text 印刷电路板将布线区域划分成n×m个个方格如图一个所示。精确的电路布线问题要求确定连接方格一个的中点到方格b的中点的最短布线方案。在布线时，电路只能沿直线或直角布线，为了避免线路相交

Posted 2021-05-01

#include<iostream>
using namespace std;
 
template <class T>
class Queue
{
	public:
		Queue(int MaxQueueSize=50);
		~Queue(){delete [] queue;}
		bool IsEmpty()const{return front==rear;}
		bool IsFull(){return ( (  (rear+1)  %MaxSize==front )?1:0);}
		T Top() const;
		T Last() const;
		Queue<T>& Add(const T& x);
		Queue<T>& AddLeft(const T& x);
		Queue<T>& Delete(T &x);
		void Output(ostream& out)const;
		int Length(){return (rear-front);}
	private:
		int front;
		int rear;
		int MaxSize;
		T *queue;
};
 
template<class T>
Queue<T>::Queue(int MaxQueueSize)
{
	MaxSize=MaxQueueSize+1;
	queue=new T[MaxSize];
	front=rear=0;
}
 
template<class T >
T Queue<T>::Top()const
{
	if(IsEmpty())
	{
		cout<<"queue:no element,no!"<<endl;
		return 0;
	}
	else return queue[(front+1) % MaxSize];
}
 
template<class T>
T Queue<T> ::Last()const
{
	if(IsEmpty())
	{
		cout<<"queue:no element"<<endl;
		return 0;
	}
	else return queue[rear];
}
 
template<class T>
Queue<T>&  Queue<T>::Add(const T& x)
{
	if(IsFull())cout<<"queue:no memory"<<endl;
	else
	{
		rear=(rear+1)% MaxSize;
	    queue[rear]=x;
	}
	return *this;
}
 
template<class T>
Queue<T>&  Queue<T>::AddLeft(const T& x)
{
	if(IsFull())cout<<"queue:no memory"<<endl;
	else
	{
		front=(front+MaxSize-1)% MaxSize;
		queue[(front+1)% MaxSize]=x;
	}
	return *this;
}
 
template<class T>
Queue<T>&  Queue<T> ::Delete(T & x)
{
	if(IsEmpty())cout<<"queue:no element(delete)"<<endl;
	else 
	{
		front=(front+1) % MaxSize;
		x=queue[front];
	}
	return *this;
}
 
 
template<class T>
void Queue <T>::Output(ostream& out)const
{
	for(int i=rear%MaxSize;i>=(front+1)%MaxSize;i--)
	   out<<queue[i];
}
 
template<class T>
ostream& operator << (ostream& out,const Queue<T>& x)
{x.Output(out);return out;}

//布线问题 队列式分支限界法求解 
#include "stdafx.h"
#include "Queue.h"
#include <fstream> 
#include <iostream>
using namespace std;
 
ifstream fin("6d4.txt"); 
 
const int n = 7;
const int m = 7;
int grid[n+2][m+2];  
 
struct Position  
{  
    int row;  
    int col;  
}; 
 
bool FindPath(Position start,Position finish,int& PathLen,Position *&path);
 
int main()
{
	int PathLen;
	
	Position start,finish,*path;
 
	start.row = 3;
	start.col = 2;
 
	finish.row = 4;
	finish.col = 6;
 
	cout<<"布线起点"<<endl;  
	cout<<start.col<<" "<<start.row<<endl;  
	cout<<"布线结束点"<<endl;  
    cout<<finish.col<<" "<<finish.row<<endl; 
 
	cout<<"布线方格阵列如下(0表示允许布线，1表示不允许布线)："<<endl;
	for(int i=1; i<=m; i++)
	{
		for(int j=1; j<=n; j++)
		{
			fin>>grid[i][j];
			cout<<grid[i][j]<<" ";
		}
		cout<<endl;
	}
	
	FindPath(start,finish,PathLen,path);
 
	cout<<"布线长度为:"<<PathLen<<endl;
	cout<<"布线路径如下："<<endl;  
    for(int i=0; i<PathLen; i++)  
    {  
        cout<<path[i].col<<" "<<path[i].row<<endl;  
    }  
 
	return 0;
}
 
bool FindPath(Position start,Position finish,int& PathLen,Position *&path)
{
	//计算从起始位置start到目标位置finish的最短布线路径
	if((start.row == finish.row) && (start.col == finish.col))
	{
		PathLen = 0;
		return true;
	}
 
	//设置方格阵列“围墙”
	for(int i=0; i<= m+1; i++)
	{
		grid[0][i]=grid[n+1][i]=1; //顶部和底部
	}
	for(int i=0; i<= n+1; i++)
	{
		grid[i][0]=grid[i][m+1]=1; //左翼和右翼
	}
 
	//初始化相对位移
	Position offset[4];
 
	offset[0].row=0;
	offset[0].col=1;//右
 
	offset[1].row=1; 
	offset[1].col=0;//下
 
	offset[2].row=0; 
	offset[2].col=-1;//左
	
	offset[3].row=-1;
	offset[3].col=0;//上
	
	int NumOfNbrs=4;//相邻方格数
	Position here,nbr;
	here.row=start.row;
	here.col=start.col;
 
	grid[start.row][start.col]=2;//标记可达方格位置
	Queue<Position> Q;
 
	do {//标记相邻可达方格
		for(int i=0; i<NumOfNbrs; i++)
		{
			nbr.row=here.row + offset[i].row;
			nbr.col=here.col+offset[i].col;
 
			if(grid[nbr.row][nbr.col]==0)//该方格未被标记
			{
				grid[nbr.row][nbr.col]=grid[here.row][here.col]+1;
				if((nbr.row==finish.row) && (nbr.col==finish.col))
				{
					break; //完成布线
				}
				Q.Add(nbr);
			}
		}
		//是否到达目标位置finish？
		if((nbr.row==finish.row) && (nbr.col==finish.col))
		{
			break;//完成布线
		}
 
		//活结点队列是否非空？
		if(Q.IsEmpty())
		{
			return false;//无解
		}
		Q.Delete(here);//取下一个扩展结点
	}while(true);
 
	//构造最短布线路径
	PathLen=grid[finish.row][finish.col]-2;
	path=new Position[PathLen];//从目标位置finish开始向起始位置回溯
	here=finish;
	for(int j=PathLen-1; j>=0; j--)
	{
		path[j]=here;//找前驱位置
		for(int i=0; i<NumOfNbrs; i++)
		{
			nbr.row=here.row+offset[i].row;
			nbr.col=here.col+offset[i].col;
			if(grid[nbr.row][nbr.col]==j+2)
			{
				break;
			}
		}
		here=nbr;//向前移动
	}
	return true;
}

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0 0 1 1 0 0 0
0 0 0 0 1 0 0
0 0 0 1 1 0 0
1 0 0 0 1 0 0
1 1 1 0 0 0 0
1 1 1 0 0 0 0