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ClosestPair.py
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# -*- coding: utf-8 -*-
# @Time : 2018/10/31 上午10:37
# @Author : 韩字杰
# @Site :
# @File : ClosestPair.py
# @Software: PyCharm
# 华中科技大学算法导论实验：最小点对问题
# Huazhong University of Sci & Tech Algotithms Experiment: The Closest Pair
import math
class Pair(object):
def __init__(self,L = []):
self.L = L
#
# 首先使用快速排序方式，将点对以X轴的坐标排序好
# 函数 mQuickSort 和 mPartition 是将点对进行快速排序的算法
# mQuickSort and mPartition quick sort the pairs(x , y) by x
#
def mQuickSort(self , p , r ):
if p < r:
q = self.mPartition(p , r)
self.mQuickSort(p , q - 1)
self.mQuickSort(q + 1 , r)
return 0
def mPartition(self , p , r ):
x = self.L[r][0]
i = p - 1
j = p
while j <= r - 1:
if self.L[j][0] < x:
i = i + 1
t = self.L[i]
self.L[i] = self.L[j]
self.L[j] = t
j += 1
t = self.L[i+1]
self.L[i+1] = self.L[r]
self.L[r] = t
return i + 1
def getMinPairList(self, p , r):
"""
:param p: 点对的左边界 (left border)
:param r: 点对的右边界 (right border)
:return: 最小点对距离，最小距离点对 (Distance, (Pair,Piar)
"""
self.minDistance,tupple = self.closestPair(p,r)
self.minPairList = []
self.minPairList.append(self.L[tupple[0]])
self.minPairList.append(self.L[tupple[1]])
return self.minDistance,self.minPairList
def closestPair(self, p , r):
"""
:param p: 点对的左边界
:param r: 点对的右边界
:return: 最小的点对距离，最小点对元素下标
"""
self.mQuickSort(0,len(self.L) - 1)
x = int((p + r)/2)
if x - p <= 3 or r - x <= 3:
# When element num less than 3, Calculate the closest distance directly.
# 当左右两边元素个数少于 3 时，直接计算最小点对。
leftMin,leftPair = self.subClosest(p , x)
rightMin,rightPair = self.subClosest(x , r)
normalMin = 0
normalPair = (0,0)
if leftMin < rightMin:
normalMin , normalPair = leftMin,leftPair
else:
normalMin , normalPair = rightMin,rightPair
else:
# To calculate the minimun pair of the left or right side
# 计算左右两边的最小点对
leftMin,leftPair = self.closestPair(p , x)
rightMin,rightPair = self.closestPair(x , r)
if leftMin < rightMin:
normalMin = leftMin
normalPair = leftPair
else:
normalMin = rightMin
normalPair = rightPair
# To calculate the minimum pair of the cross ones
# 计算中间部分的最小点对
tMiddleLeft = x - 1
tMiddleRight = x + 1
while self.L[x][0] - self.L[tMiddleLeft][0] < normalMin and tMiddleLeft > p:
tMiddleLeft -= 1
while self.L[tMiddleRight][0] - self.L[x][0] < normalMin and tMiddleRight < r:
tMiddleRight += 1
tMiddleLeft += 1
tMiddleRight += 1
crossMin = normalMin
crossPair = normalPair
if tMiddleLeft != tMiddleRight:
crossMin,crossPair = self.subClosest(tMiddleLeft,tMiddleRight)
if crossMin < normalMin:
normalMin = crossMin
normalPair = crossPair
return normalMin,normalPair
def subClosest(self , p , r):
i = p
min = self.calDistance(p, r)
minPair = (p , r)
while i < r:
j = i + 1
while j <= r:
t = self.calDistance(i,j)
if t < min:
min = t
minPair = (i , j)
j += 1
i += 1
return min,minPair
def calDistance(self , x , y):
a = self.L[x][0] - self.L[y][0]
a = a*a
b = self.L[x][1] - self.L[y][1]
b = b*b
return math.sqrt(a + b)
if __name__ == '__main__':
# L = [(7,5),(5,5),(2,2),(4,1),(100,8),(14,5),(6,7)]
# mPair = Pair(L)
# min,minPair = mPair.getMinPairList(0,len(L)-1)
# print(mPair.L)
# print(min)
# print(minPair)
a = "hello world"
l = a[:5]
print(l)