After, the preliminary reading above, write the function: def MPE(CPTs,Os) in Python API for Z3

The inputs for MPE are: (1) a list of Conditional Probability Tables (CPTs) and (2) a list of Observations (Os). Both CPTs and Os have as many number of entries as there are random variables, with the i-th entry in each of the two inputs corresponding to the i-th random variable. We are considering only random variables whose range is a subset of integers.

For some of the random variables their value is observed, and for some it is not. If the value of the i-th random variable was not observed, the i-th entry of Os is None, and if it was observed the i-th entry of Os is the value that was observed.

A Conditional Probability Table (CPT) T is a list of conditional probabilities. Let x be the random variable corresponding to T. A conditional probability in T is encoded as a triplet [Cs,v,p], where p is the probability of the random variable x having value v when the conditions Cs are fulfilled. Cs is a list of conditions and a condition is a pair [rvid,v], where rvid is the index of a random variable y on which x depends when y is set to the value v.

The function MPE returns the most probable explanation for observed values, which will be a list of integers where the i-th entry in the list corresponds to the most probable value of the i-th random variable. You can assume that the inputs are valid, namely:

Given a particular CPT T, you do not have to check that the probabilities in the triplets of T with the same conditions add up to one.

Given a particular CPT T, all the triplets in T use the same random variables in its conditions, i.e., all the conditions in T refer to the same set of rvids.

There are no cycles in the graph induced by CPTs.

Os contains only values from the range of random variables.