便利店选址问题
Update:
1、C code refactoring
2、Add Java code
【问题描述】
某小区决定在小区内部建一家便利店，现小区内部共有八栋楼，它们的地理坐标分别为：（10，20）、（30，34）、（19，25）、（38，49.1）、（9，38.1）、（2，34）、（5，8）、（29，48）。同时，其中的住户人数分别为：30, 45, 28, 8, 36, 16, 78, 56。为了方便更多的住户购物，要求实现总体最优，请问便利店应该建立在哪里？
【提示】
1）便利店无论选址何处，八栋楼的居民均可直接到达，即八栋楼与便利店均相邻，且距离为直线距离；
2）八栋楼的居民人数为权重，应该方便大多数人，实现总体最优。
【解题思路】
通过对设计要求的分析。程序将由以下几个功能模块构成。
- 地址坐标
- 距离计算函数
- 近似最优解求解模块
【算法描述】
1.地址坐标：
首先让我们假设出一张地图：为了简便，我们用A、B、C、D、E、F、G、H表示小区内部的八栋楼，设P为便利店。
我们将地图分割成若干等份：A、B、C、D、E、F、G、H分别在网格的格点上。
确立坐标：坐标原点为(0，0)，设A点坐标为（X0,Y0），B点坐标为（X1,Y1）,C点坐标为（X2,Y2），D点坐标为（X3,Y3），E点坐标为（X4,Y4），F点坐标为（X5,Y5），G点坐标为（X6,Y6），H点坐标为（X7,Y7），P点坐标为（Xp,Yp）。
2.距离计算函数：
由此，我们不难设计一个函数计算出AP、BP、CP、DP、EP、FP、GP、HP的长度。在不考虑权重的情况下，只要八者之和最短，则P点就为便利店所在地。但是，由于还要考虑人数对选址的影响，所以对数据进行如下处理：XA=X0*权重A；XB=X1*权重B；XC=X2*权重C；XD=X3*权重D；XE=X4*权重E；XF=X5*权重F；XG=X6*权重G；XH=X7*权重H；然后再从中选出使八者之和最小的P点!
3.近似最优求解模块：
由于P点的坐标是不确定的,所以P的值是变化的。考虑到实际情况下,超市不可能占地面积只有一个点。所以我们将P的精度取到1米,让D的坐标以1米为步长，其X,Y轴分别加1与各个单位求距离。
【代码实现】
1、C语言版
#include<stdio.h>
#include<math.h>
#define N 8
//结构体定义
struct chooseLocale
{
double x;
double y;
int w;
double xp;
double yp;
} location[N];
double g_minX=0;
double g_maxX=0;
double g_minY=0;
double g_maxY=0;
double g_minSum=30000;
double g_shopX=0;
double g_shopY=0;
int g_iCount=0;
double get_length(double x,double y,double x1,double y1);
void getEdgelocation();
void inputHouselocation();
void getShoplocation();
int main()
{
inputHouselocation();
getEdgelocation();
getShoplocation();
printf("count=%d\n",g_iCount);//打印sum计算次数
printf("minsum=%lf\n",g_minSum);
printf("计算出便利店建立的地理坐标为：\nlocation(%lf,%lf)\n",g_shopX,g_shopY);
return 0;
}
double get_length(double x,double y,double x1,double y1) {
return(sqrt((x-x1)*(x-x1)+(y-y1)*(y-y1)));
}
/*
输入各个单位坐标
(10，20,30) , (30，34,45) , (19，25,28) , (38，49.1,8) , (9,38.1,36) , (2,34,16) , (5,8,78) , (29,48,56)
*/
void inputHouselocation() {
for(int i=0; i<N; i++) {
printf("Please input House %d locationInfo :\n",i);
scanf("%lf%lf%d",&location[i].x,&location[i].y,&location[i].w);
}
}
/*
找到八个单位中坐标的边缘点，以缩小搜索范围。
*/
void getEdgelocation() {
for(int i=0; i<N; i++) {
if(location[i].x<g_minX) {
g_minX=location[i].x;
} else {
g_maxX=location[i].x;
}
if(location[i].y<g_minY) {
g_minY=location[i].y;
} else {
g_maxY=location[i].y;
}
}
}
void getShoplocation() {
struct chooseLocale cl;
double len[8]= {0};
double sum=0;
for(cl.xp=g_minX; cl.xp<=g_maxX; cl.xp++)
{
for(cl.yp=g_minY; cl.yp<=g_maxY; cl.yp++)
{
for(int i=0; i<N; i++)
{
len[i]=get_length(location[i].x,location[i].y,cl.xp,cl.yp);
len[i]=len[i]*location[i].w;
sum=sum+len[i];
g_iCount++;
}
if(sum<g_minSum) {
g_minSum=sum;
g_shopX=cl.xp;
g_shopY=cl.yp;
}
sum=0;
}
}
}
2、Java版
LocationInfo.java
/**
* @author john
* @created 2016-1-28
*/
public class LocationInfo
{
private double mLocationX=0;
private double mLocationY=0;
private int mWeight=0;
public double getLocationX()
{
return mLocationX;
}
public void setLocationX(double locationX)
{
mLocationX = locationX;
}
public double getLocationY()
{
return mLocationY;
}
public void setLocationY(double locationY)
{
mLocationY = locationY;
}
public int getWeight()
{
return mWeight;
}
public void setWeight(int weight)
{
mWeight = weight;
}
}
ShopVo.java
/**
* @author john
* @created 2016-1-28
*/
public class ShopVo
{
private double mDistanceMinSum = 0;
private double[] mShopLocation = { 0, 0 };
private int mCount = 0;
public double getDistanceMinSum()
{
return mDistanceMinSum;
}
public void setDistanceMinSum(double distanceMinSum)
{
mDistanceMinSum = distanceMinSum;
}
public double[] getShopLocation()
{
return mShopLocation;
}
public void setShopLocation(double[] shopLocation)
{
mShopLocation = shopLocation;
}
public int getCount()
{
return mCount;
}
public void setCount(int count)
{
mCount = count;
}
}
CalculateShopLocale.java
import java.util.List;
/**
* @author john
* @created 2016-1-28
*/
public class CalculateShopLocale
{
private int mHouseNum = 0;
private Double[] edgeMinLocation = new Double[2];
private double[] edgeMaxLocation = { 0, 0 };
private double[] distances = { 0,0};
private List<LocationInfo> mLocationInfoList = null;
/**
* 估算的最小距离
*/
private double distanceMinSum = 0;
/**
* 构造函数初始化 mHouseNum , mLocationInfoList , distanceMinSum
*
*/
public CalculateShopLocale(int mHouseNum, List<LocationInfo> mLocationInfoList, double distanceMinSum)
{
this.mHouseNum = mHouseNum;
this.mLocationInfoList = mLocationInfoList;
this.distanceMinSum = distanceMinSum;
}
/**
* 获取两地距离
*/
private double getTwoPositionDistance(double x, double y, double newX, double newY)
{
// TODO Auto-generated method stub
double distance = Math.sqrt(Math.pow(newX - x, 2)+Math.pow(newY - y, 2));
return distance;
}
/**
* 找到所有位置中坐标的边缘点，以缩小搜索范围
*/
private void getEdgeLocation()
{
if (mLocationInfoList != null)
{
edgeMinLocation[0] = mLocationInfoList.get(0).getLocationX();
edgeMinLocation[1] = mLocationInfoList.get(0).getLocationY();
for (int i = 0; i < mHouseNum; i++)
{
if (mLocationInfoList.get(i).getLocationX() < edgeMinLocation[0])
{
edgeMinLocation[0] = mLocationInfoList.get(i).getLocationX();
}
else
{
edgeMaxLocation[0] = mLocationInfoList.get(i).getLocationX();
}
if (mLocationInfoList.get(i).getLocationY() < edgeMinLocation[1])
{
edgeMinLocation[1] = mLocationInfoList.get(i).getLocationY();
}
else
{
edgeMaxLocation[1] = mLocationInfoList.get(i).getLocationY();
}
}
}
}
/**
* 获取便利店最佳选址位置，并打印出该位置到所有住户最小距离和，同时打印出计算次数
*/
public void getShopLocation(ShopVo sv)
{
System.out.println("CalculateShopLocale <<< mList = "+mLocationInfoList);
getEdgeLocation();
double distanceSum = 0;
double[] shopLocation = { 0, 0 };
int iCount = 0;
for (double x = edgeMinLocation[0]; x <= edgeMaxLocation[0]; x++)
{
for (double y = edgeMinLocation[1]; y <= edgeMaxLocation[1]; y++)
{
for (int i = 0; i < mHouseNum; i++)
{
distances[i] = getTwoPositionDistance(mLocationInfoList.get(i).getLocationX(), mLocationInfoList.get(i).getLocationY(), x, y);
distances[i] *= mLocationInfoList.get(i).getWeight();
distanceSum += distances[i];
iCount++;
}
if (distanceSum < distanceMinSum)
{
distanceMinSum = distanceSum;
shopLocation[0] = x;
shopLocation[1] = y;
}
distanceSum = 0;
}
}
sv.setDistanceMinSum(distanceMinSum);
sv.setCount(iCount);
sv.setShopLocation(shopLocation);
}
}
Main.java
import java.util.ArrayList;
import java.util.List;
import java.util.Scanner;
/**
* @author john
* @created 2016-1-28
*/
public class Main
{
/**
* 住户数
*/
private static final int HOUSE_NUM = 8;
private static Scanner sc = new Scanner(System.in);
/**
* 控制台输入住户位置信息参数(x,y,w)
*
* (10，20,30) , (30，34,45) , (19，25,28) , (38，49.1,8) , (9,38.1,36) ,
* (2,34,16) , (5,8,78) , (29,48,56)
*
*/
private static LocationInfo getHouseLocationItem(LocationInfo locationInfo)
{
System.out.println("Please input LocationX : ");
double locationX = sc.nextDouble();
System.out.println("Please input LocationY : ");
double locationY = sc.nextDouble();
System.out.println("Please input weight : ");
int weight = sc.nextInt();
locationInfo.setLocationX(locationX);
locationInfo.setLocationY(locationY);
locationInfo.setWeight(weight);
return locationInfo;
}
/**
* 获取各个位置地理坐标和权值
*/
private static List<LocationInfo> getHouseLocationList(LocationInfo locationInfo)
{
List<LocationInfo> list = new ArrayList<LocationInfo>();
for (int i = 0; i < HOUSE_NUM; i++)
{
System.out.println("Please input House " + i + " LocationInfo");
locationInfo = getHouseLocationItem(locationInfo);
list.add(locationInfo);
}
return list;
}
/**
* @param args
*/
public static void main(String[] args)
{
// TODO Auto-generated method stub
// 估算的最小距离
double distanceMinSum = 30000;
ShopVo shopVo = new ShopVo();
LocationInfo locationInfo = new LocationInfo();
List<LocationInfo> mList = getHouseLocationList(locationInfo);
System.out.println("Main <<< mList = " + mList);
CalculateShopLocale csl = new CalculateShopLocale(HOUSE_NUM, mList, distanceMinSum);
csl.getShopLocation(shopVo);
sc.close();
System.out.println("计算总次数 : " + shopVo.getCount() + "\n" + "便利店最佳选址位置到所有住户最小距离和 : " + shopVo.getDistanceMinSum() + "\n" + "便利店建立的地理坐标 : " + shopVo.getShopLocation());
}
}
