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Floyd算法:
在两点之间插入节点,如果插入后能减少两点间的距离,则更新距离;
模板如下:
void Floyd()
{
for(int k=1;k<=n;k++)
for(int i=1;i<=n;i++)
for(int j=1;j<=n;j++)
e[i][j]=min(e[i][k]+e[k][j],e[i][j]);
}
Dijkstra算法:
void Dijkstra(int s)
{
int vis[1010];
for (int i = 1; i <= n; i++)
{
vis[i] = 0;
dis[i] = g[s][i];
}
vis[s] = 1;
for (int i = 1; i <= n - 1; i++)
{
int minn = inf,u;
for (int j = 1; j <= n; j++)
{
if (!vis[j] && dis[j] < minn)
{
minn = dis[j];
u = j;
}
}
vis[u] = 1;
for (int j = 1; j <= n; j++)
{
dis[j] = min(dis[j],dis[u] + g[u][j]);
}
}
}
Bellman算法
struct Point
{
int u, v, w;
}edge[6000];
int x;//代表总共的边数
int dis[1000];
int bellman()
{
for (int i = 1; i <= n; i++)
{
dis[i] = inf;
}
dis[1] = 0;
for (int i = 1; i <= n - 1; i++)
{
int flag = 0;
for (int j = 1; j < x; j++)
{
if (dis[edge[j].v] > dis[edge[j].u] + edge[j].w)
{
flag = 1;
dis[edge[j].v] = dis[edge[j].u] + edge[j].w;
}
}
if (!flag)
break;
}
for (int j = 1; j < x; j++)
{
if (dis[edge[j].v] > dis[edge[j].u] + edge[j].w)//如果还能减小,说明存在负权边
return 1;
}
return 0;
}