algorithm-in-python/divideAndConquer/min_distance_of_n_points.py
2019-01-31 12:09:46 +08:00

136 lines
4.2 KiB
Python

''' mbinary
#########################################################################
# File : min_distance_of_n_points.py
# Author: mbinary
# Mail: zhuheqin1@gmail.com
# Blog: https://mbinary.xyz
# Github: https://github.com/mbinary
# Created Time: 2018-11-24 22:03
# Description:
#########################################################################
'''
from random import randint
from time import time
from functools import total_ordering
@total_ordering
class point:
def __init__(self,x,y):
self.x=x
self.y=y
def __neg__(self):
return pont(-self.x, -self.y)
def __len__(self):
return self.norm(2)
def __lt__(self,p):
return self.x<p.x or (self.x==p.x and self.y<p.y)
def __eq__(self,p):
return self.x==p.x and self.y == p.y
def __hash__(self):
return hash((self.x,self.y))
def __repr__(self):
return 'point({},{})'.format(self.x,self.y)
def __str__(self):
return self.__repr__()
def norm(self,n=2):
if n<=0: return max(abs(self.x),abs(self.y))
return (abs(self.x)**n+abs(self.y)**n)**(1/n)
def distance(self,p):
return ((self.x-p.x)**2+(self.y-p.y)**2)**0.5
def minDistance_n2(points):
n = len(points)
if n<=1: return 0
p,q=points[:2]
minD = points[0].distance(points[1])
for i in range(n-1):
for j in range(i+1,n):
d = points[i].distance(points[j])
if d<minD:
minD = d
p = points[i]
q= points[j]
return minD, p,q
def findif(points, f,reverse = False):
n = len(points)
rg = range(n-1,-1,-1) if reverse else range(n)
for i in rg:
if not f(points[i]):
return points[i+1:] if reverse else points[:i]
return points.copy() # note that don't return exactly points, return a copy one
def floatEql(f1,f2,epsilon=1e-6):
return abs(f1-f2)<epsilon
def minDistance_nlogn(n_points):
def _min(pts):
n = len(pts)
if n==2: return pts[0].distance(pts[1]) , pts[0],pts[1]
if n==3:
minD = pts[0].distance(pts[1])
p,q = pts[0],pts[1]
d2 = pts[2].distance(pts[1])
if minD>d2:
minD = d2
p,q = pts[1], pts[2]
d2 = pts[0].distance(pts[2])
if minD>d2: return d2, pts[0],pts[2]
else : return minD, p,q
n2 = n//2
mid = (pts[n2].x +pts[n2-1].x)/2
s1 = pts[:n2]
s2 = pts[n2:]
minD ,p,q = _min(s1)
d2, p2, q2 = _min(s2)
#print('\n\n',minD,p,q,s1)
#print(d2,p2,q2,s2)
if minD> d2:
minD,p,q = d2, p2, q2
linePoints = findif(s1,lambda pt:floatEql(pt.x,mid),reverse=True)
linePoints += findif(s2,lambda pt:floatEql(pt.x,mid))
n = len(linePoints)
if n>1:
for i in range(1,n):
dis = linePoints[i].y -linePoints[i-1].y
if dis<minD:
minD = dis
p,q = linePoints[i-1], linePoints[i]
leftPoints = findif(s1,lambda pt:pt.x>= mid-minD,reverse=True)
rightPoints = findif(s2,lambda pt:pt.x<= mid+minD)
for lp in leftPoints:
y1,y2 = lp.y-minD, lp.y+minD
for rp in rightPoints:
if y1< rp.y <y2:
dis = lp.distance(rp)
if dis< minD:
minD = dis
p,q = lp,rp
return minD, p,q
return _min(sorted(n_points))
def test(f=minDistance_n2):
print('\ntest : ', f.__name__)
begin = time()
minD, p, q = f(points)
print('time : {:.6f} s'.format(time()-begin))
print('result: {:.2f} {} {}\n'.format(minD, p,q))
def genData(n,unique=True):
upper = 1000000
if unique:
points = set()
for i in range(n):
points.add(point(randint(1,upper),randint(1,upper)))
return list(points)
else:return [point(randint(1,upper),randint(1,upper)) for i in range(n)]
if __name__ =='__main__':
n = 1000
points = genData(n, unique=True)
print('min distance of {} points'.format(n))
#print(sorted(points))
test(minDistance_n2)
test(minDistance_nlogn)