队列的应用：电路布线问题

题目源自于C++数据结构第二版课本

7*7的迷宫

实现代码如下：

Position类：

#pragma once
#include<iostream>
using namespace std;
class Position
{
public:
	int row;//矩阵 行
	int col;//矩阵 列
public:
	Position();
	Position(int r,int c);
	~Position();
	bool operator== (Position &P);
	void operator= (Position &P);
	friend ostream& operator<< (ostream& output,Position &P);
	friend istream& operator>> (istream& input,Position &P);
};

Position::Position()
{}
Position::Position(int r,int c)
{
	row = r;
	col = c;
}
Position::~Position()
{}
bool Position::operator== (Position &P)
{
	return ((row == P.row && col == P.col) ? true : false);
}
void Position::operator= (Position &P)
{
	row = P.row;
	col = P.col;
}
ostream& operator<< (ostream& output,Position &P)
{
	output<<"("<<P.row<<","<<P.col<<")" ;
	return output;
}
istream& operator>> (istream& input,Position &P)
{
	input>>P.row>>P.col ;
	return input;
}

 

下面是Find类

#include <iostream>
#include "Position.h"
#include <queue>
using namespace std;

int m=7;
int n=7;
int grid[9][9];
int indexcount=0;

/*struct Position
{
    int row;
    int col;
};*/
void showPath()
{
    for(int i=0; i<9; i++)
    {

        for(int j=0; j<9; j++)
            cout<<grid[i][j]<<" ";
        cout<<endl;
    }
    cout<<"------------------"<<endl;
}
bool FindPath(Position start,Position finish,int &PathLen,Position  *&path)
{
    //计算从起点位置start到目标位置finish的最短布线路径，找到最短布线路//径则返回true，否则返回false

    if((start.row==finish.row) && (start.col==finish.col))
    {
        PathLen=0;
        cout<<"start=finish"<<endl;
        return true;
    } //start=finish
//设置方格阵列“围墙”
//初始化图，-1为未访问
    for(int i=1; i<8; i++)
    {
        for(int j=1; j<8; j++)
            grid[i][j]=-1;

    }
    //添加阻挡点
    grid[1][3]=-2;
	grid[2][3]=-2;
	grid[2][4]=-2;
	grid[3][5]=-2;
	grid[4][4]=-2;
	grid[4][5]=-2;
	grid[5][5]=-2;
    for(int i=0; i<= m+1; i++)
        grid[0][i]=grid[n+1][i]=-2; //顶部和底部
    for(int i=0; i<= n+1; i++)
        grid[i][0]=grid[i][m+1]=-2; //左翼和右翼
//初始化相对位移
    cout<<"完整图"<<endl;
    showPath();
    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]=0;
	//标记可达方格位置
	cout<<"电路布线之前的情况："<<endl;
    showPath();

    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]==-1)
            {
				//该方格未被标记
                //cout<<grid[nbr.row][nbr.col]<<endl;//显示路标值
                grid[nbr.row][nbr.col]=grid[here.row][here.col]+1;
                 //cout<<nbr.col<<"   "<<nbr.row<<endl;//显示坐标
            
            if((nbr.row==finish.row) &&(nbr.col==finish.col)) break; //完成布线
			Q.push(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.empty()) return false;//无解
        here = Q.front();
        //cout<<here.col<<" "<<here.row<<endl;
        Q.pop();//取下一个扩展结点
    }while(true);
		//构造最短布线路径
    PathLen=grid[finish.row][finish.col];
    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)
            {
               // cout<<j<<endl;
                break;
            }
        }
        here=nbr;//向前移动
    }
    return PathLen;
}

 

下面是实现主函数

#include <iostream>
#include <queue>
#include "Position.h"
#include "Find.h"
using namespace std;

int main(){		    
    Position start;
    start.row=3;
    start.col=2;
    cout<<"布线起点为："<<endl;
    cout<<start.row<<" "<<start.col<<endl;
    Position finish;
    finish.row=4;
    finish.col=6;
    cout<<"布线结束点为："<<endl;
    cout<<finish.row<<" "<<finish.col<<endl;
    int PathLen=0;
    Position *path;

    FindPath(start,finish,PathLen,path);
    cout<<"电路布线之后的情况："<<endl;
    showPath();
    cout<<"最短路径为："<<endl;
    for(int i=0; i<PathLen; i++)
    {
        cout<<path[i].row<<" "<<path[i].col<<endl;
    }
    cout << "布线问题解决啦!" << endl;

	system("pause");

	return 0;
}