Science
Semester 07 (Spring 2015)
Lab06: Greedy and A* Algorithms
Objectives
Introducing the search technique and write programs to implement the following techniques:
1. Greedy Searching Algorithm
2. A* Searching Algorithm
3. Exercise
1. Greedy Searching Algorithm
The greedy best-first search algorithm is incomplete without cycle checking. If a closed list is used to
not visit nodes which have already been visited, then the search is complete. The algorithm is also
not optimal. Since the algorithm is only based on the heuristic value, if the heuristic is not exactly
equal to the actual cost, it might go down a less optimal path than the ideal one.
The greedy best-first search algorithm is O(bm) in terms of space and time complexity. (Where b is
the average branching factor (the average number of successors from a state), and m is the maximum
depth of the search tree.) A good heuristic can bring this down substantially for the common case,
but all nodes are visited in the worst case.
Example of the algorithm:
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Lab 06: Greedy and A* Algorithms
Now there is a choice on which node to visit next. Because we are using greedy best-first search, the
node with the lowest heuristic is used. If this solution was implemented, a priority queue would be
used for the fringe, so it would always return the node with the lowest heuristic. Since node D has
the lowest heuristic value, we visit at that node and add its neighbors to the fringe.
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Lab 06: Greedy and A* Algorithms
The path found from Start to Goal is: Start -> A -> D -> E -> Goal. In this case, it was the optimal
path, but only because the heuristic values were fairly accurate.
Ref: http://www.cs.utah.edu/~hal/courses/2009S_AI/Walkthrough/GreedyBFS/
2. A* Searching Algorithm
A * is a best-firstgraph search algorithm that finds the least-cost path from a given initial node to one
goal node (out of one or more possible goals).It uses a distance-plus-cost heuristic function (usually
denoted f(x)) to determine the order in which the search visits nodes in the tree. The distance-pluscost heuristic is a sum of two functions:

the path-cost function, which is the cost from the starting node to the current node (usually
denoted g(x))
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
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Semester 7 (Spring 2015)
Lab 06: Greedy and A* Algorithms
and an admissible "heuristic estimate" of the distance to the goal (usually denoted h(x)).
The h(x) part of the f(x) function must be an admissible heuristic; that is, it must not overestimate the
distance to the goal. Thus for an application like routing, h(x) might represent the straight-line
distance to the goal, since that is physically the smallest possible distance between any two points (or
nodes for that matter).The algorithm traverses various paths from start to goal. For each node x
traversed, it maintains 3 values:
• g(x): the actual shortest distance traveled from initial node to
current node
•h(x): the estimated (or "heuristic") distance from current node to
goal
•f(x): the sum of g(x) and h(x)
Exercises
Exercise 1 & 2
(Greedy and Astar)
Write C# or Java program to implement Greedy Best First and A* Search Algorithms for following
rout finding problem from Arad to Bucharest.
Arad
Bucharest
Craiova
Dobreta
Eforie
Fagaras
Giurgiu
Hirsova
Iasi
Lugoj
Mehadia
Neamt
Oradea
Pitesti
RimnicuVilcea
Sibiu
Timisoara
Urziceni
Vaslui
Zerind
366
0
160
242
161
178
77
151
226
244
241
234
380
98
193
253
329
80
199
374