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Topological sorting

Topological order: If there is a forward path from V to W in the figure, V must precede w. The sequence of vertices that satisfy this condition is called a topological order.

The process of obtaining a topological order is the topological ordering

A sequence is obtained after the topology is sorted

Each time we want to output a node without a precursor vertex, that is, a point with no degree of penetration. After the output, set the vertex to 0

AOV (Activity on vertex Network) if there is a reasonable topological order it must be a directed acyclic graph (Directed acyclic graph, DAG)

V must end before the start of v,,,, obvious error,,, so a reasonable topological order cannot exist ring.

voidTopsort () { for(cnt=0; cnt<v;cnt++) {V= a vertex with an input level of 0 not being output;//This step is discussed below.        if(Such a v does not exist) {Error ("There is a circuit in the diagram");  Break; } output V, or record the output sequence of V for(V for each pro contact W) Indegree[w]--;//a reduction of V so that the penetration of each of the pro contacts will be reduced by one.    }}

The first solution is to iterate over the time complexity to n^2.

The second solution is to put the degree of entry into a different container at any time by turning it into 0. Time complexity is a constant number of levels

The second method uses the queue when the code is as follows

voidTopsort () { for(each vertex on the way V)if(indegree[v]==0) Enqueue[v,q];  while(!IsEmpty (Q)) {V=Dequeue (Q);        Output V, or record the output serial number of V.  for(V for each pro contact W) {if(--indegree[w]==0) Enqueue[w,q]; }    }    if(the number of vertices not enough to output) Error ("There is a circuit in the diagram");}

AOE (Activity on Edge) network

Critical path Issues

AOV

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