SPFA即shotest path faster algorithm,由意思就可以看出该算法效率比较高。
其实SPFA就是bellman-ford算法的一个优化。
具体做法是用一个队列保存待松弛的点,然后对于每个出队的点依次遍历每个与他有边相邻的点(用邻接表效率较高),如果该点可以松弛并且队列中没有该点则将它加入队列中,如此迭代直到队列为空。
据说平均效率是O(E),可见对边稀疏的图用此算法效果是相当可观的。
若要判负环路,则记录一个点的入队次数,若超过边数,则有负权环。
#include <iostream>
#include <queue>
using namespace std;
![](https://www.cnblogs.com/Images/OutliningIndicators/None.gif)
const long MAXN=10000;
const long lmax=0x7FFFFFFF;
![](https://www.cnblogs.com/Images/OutliningIndicators/None.gif)
typedef struct
![](https://www.cnblogs.com/Images/OutliningIndicators/ExpandedBlockStart.gif)
![](https://www.cnblogs.com/Images/OutliningIndicators/ContractedBlock.gif)
{
long v;
long next;
long cost;
}Edge;
![](https://www.cnblogs.com/Images/OutliningIndicators/None.gif)
![](https://www.cnblogs.com/Images/OutliningIndicators/None.gif)
Edge e[MAXN];
long p[MAXN];
long Dis[MAXN];
bool vist[MAXN];
![](https://www.cnblogs.com/Images/OutliningIndicators/None.gif)
queue<long> q;
![](https://www.cnblogs.com/Images/OutliningIndicators/None.gif)
long m,n;//点,边
void init()
![](https://www.cnblogs.com/Images/OutliningIndicators/ExpandedBlockStart.gif)
![](https://www.cnblogs.com/Images/OutliningIndicators/ContractedBlock.gif)
{
long i;
long eid=0;
![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
memset(vist,0,sizeof(vist));
memset(p,-1,sizeof(p));
fill(Dis,Dis+MAXN,lmax);
![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
while (!q.empty())
![](https://www.cnblogs.com/Images/OutliningIndicators/ExpandedSubBlockStart.gif)
{
q.pop();
}
![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
for (i=0;i<n;++i)
![](https://www.cnblogs.com/Images/OutliningIndicators/ExpandedSubBlockStart.gif)
{
long from,to,cost;
scanf("%ld %ld %ld",&from,&to,&cost);
![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
e[eid].next=p[from];
e[eid].v=to;
e[eid].cost=cost;
p[from]=eid++;
![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
//以下适用于无向图
swap(from,to);
e[eid].next=p[from];
e[eid].v=to;
e[eid].cost=cost;
p[from]=eid++;
![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
}
}
![](https://www.cnblogs.com/Images/OutliningIndicators/None.gif)
void print(long End)
![](https://www.cnblogs.com/Images/OutliningIndicators/ExpandedBlockStart.gif)
![](https://www.cnblogs.com/Images/OutliningIndicators/ContractedBlock.gif)
{
//若为lmax 则不可达
printf("%ld\n",Dis[End]);
}
![](https://www.cnblogs.com/Images/OutliningIndicators/None.gif)
void SPF()
![](https://www.cnblogs.com/Images/OutliningIndicators/ExpandedBlockStart.gif)
![](https://www.cnblogs.com/Images/OutliningIndicators/ContractedBlock.gif)
{
![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
init();
![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
long Start,End;
scanf("%ld %ld",&Start,&End);
Dis[Start]=0;
vist[Start]=true;
q.push(Start);
![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
while (!q.empty())
![](https://www.cnblogs.com/Images/OutliningIndicators/ExpandedSubBlockStart.gif)
{
long t=q.front();
q.pop();
vist[t]=false;
long j;
for (j=p[t];j!=-1;j=e[j].next)
![](https://www.cnblogs.com/Images/OutliningIndicators/ExpandedSubBlockStart.gif)
{
long w=e[j].cost;
if (w+Dis[t]<Dis[e[j].v])
![](https://www.cnblogs.com/Images/OutliningIndicators/ExpandedSubBlockStart.gif)
{
Dis[e[j].v]=w+Dis[t];
if (!vist[e[j].v])
![](https://www.cnblogs.com/Images/OutliningIndicators/ExpandedSubBlockStart.gif)
{
vist[e[j].v]=true;
q.push(e[j].v);
}
}
}
}
![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
print(End);
![](https://www.cnblogs.com/Images/OutliningIndicators/InBlock.gif)
}
![](https://www.cnblogs.com/Images/OutliningIndicators/None.gif)
int main()
![](https://www.cnblogs.com/Images/OutliningIndicators/ExpandedBlockStart.gif)
![](https://www.cnblogs.com/Images/OutliningIndicators/ContractedBlock.gif)
{
while (scanf("%ld %ld",&m,&n)!=EOF)
![](https://www.cnblogs.com/Images/OutliningIndicators/ExpandedSubBlockStart.gif)
{
SPF();
}
return 0;
}