# Implementation of AO Star Search Algorithm in python

## Implementation of AO Star Search Algorithm in python – Artificial Intelligence

In this tutorial, we will understand the AO Star Search Algorithm with a solved numerical example and implementation in python.

## Implementation of AO Star Search Algorithm in python

```class Graph:
def __init__(self, graph, heuristicNodeList, startNode): #instantiate graph object with graph topology, heuristic values, start node
self.graph = graph
self.H=heuristicNodeList
self.start=startNode
self.parent={}
self.status={}
self.solutionGraph={}

def applyAOStar(self): # starts a recursive AO* algorithm
self.aoStar(self.start, False)

def getNeighbors(self, v): # gets the Neighbors of a given node
return self.graph.get(v,'')

def getStatus(self,v): # return the status of a given node
return self.status.get(v,0)

def setStatus(self,v, val): # set the status of a given node
self.status[v]=val

def getHeuristicNodeValue(self, n):
return self.H.get(n,0) # always return the heuristic value of a given node

def setHeuristicNodeValue(self, n, value):
self.H[n]=value # set the revised heuristic value of a given node

def printSolution(self):
print("FOR GRAPH SOLUTION, TRAVERSE THE GRAPH FROM THE START NODE:",self.start)
print("------------------------------------------------------------")
print(self.solutionGraph)
print("------------------------------------------------------------")

def computeMinimumCostChildNodes(self, v): # Computes the Minimum Cost of child nodes of a given node v
minimumCost=0
costToChildNodeListDict={}
costToChildNodeListDict[minimumCost]=[]
flag=True
for nodeInfoTupleList in self.getNeighbors(v): # iterate over all the set of child node/s
cost=0
nodeList=[]
for c, weight in nodeInfoTupleList:
cost=cost+self.getHeuristicNodeValue(c)+weight
nodeList.append(c)
if flag==True: # initialize Minimum Cost with the cost of first set of child node/s
minimumCost=cost
costToChildNodeListDict[minimumCost]=nodeList # set the Minimum Cost child node/s
flag=False
else: # checking the Minimum Cost nodes with the current Minimum Cost
if minimumCost>cost:
minimumCost=cost
costToChildNodeListDict[minimumCost]=nodeList # set the Minimum Cost child node/s
return minimumCost, costToChildNodeListDict[minimumCost] # return Minimum Cost and Minimum Cost child node/s

def aoStar(self, v, backTracking): # AO* algorithm for a start node and backTracking status flag
print("HEURISTIC VALUES :", self.H)
print("SOLUTION GRAPH :", self.solutionGraph)
print("PROCESSING NODE :", v)
print("-----------------------------------------------------------------------------------------")
if self.getStatus(v) >= 0: # if status node v >= 0, compute Minimum Cost nodes of v
minimumCost, childNodeList = self.computeMinimumCostChildNodes(v)
print(minimumCost, childNodeList)
self.setHeuristicNodeValue(v, minimumCost)
self.setStatus(v,len(childNodeList))
solved=True # check the Minimum Cost nodes of v are solved
for childNode in childNodeList:
self.parent[childNode]=v
if self.getStatus(childNode)!=-1:
solved=solved & False
if solved==True: # if the Minimum Cost nodes of v are solved, set the current node status as solved(-1)
self.setStatus(v,-1)
self.solutionGraph[v]=childNodeList # update the solution graph with the solved nodes which may be a part of solution
if v!=self.start: # check the current node is the start node for backtracking the current node value
self.aoStar(self.parent[v], True) # backtracking the current node value with backtracking status set to true
if backTracking==False: # check the current call is not for backtracking
for childNode in childNodeList: # for each Minimum Cost child node
self.setStatus(childNode,0) # set the status of child node to 0(needs exploration)
self.aoStar(childNode, False) # Minimum Cost child node is further explored with backtracking status as false
```

### Graph – 1 as Input to AO Star Search Algorithm

```#for simplicity we ll consider heuristic distances given
print ("Graph - 1")
h1 = {'A': 1, 'B': 6, 'C': 2, 'D': 12, 'E': 2, 'F': 1, 'G': 5, 'H': 7, 'I': 7, 'J': 1}
graph1 = {
'A': [[('B', 1), ('C', 1)], [('D', 1)]],
'B': [[('G', 1)], [('H', 1)]],
'C': [[('J', 1)]],
'D': [[('E', 1), ('F', 1)]],
'G': [[('I', 1)]]
}

G1= Graph(graph1, h1, 'A')
G1.applyAOStar()
G1.printSolution()
```

### Output of AO Star Search Algorithm

Graph – 1

HEURISTIC VALUES : {‘A’: 1, ‘B’: 6, ‘C’: 2, ‘D’: 12, ‘E’: 2, ‘F’: 1, ‘G’: 5, ‘H’: 7, ‘I’: 7, ‘J’: 1}
SOLUTION GRAPH : {}

PROCESSING NODE : A

10 [‘B’, ‘C’]
HEURISTIC VALUES : {‘A’: 10, ‘B’: 6, ‘C’: 2, ‘D’: 12, ‘E’: 2, ‘F’: 1, ‘G’: 5, ‘H’: 7, ‘I’: 7, ‘J’: 1}
SOLUTION GRAPH : {}

PROCESSING NODE : B

6 [‘G’]
HEURISTIC VALUES : {‘A’: 10, ‘B’: 6, ‘C’: 2, ‘D’: 12, ‘E’: 2, ‘F’: 1, ‘G’: 5, ‘H’: 7, ‘I’: 7, ‘J’: 1}
SOLUTION GRAPH : {}

PROCESSING NODE : A

10 [‘B’, ‘C’]
HEURISTIC VALUES : {‘A’: 10, ‘B’: 6, ‘C’: 2, ‘D’: 12, ‘E’: 2, ‘F’: 1, ‘G’: 5, ‘H’: 7, ‘I’: 7, ‘J’: 1}
SOLUTION GRAPH : {}

PROCESSING NODE : G

8 [‘I’]
HEURISTIC VALUES : {‘A’: 10, ‘B’: 6, ‘C’: 2, ‘D’: 12, ‘E’: 2, ‘F’: 1, ‘G’: 8, ‘H’: 7, ‘I’: 7, ‘J’: 1}
SOLUTION GRAPH : {}

PROCESSING NODE : B

8 [‘H’]
HEURISTIC VALUES : {‘A’: 10, ‘B’: 8, ‘C’: 2, ‘D’: 12, ‘E’: 2, ‘F’: 1, ‘G’: 8, ‘H’: 7, ‘I’: 7, ‘J’: 1}
SOLUTION GRAPH : {}

PROCESSING NODE : A

12 [‘B’, ‘C’]
HEURISTIC VALUES : {‘A’: 12, ‘B’: 8, ‘C’: 2, ‘D’: 12, ‘E’: 2, ‘F’: 1, ‘G’: 8, ‘H’: 7, ‘I’: 7, ‘J’: 1}
SOLUTION GRAPH : {}

PROCESSING NODE : I

0 []
HEURISTIC VALUES : {‘A’: 12, ‘B’: 8, ‘C’: 2, ‘D’: 12, ‘E’: 2, ‘F’: 1, ‘G’: 8, ‘H’: 7, ‘I’: 0, ‘J’: 1}
SOLUTION GRAPH : {‘I’: []}

PROCESSING NODE : G

1 [‘I’]
HEURISTIC VALUES : {‘A’: 12, ‘B’: 8, ‘C’: 2, ‘D’: 12, ‘E’: 2, ‘F’: 1, ‘G’: 1, ‘H’: 7, ‘I’: 0, ‘J’: 1}
SOLUTION GRAPH : {‘I’: [], ‘G’: [‘I’]}

PROCESSING NODE : B

2 [‘G’]
HEURISTIC VALUES : {‘A’: 12, ‘B’: 2, ‘C’: 2, ‘D’: 12, ‘E’: 2, ‘F’: 1, ‘G’: 1, ‘H’: 7, ‘I’: 0, ‘J’: 1}
SOLUTION GRAPH : {‘I’: [], ‘G’: [‘I’], ‘B’: [‘G’]}

PROCESSING NODE : A

6 [‘B’, ‘C’]
HEURISTIC VALUES : {‘A’: 6, ‘B’: 2, ‘C’: 2, ‘D’: 12, ‘E’: 2, ‘F’: 1, ‘G’: 1, ‘H’: 7, ‘I’: 0, ‘J’: 1}
SOLUTION GRAPH : {‘I’: [], ‘G’: [‘I’], ‘B’: [‘G’]}

PROCESSING NODE : C

2 [‘J’]
HEURISTIC VALUES : {‘A’: 6, ‘B’: 2, ‘C’: 2, ‘D’: 12, ‘E’: 2, ‘F’: 1, ‘G’: 1, ‘H’: 7, ‘I’: 0, ‘J’: 1}
SOLUTION GRAPH : {‘I’: [], ‘G’: [‘I’], ‘B’: [‘G’]}

PROCESSING NODE : A

6 [‘B’, ‘C’]
HEURISTIC VALUES : {‘A’: 6, ‘B’: 2, ‘C’: 2, ‘D’: 12, ‘E’: 2, ‘F’: 1, ‘G’: 1, ‘H’: 7, ‘I’: 0, ‘J’: 1}
SOLUTION GRAPH : {‘I’: [], ‘G’: [‘I’], ‘B’: [‘G’]}

PROCESSING NODE : J

0 []
HEURISTIC VALUES : {‘A’: 6, ‘B’: 2, ‘C’: 2, ‘D’: 12, ‘E’: 2, ‘F’: 1, ‘G’: 1, ‘H’: 7, ‘I’: 0, ‘J’: 0}
SOLUTION GRAPH : {‘I’: [], ‘G’: [‘I’], ‘B’: [‘G’], ‘J’: []}

PROCESSING NODE : C

1 [‘J’]
HEURISTIC VALUES : {‘A’: 6, ‘B’: 2, ‘C’: 1, ‘D’: 12, ‘E’: 2, ‘F’: 1, ‘G’: 1, ‘H’: 7, ‘I’: 0, ‘J’: 0}
SOLUTION GRAPH : {‘I’: [], ‘G’: [‘I’], ‘B’: [‘G’], ‘J’: [], ‘C’: [‘J’]}

PROCESSING NODE : A

5 [‘B’, ‘C’]

FOR GRAPH SOLUTION, TRAVERSE THE GRAPH FROM THE START NODE: A

{‘I’: [], ‘G’: [‘I’], ‘B’: [‘G’], ‘J’: [], ‘C’: [‘J’], ‘A’: [‘B’, ‘C’]}

## Graph – 2 as Input to AO Star Search Algorithm

```print ("Graph - 2")
h2 = {'A': 1, 'B': 6, 'C': 12, 'D': 10, 'E': 4, 'F': 4, 'G': 5, 'H': 7} # Heuristic values of Nodes
graph2 = { # Graph of Nodes and Edges
'A': [[('B', 1), ('C', 1)], [('D', 1)]], # Neighbors of Node 'A', B, C & D with repective weights
'B': [[('G', 1)], [('H', 1)]], # Neighbors are included in a list of lists
'D': [[('E', 1), ('F', 1)]] # Each sublist indicate a "OR" node or "AND" nodes
}

G2 = Graph(graph2, h2, 'A') # Instantiate Graph object with graph, heuristic values and start Node
G2.applyAOStar() # Run the AO* algorithm
G2.printSolution() # Print the solution graph as output of the AO* algorithm search```

### Output of AO Star Search Algorithm

Graph – 2

HEURISTIC VALUES : {‘A’: 1, ‘B’: 6, ‘C’: 12, ‘D’: 10, ‘E’: 4, ‘F’: 4, ‘G’: 5, ‘H’: 7}
SOLUTION GRAPH : {}

PROCESSING NODE : A

11 [‘D’]
HEURISTIC VALUES : {‘A’: 11, ‘B’: 6, ‘C’: 12, ‘D’: 10, ‘E’: 4, ‘F’: 4, ‘G’: 5, ‘H’: 7}
SOLUTION GRAPH : {}

PROCESSING NODE : D

10 [‘E’, ‘F’]
HEURISTIC VALUES : {‘A’: 11, ‘B’: 6, ‘C’: 12, ‘D’: 10, ‘E’: 4, ‘F’: 4, ‘G’: 5, ‘H’: 7}
SOLUTION GRAPH : {}

PROCESSING NODE : A

11 [‘D’]
HEURISTIC VALUES : {‘A’: 11, ‘B’: 6, ‘C’: 12, ‘D’: 10, ‘E’: 4, ‘F’: 4, ‘G’: 5, ‘H’: 7}
SOLUTION GRAPH : {}

PROCESSING NODE : E

0 []
HEURISTIC VALUES : {‘A’: 11, ‘B’: 6, ‘C’: 12, ‘D’: 10, ‘E’: 0, ‘F’: 4, ‘G’: 5, ‘H’: 7}
SOLUTION GRAPH : {‘E’: []}

PROCESSING NODE : D

6 [‘E’, ‘F’]
HEURISTIC VALUES : {‘A’: 11, ‘B’: 6, ‘C’: 12, ‘D’: 6, ‘E’: 0, ‘F’: 4, ‘G’: 5, ‘H’: 7}
SOLUTION GRAPH : {‘E’: []}

PROCESSING NODE : A

7 [‘D’]
HEURISTIC VALUES : {‘A’: 7, ‘B’: 6, ‘C’: 12, ‘D’: 6, ‘E’: 0, ‘F’: 4, ‘G’: 5, ‘H’: 7}
SOLUTION GRAPH : {‘E’: []}

PROCESSING NODE : F

0 []
HEURISTIC VALUES : {‘A’: 7, ‘B’: 6, ‘C’: 12, ‘D’: 6, ‘E’: 0, ‘F’: 0, ‘G’: 5, ‘H’: 7}
SOLUTION GRAPH : {‘E’: [], ‘F’: []}

PROCESSING NODE : D

2 [‘E’, ‘F’]
HEURISTIC VALUES : {‘A’: 7, ‘B’: 6, ‘C’: 12, ‘D’: 2, ‘E’: 0, ‘F’: 0, ‘G’: 5, ‘H’: 7}
SOLUTION GRAPH : {‘E’: [], ‘F’: [], ‘D’: [‘E’, ‘F’]}

PROCESSING NODE : A

3 [‘D’]

FOR GRAPH SOLUTION, TRAVERSE THE GRAPH FROM THE START NODE: A

{‘E’: [], ‘F’: [], ‘D’: [‘E’, ‘F’], ‘A’: [‘D’]}

Summary:

In this tutorial, we understood the AO Star Search Algorithm with a solved numerical example and implementation in python. If you like the tutorial share it with your friends. Like the Facebook page for regular updates and YouTube channel for video tutorials.