Dijkstra algorithm---slack through edges

Picture material for reference Ah Halle's Blog

The algorithm is used to solve the shortest path of one point to the remaining vertices

Let's start with a diagram and ask for the shortest path from 1 to 6.

It reminds me of the almost-hung branch of operations research.

Use a two-dimensional array first

There is also a one-dimensional array that stores the distance from 1 points to each point

The value of this one-dimensional array is called an estimate. Select a nearest point, point 2, at a point that can be reached directly at 1 points. Then the value of point 2 becomes the determined value.

Why Because the path is positive, it is not possible to shorten the distance from point 1 to 2 by other transit points.

After a bit of 2, look at what points 2 can reach. Point 3 and point 4. Let's discuss whether the transit point of point 2 can shorten the distance from point 1 to 3. The answer is yes. 1+9<12. Modifies the value of a one-dimensional array.

This is called relaxation .

In the same way compare points 1 to 4 distance and distance through point 2 relay.

The rest of the 3,4,5,6 points to try it out for themselves. Otherwise, operational research is easy to hang.

The final answer is

Sticking out the core algorithm

  for (i=1;i<=n-1;i++)    {        //finds the vertex closest to number 1th vertex        min=inf;//initial min is positive infinity for        (j=1;j<=n;j++)        {            if ( Book[j]==0 && dis[j]<min)            {                min=dis[j];//gets the distance from the nearest point directly connected to the source point                u=j;            }        }        book[u]=1;//the point into the set of points that have been determined to go for        (v=1;v<=n;v++)//This is like traversing the brother to point 2 distance        {            if (E[u][v]<inf)            {                if (Dis[v]>dis[u]+e[u][v])                     dis[v]=dis[u]+e[u][v];}}        }

　　

Dijkstra algorithm---slack through edges