本文介绍了一种实现Dijkstra最短路径算法的方法，并通过一个具体的有向图实例展示了如何寻找从源节点到所有其他节点的最短路径。算法采用C++编写，通过迭代改进路径来更新最短距离。
#include "stdafx.h"
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#include <iostream>
#include <list>
// -1 表示无路径可以到达
const static int _VERTEX_NUM =
5;
int arrayPathScheme[ _VERTEX_NUM][_VERTEX_NUM ]
=
{
0, 10, -1, 30, 100,
-1, 0, 50, -1, -1,
-1, -1, 0, -1, 10,
-1, -1, 20, 0, 60,
-1, -1, -1, -1, 0,
};
// 路由算法 有向图的情况下
-1 表示无路径可以达到
enum { EndTag =
-1, };
int _tmain( int argc , _TCHAR* argv[])
{
// 选取输入的顶点
int nSourceVertex =
0; // V0
bool bSelectedVertex [_VERTEX_NUM]; // 是否已被选取到已选取集合之中
for( int i =
0; i < _VERTEX_NUM ;
++i )
bSelectedVertex[i ]
= false;
int nSourceToDestN [_VERTEX_NUM];
for( int i =
0; i< _VERTEX_NUM ;
++i )
{
nSourceToDestN[i ]
= arrayPathScheme [nSourceVertex][ i];
}
bSelectedVertex[nSourceVertex ]
= true;
int nPreVertex [_VERTEX_NUM];
nPreVertex[nSourceVertex ]
= EndTag;
for( int i =
0; i < _VERTEX_NUM ;
++i )
{
if( i != nSourceVertex )
nPreVertex[i ]
= nSourceVertex;
}
// 每次选取一个顶点
n - 1次选取
int nMaxEdgeValue =
10000;
int nMinEdgeValue ;
for( int i =
0; i < _VERTEX_NUM -
1 ; ++i )
{
nMinEdgeValue = nMaxEdgeValue ;
int nDestVertex =
-1;
int nDestEdgeValue =
-1;
for( int j =
0; j < _VERTEX_NUM ;
++j )
{
if( true == bSelectedVertex[ j]
)
continue;
if(
0 == nSourceToDestN [j]
)
continue;
if(
-1 == nSourceToDestN [j]
)
continue;
if( nSourceToDestN [j]
< nMinEdgeValue )
{
nMinEdgeValue
= nSourceToDestN [j];
nDestVertex
= j;
nDestEdgeValue = nSourceToDestN [j];
}
}
// 将该顶点放入集合中
bSelectedVertex[nDestVertex ]
= true;
//
Update nSourceToDest Value
for( int j =
0; j < _VERTEX_NUM ;
++j )
{
if( true == bSelectedVertex[ j]
)
continue;
if( arrayPathScheme [nDestVertex][ j]
== 0 || arrayPathScheme [nDestVertex][ j]
== -1 )
continue;
if( nDestEdgeValue + arrayPathScheme [nDestVertex][ j]
< nSourceToDestN [j]
|| nSourceToDestN [j]
== -1 )
{
nSourceToDestN[j ]
= nDestEdgeValue + arrayPathScheme [nDestVertex][ j];
nPreVertex[j ]
= nDestVertex;
}
}
}
std::list <int> vecPathVertex;
for( int i =
0; i < _VERTEX_NUM ;
++i )
{
vecPathVertex.clear ();
std::cout <<"[
"<< i<<"
]___"<< nSourceToDestN[i ]<<std:: endl;
std::cout <<std:: endl<<"
From " <<nSourceVertex<< "
To "<< i<<"
Shortest Path Is:" <<std:: endl;
int nIndex = i;
while(
1 )
{
vecPathVertex.push_front ( nIndex );
if( nPreVertex [nIndex]
== EndTag )
break;
nIndex = nPreVertex [nIndex];
}
std::list <int>:: iterator iBegin = vecPathVertex .begin();
std::list <int>:: iterator iEnd
= vecPathVertex. end();
for(
; iBegin != iEnd;
++ iBegin )
std::cout <<"
"<<(*iBegin )<<"------";
std::cout <<std:: endl<<std ::endl;
}
system("pause" );
return 0;
}
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