算法导论 22.2-3 邻接矩阵实现图的广度优先搜索

一、题目

如果BFS的输入图是用邻接矩阵表示的，且对该算法加以修改以处理这种输入图表示，那么该算法的运行时间如何？

二、答案与代码

运行时间为O(n^2)，处理方法见代码。

1.Mat_Graph.h

#include <iostream>
#include <queue>
using namespace std;

#define N 100
#define WHITE 0
#define GRAY 1
#define BLACK 2

queue<int> Q;

class Mat_Graph
{
public:
	int n;
	int color[N+1];
	int d[N+1];
	int Pie[N+1];
	int Map[N+1][N+1];

	Mat_Graph(int num):n(num)
	{
		memset(Map, 0, sizeof(Map));
	}
	void AddDoubleEdge(int a, int b, int value = 1)
	{
		AddSingleEdge(a, b, value);
		AddSingleEdge(b, a, value);
	}
	void AddSingleEdge(int start, int end, int value = 1)
	{
		Map[start][end] = value;
	}
	void DeleteDoubleEdge(int a, int b)
	{
		DeleteSingleEdge(a, b);
		DeleteSingleEdge(b, a);
	}
	void DeleteSingleEdge(int start, int end)
	{
		Map[start][end] = 0;
	}
	//22.2-3
	void BFS(int s);
	void Print_Path(int s, int v);
};

void Mat_Graph::BFS(int s)
{
	int u, v;
	for(u = 1; u <= n; u++)
	{
		color[u] = WHITE;
		d[u] = 0x7fffffff;
		Pie[u] = 0;
	}
	color[s] = GRAY;
	d[s] = 0;
	Pie[s] = 0;
	while(!Q.empty())Q.pop();
	Q.push(s);
	while(!Q.empty())
	{
		u = Q.front();Q.pop();
		for(v = 1; v <= n; v++)
		{
			if(Map[u][v] == 0)continue;
			if(color[v] == WHITE)
			{
				color[v] = GRAY;
				d[v] = d[u] + 1;
				Pie[v] = u;
				Q.push(v);
			}
		}
		color[u] = BLACK;
	}
}

void Mat_Graph::Print_Path(int s, int v)
{
	BFS(s);
	if(v == s)
		cout << s<<' ';
	else
	{
		if(Pie[v] == 0)
			cout<<"no path from "<<s<<" to "<<v<<" exists."<<endl;
		else
		{
			Print_Path(s, Pie[v]);
			cout<<v<<' ';
		}
	}
}

2.main.cpp

#include <iostream>
#include "Mat_Graph.h"
using namespace std;
/*
1 2
1 5
2 6
6 7
6 3
3 7
3 4
7 8
7 4
4 8
*/
int main()
{
	Mat_Graph *G = new Mat_Graph(8);
	int i = 0, a, b;
	for(i = 1; i <= 10; i++)
	{
		cin>>a>>b;
		G->AddDoubleEdge(a,b);
	}
	G->BFS(2);
	for(i = 1; i <= 8; i++)
		cout<<G->d[i]<<' ';
	cout<<endl;
	int s, v;
	while(cin>>s>>v)
	{
		G->Print_Path(s, v);
		cout<<endl;
	}
	delete G;
	return 0;
}