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算法导论第22章图算法 22.2 广度优先搜索

2016-06-13 00:00 711 查看

一、综述

BFS蛮简单的，没什么好的综述的。

BFS算法的算法过程与它是有向图还是无向图没有关系，也与用邻接图还是用矩阵表示也没有关系。本文的代码是用邻接图实现的，例子是22-3的有向图。

用邻接矩阵实现的BFS 见算法导论-22.2-3-邻接矩阵实现图的广度优先搜索

二、代码

1.Link_Graph.h

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

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

queue<int> Q;
struct Vertex;
struct Edge
{
int start;
int end;
int value;
Edge *next;
Edge(int s, int e, int v):start(s),end(e),value(v),next(NULL){}
};
struct Vertex
{
int color;
int d;
int Pie;
Edge *head;
Vertex():head(NULL),color(WHITE),d(0x7fffffff),Pie(0){};
};
class Link_Graph
{
public:
int n;
Vertex *V;
Link_Graph(int num):n(num)
{
V = new Vertex[n+1];
}
~Link_Graph(){delete []V;}
void AddSingleEdge(int start, int end, int value = 1)
{
Edge *NewEdge = new Edge(start, end, value);
if(V[start].head == NULL || V[start].head->end > end)
{
NewEdge->next = V[start].head;
V[start].head = NewEdge;
}
else
{
Edge *e = V[start].head, *pre = e;
while(e != NULL && e->end < end)
{
pre = e;
e = e->next;
}
if(e && e->end == end)
{
delete NewEdge;
return;
}
NewEdge->next = e;
pre->next = NewEdge;
}
}
void AddDoubleEdge(int a, int b, int value = 1)
{
AddSingleEdge(a, b, value);
AddSingleEdge(b, a, value);
}
void DeleteSingleEdge(int start, int end)
{
Edge *e = V[start].head, *pre = e;
while(e && e->end < end)
{
pre = e;
e = e->next;
}
if(e == NULL || e->end > end) return;
if(e == V[start].head)
V[start].head = e->next;
else
pre->next = e->next;
delete e;
}
void DeleteDoubleEdge(int a, int b)
{
DeleteSingleEdge(a, b);
DeleteSingleEdge(b, a);
}
//22.2
//广度优先搜索
void BFS(int s);
//广度优先树
void Print_Path(int s, int v);
};

void Link_Graph::BFS(int s)
{
int i;
for(i = 1; i <= n; i++)
{
V[i].color = WHITE;
V[i].d = 0x7fffffff;
V[i].Pie = 0;
}
V[s].color = GRAY;
V[s].d = 0;
V[s].Pie = 0;
while(!Q.empty())Q.pop();
Q.push(s);
while(!Q.empty())
{
int u, v;
u = Q.front();Q.pop();
Edge *e = V[u].head;
while(e)
{
v = e->end;
if(V[v].color == WHITE)
{
V[v].color = GRAY;
V[v].d = V[u].d + 1;
V[v].Pie = u;
Q.push(v);
}
e = e->next;
}
V[u].color = BLACK;
}
}

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

2.main.cpp

#include <iostream>
#include "Link_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()
{
Link_Graph *G = new Link_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->V[i].d<<' ';
cout<<endl;
int s, v;
while(cin>>s>>v)
{
G->Print_Path(s, v);
cout<<endl;
}
return 0;
}