Find median of three numbers without using a list

median.py

# The principle is to exhaustively compare all three numbers, so that we can know
# the order of the three numbers. We can do this with 3 levels of if statements.
# At first level we compare two of the three numbers (here a and b) and then 
# at the next level we compare another pair (such as b and c or a and c). And then
# at the last level we compare the last remaining pair, if necessary. This way
# we exhaust all possibilities.


def median(a, b, c):
#    First compare the first two numbers a and b.
#    For a and b, there are only two possibilities. Either a > b or b >= a
#    (We don't need to check a == b, because if they're equal it doesn't matter which one we choose)
#    If a is greater than b then execute Block 1. Else execute Block 2
    
#    Block 1
    if a > b:
#        If a is greater than b, then let's first compare a and c and then compare b and c
#        There are only two possibilities. Either a > c or c >= a
        if a > c:
            if b > c:
#                If a > b, a > c, and b > c, we can infer a > b > c. So b is median
                return b
            else:
#                This "else" covers the condition c >= b
#                If a > b, a > c, c >= b, we can infer a > c >= b. So c is median
                return c
        else:
#            If a is not greater than c, then c >= a.
#            This "else" covers the conditions a > b and c >= a. We don't need to check b and c here
#            Because we can already infer c >= a > b. So median is a
            return a


#    Possibility 2: If a is not greater than b, then b must be greater than or equal to a.
#    Both of these situations are covered in the "else" block below. 
#    Because "else" covers all all remaining conditions 
#    So we have covered all possibilities as far as the first two numbers a and b are concerned
#    We can be sure either Block 1 or Block 2 will run.
            
#    Block 2
#    Follow the same logic as above. 
    else:
        if b > c:
            if a > c:
#                We now know b >= a, b > c, and a > c. So b >= a > c. So a is median
                return a
            else:
                return c
        else:
            return b