凸包 Graham 算法

import math

class Point( object ):

    def __init__( self, x, y ):
        self.x = x
        self.y = y

    def __cmp__( self, other ):
        if self.y < other.y:
            return -1
        elif self.y == other.y:
            if self.x < other.x:
                return -1
            elif self.x == other.x:
                return 0
            else:
                return 1
        else:
            return 1

    def __repr__( self ):
        return "(X: {x}, Y:{y})".format( x = self.x, y = self.y )

    @staticmethod
    def distance( p1, p2 ):
        return math.sqrt( ( p1.x - p2.x ) * ( p1.x - p2.x ) +                           ( p1.y - p2.y ) * ( p1.y - p2.y ) )

    @staticmethod
    def crossMultiply( p1, p2, p3 ):
        return ( p2.x - p1.x ) * ( p3.y - p1.y ) -                ( p2.y - p1.y ) * ( p3.x - p1.x )

points  = []
results = []

def graham():

    def find_start_point():
        res = Point( float( 'inf' ), float( 'inf' ) )
        for p in points:
            if res > p:
                res = p
        return res

    def _cmp( p1, p2 ):
        m = Point.crossMultiply( start_point, p1, p2 )
        if m < 0:
            return 1
        elif m == 0 and              Point.distance( start_point, p1 ) < Point.distance( start_point, p2 ):
            return 1
        else:
            return -1

    global points, results

    start_point = find_start_point()
    points.remove( start_point )
    points = sorted( points, _cmp )
    results.extend( [start_point, points.pop( 0 ), points.pop( 0 )] )

    for p in points:
        while ( Point.crossMultiply( results[-2], results[-1], p ) ) <= 0:
            results.pop()
        results.append( p )

    return results

if __name__ == "__main__":

    points.extend( [ Point( 30, 30 ),
                     Point( 50, 60 ),
                     Point( 60, 20 ),
                     Point( 70, 45 ),
                     Point( 86, 39 ),
                     Point( 112, 60 ),
                     Point( 200, 113 ),
                     Point( 250, 50 ),
                     Point( 300, 200 ),
                     Point( 130, 240 ),
                     Point( 76, 150 ),
                     Point( 47, 76 ),
                     Point( 36, 40 ),
                     Point( 33, 35 ) ] )
    res = graham()
    print res