Let L be a list containing distinct (non-repeating) integers. Moreover, assume L contains an odd number of values. Assume we want to define a Prolog predicate median(L,M) that is true when M is the median of L. One way to implement this predicate is to sort L and then extract the "middle" element of the sorted list.
A more elegant Prolog implementation, however, can be found by considering the definition of what it means for M to be L's median: First: M must occur in L.Second: if M is used to partition L into two sublists, one containing values greater than M and the other containing values smaller than M, then the resulting sublists must be equal in length.
Use this definition to implement median(L,M). You may
assume that L is always fixed as a list, but M may be a value or a
variable.
Submit your code in a file called median.prolog.