On Programming Assignment 1, you will receive 20 points simply if your
program compiles and runs.  We will then test your program on three
networks, 3 queries per network, for a total of 9 queries worth 5
points each.  For a given query, you should provide the probability
distribution over the query variable.  Because these are Boolean, it
is sufficient to provide just the probability that the variable is
true.  For each query, you will receive 5 points if your answer is
the correct answer plus/minus 0.05, and 0 points otherwise.

Below are two networks on which to test your program.  These are in the
same format that we will use for testing.  After each network are the
queries.  The first network is followed by 3 queries (2 settings of evidence
variables, 2 queries for the first setting and 1 for the second setting).
These are in exactly the form we will use in testing.

The remaining 35 points for this assignment will be based on your
one-page write-up describing your own experiments with your implementation.




// First Test Network
8 // number of nodes in the network
{
    // NODE 1: empty line means first node has no parents
0.05 // prior probability of true is 0.05
}
{
   // NODE 2: empty line means second node has no parents
0.13 // prior probability of true is 0.13
}
{
1 // NODE 3: parent of node 3 is node 1
0 0.32 // if node 1 is false, probability of true is 0.32
1 0.81 // if node 1 is true, prob of true is 0.81
}
{
1 2 // NODE 4: parents of node 4 are nodes 1 and 2
0 0 0.2
0 1 0.3
1 0 0.4
1 1 0.5
}
{
2 // NODE 5: parent of node 5 is node 2
0 0.9 
1 0.7
}
{
3 4 // NODE 6: parents of node 6 are nodes 3 and 4
0 0 0.35
0 1 0.12
1 0 0.77
1 1 0.56
}
{
4 5 // NODE 7: parents of node 7 are nodes 4 and 5
0 0 0.4
0 1 0.2
1 0 0.3
1 1 0.1
}
{
6 7 // NODE 8: parents of node 8 are nodes 6 and 7
0 0 0.39
0 1 0.11
1 0 0.09
1 1 0.68
}
// Here are 3 queries for the preceeding network
// The first 2 ask about variables 2 and 5, respectively, given that
//     variable 1 is true and variable 8 is false
// The last query asks about variable 1 given variables 6 and 7 are true
E 1 t 8 f
Q 2
Q 5
E 6 t 7 t
Q 1



// Second Test Network
8 // number of nodes in the network
{
    // NODE 1: empty line means first node has no parents
0.93 // prior probability of true is 0.93
}
{
   // NODE 2: empty line means second node has no parents
0.71 // prior probability of true is 0.71
}
{
  // NODE 3: empty line means third node has no parents 
.55 // prior probability of true is 0.55
}
{
2 // NODE 4: parent of node 4 is node 2
0 0.9 
1 0.7
}
{
2 // NODE 5: parent of node 5 is node 2
0 0.3 
1 0.5
}
{
1 4 // NODE 6: parents of node 6 are nodes 1 and 4
0 0 0.2
0 1 0.3
1 0 0.4
1 1 0.5
}
{
3 5 // NODE 7: parents of node 7 are nodes 3 and 5
0 0 0.4
0 1 0.7
1 0 0.8
1 1 0.5
}
{
2 6 7 // NODE 8: parents of node 8 are nodes 2, 6, and 7
0 0 0 0.9
0 0 1 0.1
0 1 0 0.7
0 1 1 0.6
1 0 0 0.2
1 0 1 0.3
1 1 0 0.5
1 1 1 0.8
}


// Here are the two queries for the preceeding network
// These queries ask about variables 2 and 3, respectively, given that
//     variable 6 is true and variable 8 is false
E 6 t 8 f
Q 2
Q 3