Programming for Mathematics
Assignment, 20 August 2014

Extend the definition of the class Point (see below) with a
function nearestpoint() such that p.nearestpoint() returns the
nearest point to p (as a Point object), other than p itself.  

a. If there are multiple points at the same distance, return any
   one of them as the nearest one.

b. It is possible that there is another point q, different from
   p, that is at distance 0 from p (i.e. q and p have same
   coordinates).  In such a situation it is OK to return q as the
   nearest point.

Hint:

Go through Point.allpoints ("for p in Point.allpoints:") and
identify the point that is closest to self, using the function
self.distance(p).  Note that the current point also belongs to
Point.allpoints, so be careful to exclude it from consideration.

Note:

I have intentionally modified the code to use simultaneous
assignment of the form (self.x,self.y) = (a,b) to remind you that
this can be done, and to illustrate that it can add clarity to
your code by grouping together simultaneous updates to related
variables.

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from math import *

class Point:

    allpoints = []

    def __init__(self,a,b):
        (self.x,self.y) = (a,b)
        Point.allpoints.append(self)

    def setpoint(self,a,b):
        (self.x,self.y) = (a,b)

    def getpoint(self):
        return(self.x,self.y)

    def distance(self,p):
        return(sqrt((p.x-self.x)**2 + (p.y-self.y)**2))

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