# ShowPointClass.py

from copy import copy,deepcopy
from math import sqrt
from random import uniform as randu

class Point:
    """
    Attributes:
        x: float, the x-coordinate of a point
        y: float, the y-coordinate of a point
    """
    def __init__(self,x,y):
        """ Creates a point.
        PreC: x and y are floats
        """
        self.x = x
        self.y = y

    def __str__(self):
        """ Pretty prints a point object.
        
        To apply this function to a point P, write
              print P
        """
        return '(%6.3f,%6.3f)' %(self.x,self.y)
    
def MidPoint(P1,P2):
    """ Returns a point that is the midpoint of
    a line segment that connects P1 and P2.
    
    PreC: P1 and P2 are points.
    """
    xm = (P1.x+P2.x)/2.0
    ym = (P1.y+P2.y)/2.0
    Q = Point(xm,ym)
    return Q

def Dist(P1,P2):
    """ Returns a float that is the distance from P1 to P2.
    
    PreC: P1 and P2 are points
    """
    d = sqrt((P1.x-P2.x)**2+(P1.y-P2.y)**2)
    return d

def RandomPoint(L,R):
    """ Returns a point that is randomly chosen
    randomly from the square L<=x<=R, L<=y<=R.
    
    PreC: L and R are floats with L<R
    """
    x = randu(L,R)
    y = randu(L,R)
    P = Point(x,y)
    return P

def RandomCloud(L,R,n):
    """ Returns a length-n list of points, each chosen
    randomly from the square L<=x<=R, L<=y<=R.
    
    PreC: L and R are floats with L<R, n is a positive int.
    """
    A = []
    for k in range(n):
        P = RandomPoint(L,R)
        A.append(P)
    return A

def printCloud(A):
    """ Prints the points in A
    
    PreC : A is a list of points.
    """
    for a in A:
        print a

def odometer(A):
    """ Returns a float that is the perimeter of
    the polygon whose vertices are the points in A.
    Equivalently, the length of a round trip that visits
    all the points in A in order.
    
    PreC: A is a list of points.
    """
    d = 0
    n = len(A)
    for k in range(n-1):
        d = d + Dist(A[k],A[k+1])
    d = d + Dist(A[n-1],A[0])
    return d