mirror of
https://github.com/heqin-zhu/algorithm.git
synced 2024-03-22 13:30:46 +08:00
136 lines
4.2 KiB
Python
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)
|