Topological sort Topsort Detailed

1. Definition

Topological ordering of a direction-free graph G is a linear sequence of all vertices in g, usually such a linear sequence is called a sequence that satisfies the topological order (topological order), or a topological sequence.

Example:

when we get up and wear pants and shoes, I believe most people are in the order that they put on their underwear, then put on their pants, put on their socks, and then the shoes. So , Let's break down these steps:

(1) wear underwear

(2) wear pants

(3) wear Socks

(4) wear Shoes

Let's take these four steps and arrange them in the order described above. , is the so-called topological sort.

2. Note

1) A topological sequence exists only in the direction-free graph;

2) for a DAG, there may be multiple topological sequences;

Such as:

The topology sequence for the DAG is a B c D or a C b d

There is no topological sequence for this graph, as there are loops in the diagram

3. Topology Sequence algorithm idea

(1) Selecting a vertex with no precursor (i.e., 0) from the graph, and outputting it;

(2) Delete this vertex and all arcs with its tail from the graph;

Repeat the above two steps until the diagram is empty, or the diagram is not empty but cannot find a vertex without a precursor. 4. Code

#include <cstdio>#include<cstring>intans[510][510];//to record whether the two men had a match.intn,indegree[510];//record the number of precursorsintqueue[510];//Save TopologyvoidTopsort () {inti,j,top,k=0;  for(j=0; j<n; ++j) { for(i=1; i<=n; ++i) {if(indegree[i]==0)//The precursor is zero, which is the current first place .{Top=i;  Break; }} queue[k++]=top;//the current first name into the queue, can also be directly outputindegree[top]=-1;//The number of precursors is updated to-1 to avoid repeating the queue         for(i=1; i<=n; ++i) {if(Ans[top][i])//reduce the number of precursors that contain the current first name to oneindegree[i]--; }    }     for(i=0; i<k-1; ++i) printf ("%d", Queue[i]); printf ("%d\n", queue[n-1]);}intMain () {inti,a,b,m;  while(SCANF ("%d%d", &n,&m)! =EOF) {memset (Indegree,0,sizeof(Indegree));//array initialized to 0memset (ans,0,sizeof(ans));//array initialized to 0         for(i=0; i<m; ++i) {scanf ("%d%d",&a,&b); if(ans[a][b]==0) {Ans[a][b]=1;//record whether the contest was conductedindegree[b]++;//record number of precursors}} topsort (); }    return 0;}

Topological sort Topsort Detailed