Question

def solve(numLegs, numHeads):
    for numChicks in range(0, numHeads + 1):
        numPigs = numHeads - numChicks
        totLegs = 4*numPigs + 2*numChicks
        if totLegs == numLegs:
            return [numPigs, numChicks]
    return [None, None]

def barnYard(heads, legs):
    pigs, chickens = solve(legs, heads)
    if pigs == None:
        print "There is no solution."
    else:
        print 'Number of pigs: ', pigs
        print 'Number of Chickens: ', chickens

I’m learning Python and came across this example, can someone please explain in plain english (or pseudo-code) what this is doing line by line.

Many thanks

Answer 1

solve is computing how many chicks (1 head, 2 legs) and how many pigs (1 head, 4 legs) it takes to total up to the given numbers of heads and legs.

It uses a “brute force”, that is, maximally simple, approach:

• it tries even possible number of
  chicks from none at all to as many as
  was specified as number of heads
  (that’s the role of the loop for
numChicks in range(0, numHeads +
1):, since range gives integers
  from the starting value included
  to the ending value excluded);
• for each given numChicks it computes
  how many pigs there would be to give
  the requested number of heads, by the
  statement numPigs = numHeads - numChicks
• then it computes how many total legs
  those chicks and pigs would have, by
  totLegs = 4*numPigs + 2*numChicks
• then it checks if the totLegs equal
  the requested number: if so, it returns
  a list with two items, the numbers of
  chicks and pigs that solve the problem
• lastly, if it “falls of the bottom” of
  the for loop without having returned
  a value yet, it knows there’s no solution,
  and signifies that by returning a list
  each of whose two items is None.

barnYard just delegates the solution to solve, and prints it out in a nice readable way, either as “no solution” or as nicely decorated numbers of chicks and pigs.

Now, to keep progressing, ask yourself if solve could be written more efficiently. Clearly there is no solution if the number of legs is less than twice the number of heads, or more than four times the number of heads, or odd — maybe solve could test for those case and return [None, None] immediately. Could you code that…?

It may not be obvious, but every other combination of numbers of heads and legs has a solution — and there IS a way to find it just by arithmetic, without looping. Think about it, maybe with the help of elementary middle-school algebra…