238 – Fixed point

You can apply a function f successively on a value x until applying the function doesn’t change with the auxiliary function fixedpoint:

def fixedpoint(f, x):
    while x != f(x):
        x = f(x)
    return x

The function fixedpoint computes the value f(x) twice for each given value of x. If that is a significant performance hit, you can use an assignment expression to merge the comparison and the assignment:

def fixedpoint(f, x):
    while x != (x := f(x)):
        pass
    return x

In the new version of the function fixedpoint, it is important that the comparison starts with x != ..., otherwise the function fixedpoint would be wrong.

Further reading:

• Assignment expressions and the walrus operator, https://mathspp.com/blog/pydonts/assignment-expressions-and-the-walrus-operator